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def maybe_name_or_idx(idx, model):
"""
Give a name or an integer and return the name and integer location of the
column in a design matrix.
"""
if idx is None:
idx = lrange(model.exog.shape[1])
if isinstance(idx, int):
exog_name = model.exog_names[idx]
exog_idx = idx
# anticipate index as list and recurse
elif isinstance(idx, (tuple, list)):
exog_name = []
exog_idx = []
for item in idx:
exog_name_item, exog_idx_item = maybe_name_or_idx(item, model)
exog_name.append(exog_name_item)
exog_idx.append(exog_idx_item)
else: # assume we've got a string variable
exog_name = idx
exog_idx = model.exog_names.index(idx)
return exog_name, exog_idx | Give a name or an integer and return the name and integer location of the
column in a design matrix. | maybe_name_or_idx | python | statsmodels/statsmodels | statsmodels/graphics/utils.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/graphics/utils.py | BSD-3-Clause |
def get_data_names(series_or_dataframe):
"""
Input can be an array or pandas-like. Will handle 1d array-like but not
2d. Returns a str for 1d data or a list of strings for 2d data.
"""
names = getattr(series_or_dataframe, 'name', None)
if not names:
names = getattr(series_or_dataframe, 'columns', None)
if not names:
shape = getattr(series_or_dataframe, 'shape', [1])
nvars = 1 if len(shape) == 1 else series_or_dataframe.shape[1]
names = ["X%d" for _ in range(nvars)]
if nvars == 1:
names = names[0]
else:
names = names.tolist()
return names | Input can be an array or pandas-like. Will handle 1d array-like but not
2d. Returns a str for 1d data or a list of strings for 2d data. | get_data_names | python | statsmodels/statsmodels | statsmodels/graphics/utils.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/graphics/utils.py | BSD-3-Clause |
def annotate_axes(index, labels, points, offset_points, size, ax, **kwargs):
"""
Annotate Axes with labels, points, offset_points according to the
given index.
"""
for i in index:
label = labels[i]
point = points[i]
offset = offset_points[i]
ax.annotate(label, point, xytext=offset, textcoords="offset points",
size=size, **kwargs)
return ax | Annotate Axes with labels, points, offset_points according to the
given index. | annotate_axes | python | statsmodels/statsmodels | statsmodels/graphics/utils.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/graphics/utils.py | BSD-3-Clause |
def dot_plot(points, intervals=None, lines=None, sections=None,
styles=None, marker_props=None, line_props=None,
split_names=None, section_order=None, line_order=None,
stacked=False, styles_order=None, striped=False,
horizontal=True, show_names="both",
fmt_left_name=None, fmt_right_name=None,
show_section_titles=None, ax=None):
"""
Dot plotting (also known as forest and blobbogram).
Produce a dotplot similar in style to those in Cleveland's
"Visualizing Data" book ([1]_). These are also known as "forest plots".
Parameters
----------
points : array_like
The quantitative values to be plotted as markers.
intervals : array_like
The intervals to be plotted around the points. The elements
of `intervals` are either scalars or sequences of length 2. A
scalar indicates the half width of a symmetric interval. A
sequence of length 2 contains the left and right half-widths
(respectively) of a nonsymmetric interval. If None, no
intervals are drawn.
lines : array_like
A grouping variable indicating which points/intervals are
drawn on a common line. If None, each point/interval appears
on its own line.
sections : array_like
A grouping variable indicating which lines are grouped into
sections. If None, everything is drawn in a single section.
styles : array_like
A grouping label defining the plotting style of the markers
and intervals.
marker_props : dict
A dictionary mapping style codes (the values in `styles`) to
dictionaries defining key/value pairs to be passed as keyword
arguments to `plot` when plotting markers. Useful keyword
arguments are "color", "marker", and "ms" (marker size).
line_props : dict
A dictionary mapping style codes (the values in `styles`) to
dictionaries defining key/value pairs to be passed as keyword
arguments to `plot` when plotting interval lines. Useful
keyword arguments are "color", "linestyle", "solid_capstyle",
and "linewidth".
split_names : str
If not None, this is used to split the values of `lines` into
substrings that are drawn in the left and right margins,
respectively. If None, the values of `lines` are drawn in the
left margin.
section_order : array_like
The section labels in the order in which they appear in the
dotplot.
line_order : array_like
The line labels in the order in which they appear in the
dotplot.
stacked : bool
If True, when multiple points or intervals are drawn on the
same line, they are offset from each other.
styles_order : array_like
If stacked=True, this is the order in which the point styles
on a given line are drawn from top to bottom (if horizontal
is True) or from left to right (if horizontal is False). If
None (default), the order is lexical.
striped : bool
If True, every other line is enclosed in a shaded box.
horizontal : bool
If True (default), the lines are drawn horizontally, otherwise
they are drawn vertically.
show_names : str
Determines whether labels (names) are shown in the left and/or
right margins (top/bottom margins if `horizontal` is True).
If `both`, labels are drawn in both margins, if 'left', labels
are drawn in the left or top margin. If `right`, labels are
drawn in the right or bottom margin.
fmt_left_name : callable
The left/top margin names are passed through this function
before drawing on the plot.
fmt_right_name : callable
The right/bottom marginnames are passed through this function
before drawing on the plot.
show_section_titles : bool or None
If None, section titles are drawn only if there is more than
one section. If False/True, section titles are never/always
drawn, respectively.
ax : matplotlib.axes
The axes on which the dotplot is drawn. If None, a new axes
is created.
Returns
-------
fig : Figure
The figure given by `ax.figure` or a new instance.
Notes
-----
`points`, `intervals`, `lines`, `sections`, `styles` must all have
the same length whenever present.
References
----------
.. [1] Cleveland, William S. (1993). "Visualizing Data". Hobart Press.
.. [2] Jacoby, William G. (2006) "The Dot Plot: A Graphical Display
for Labeled Quantitative Values." The Political Methodologist
14(1): 6-14.
Examples
--------
This is a simple dotplot with one point per line:
>>> dot_plot(points=point_values)
This dotplot has labels on the lines (if elements in
`label_values` are repeated, the corresponding points appear on
the same line):
>>> dot_plot(points=point_values, lines=label_values)
"""
import matplotlib.transforms as transforms
fig, ax = utils.create_mpl_ax(ax)
# Convert to numpy arrays if that is not what we are given.
points = np.asarray(points)
def asarray_or_none(x):
return None if x is None else np.asarray(x)
intervals = asarray_or_none(intervals)
lines = asarray_or_none(lines)
sections = asarray_or_none(sections)
styles = asarray_or_none(styles)
# Total number of points
npoint = len(points)
# Set default line values if needed
if lines is None:
lines = np.arange(npoint)
# Set default section values if needed
if sections is None:
sections = np.zeros(npoint)
# Set default style values if needed
if styles is None:
styles = np.zeros(npoint)
# The vertical space (in inches) for a section title
section_title_space = 0.5
# The number of sections
nsect = len(set(sections))
if section_order is not None:
nsect = len(set(section_order))
# The number of section titles
if show_section_titles is False:
draw_section_titles = False
nsect_title = 0
elif show_section_titles is True:
draw_section_titles = True
nsect_title = nsect
else:
draw_section_titles = nsect > 1
nsect_title = nsect if nsect > 1 else 0
# The total vertical space devoted to section titles.
# Unused, commented out
# section_title_space * nsect_title
# Add a bit of room so that points that fall at the axis limits
# are not cut in half.
ax.set_xmargin(0.02)
ax.set_ymargin(0.02)
if section_order is None:
lines0 = list(set(sections))
lines0.sort()
else:
lines0 = section_order
if line_order is None:
lines1 = list(set(lines))
lines1.sort()
else:
lines1 = line_order
# A map from (section,line) codes to index positions.
lines_map = {}
for i in range(npoint):
if section_order is not None and sections[i] not in section_order:
continue
if line_order is not None and lines[i] not in line_order:
continue
ky = (sections[i], lines[i])
if ky not in lines_map:
lines_map[ky] = []
lines_map[ky].append(i)
# Get the size of the axes on the parent figure in inches
bbox = ax.get_window_extent().transformed(
fig.dpi_scale_trans.inverted())
awidth, aheight = bbox.width, bbox.height
# The number of lines in the plot.
nrows = len(lines_map)
# The positions of the lowest and highest guideline in axes
# coordinates (for horizontal dotplots), or the leftmost and
# rightmost guidelines (for vertical dotplots).
bottom, top = 0, 1
if horizontal:
# x coordinate is data, y coordinate is axes
trans = transforms.blended_transform_factory(ax.transData,
ax.transAxes)
else:
# x coordinate is axes, y coordinate is data
trans = transforms.blended_transform_factory(ax.transAxes,
ax.transData)
# Space used for a section title, in axes coordinates
title_space_axes = section_title_space / aheight
# Space between lines
if horizontal:
dpos = (top - bottom - nsect_title*title_space_axes) /\
float(nrows)
else:
dpos = (top - bottom) / float(nrows)
# Determine the spacing for stacked points
if styles_order is not None:
style_codes = styles_order
else:
style_codes = list(set(styles))
style_codes.sort()
# Order is top to bottom for horizontal plots, so need to
# flip.
if horizontal:
style_codes = style_codes[::-1]
# nval is the maximum number of points on one line.
nval = len(style_codes)
if nval > 1:
stackd = dpos / (2.5*(float(nval)-1))
else:
stackd = 0.
# Map from style code to its integer position
style_codes_map = {x: style_codes.index(x) for x in style_codes}
# Setup default marker styles
colors = ["r", "g", "b", "y", "k", "purple", "orange"]
if marker_props is None:
marker_props = {x: {} for x in style_codes}
for j in range(nval):
sc = style_codes[j]
if "color" not in marker_props[sc]:
marker_props[sc]["color"] = colors[j % len(colors)]
if "marker" not in marker_props[sc]:
marker_props[sc]["marker"] = "o"
if "ms" not in marker_props[sc]:
marker_props[sc]["ms"] = 10 if stackd == 0 else 6
# Setup default line styles
if line_props is None:
line_props = {x: {} for x in style_codes}
for j in range(nval):
sc = style_codes[j]
if "color" not in line_props[sc]:
line_props[sc]["color"] = "grey"
if "linewidth" not in line_props[sc]:
line_props[sc]["linewidth"] = 2 if stackd > 0 else 8
if horizontal:
# The vertical position of the first line.
pos = top - dpos/2 if nsect == 1 else top
else:
# The horizontal position of the first line.
pos = bottom + dpos/2
# Points that have already been labeled
labeled = set()
# Positions of the y axis grid lines
ticks = []
# Loop through the sections
for k0 in lines0:
# Draw a section title
if draw_section_titles:
if horizontal:
y0 = pos + dpos/2 if k0 == lines0[0] else pos
ax.fill_between((0, 1), (y0,y0),
(pos-0.7*title_space_axes,
pos-0.7*title_space_axes),
color='darkgrey',
transform=ax.transAxes,
zorder=1)
txt = ax.text(0.5, pos - 0.35*title_space_axes, k0,
horizontalalignment='center',
verticalalignment='center',
transform=ax.transAxes)
txt.set_fontweight("bold")
pos -= title_space_axes
else:
m = len([k for k in lines_map if k[0] == k0])
ax.fill_between((pos-dpos/2+0.01,
pos+(m-1)*dpos+dpos/2-0.01),
(1.01,1.01), (1.06,1.06),
color='darkgrey',
transform=ax.transAxes,
zorder=1, clip_on=False)
txt = ax.text(pos + (m-1)*dpos/2, 1.02, k0,
horizontalalignment='center',
verticalalignment='bottom',
transform=ax.transAxes)
txt.set_fontweight("bold")
jrow = 0
for k1 in lines1:
# No data to plot
if (k0, k1) not in lines_map:
continue
# Draw the guideline
if horizontal:
ax.axhline(pos, color='grey')
else:
ax.axvline(pos, color='grey')
# Set up the labels
if split_names is not None:
us = k1.split(split_names)
if len(us) >= 2:
left_label, right_label = us[0], us[1]
else:
left_label, right_label = k1, None
else:
left_label, right_label = k1, None
if fmt_left_name is not None:
left_label = fmt_left_name(left_label)
if fmt_right_name is not None:
right_label = fmt_right_name(right_label)
# Draw the stripe
if striped and jrow % 2 == 0:
if horizontal:
ax.fill_between((0, 1), (pos-dpos/2, pos-dpos/2),
(pos+dpos/2, pos+dpos/2),
color='lightgrey',
transform=ax.transAxes,
zorder=0)
else:
ax.fill_between((pos-dpos/2, pos+dpos/2),
(0, 0), (1, 1),
color='lightgrey',
transform=ax.transAxes,
zorder=0)
jrow += 1
# Draw the left margin label
if show_names.lower() in ("left", "both"):
if horizontal:
ax.text(-0.1/awidth, pos, left_label,
horizontalalignment="right",
verticalalignment='center',
transform=ax.transAxes,
family='monospace')
else:
ax.text(pos, -0.1/aheight, left_label,
horizontalalignment="center",
verticalalignment='top',
transform=ax.transAxes,
family='monospace')
# Draw the right margin label
if show_names.lower() in ("right", "both"):
if right_label is not None:
if horizontal:
ax.text(1 + 0.1/awidth, pos, right_label,
horizontalalignment="left",
verticalalignment='center',
transform=ax.transAxes,
family='monospace')
else:
ax.text(pos, 1 + 0.1/aheight, right_label,
horizontalalignment="center",
verticalalignment='bottom',
transform=ax.transAxes,
family='monospace')
# Save the vertical position so that we can place the
# tick marks
ticks.append(pos)
# Loop over the points in one line
for ji,jp in enumerate(lines_map[(k0,k1)]):
# Calculate the vertical offset
yo = 0
if stacked:
yo = -dpos/5 + style_codes_map[styles[jp]]*stackd
pt = points[jp]
# Plot the interval
if intervals is not None:
# Symmetric interval
if np.isscalar(intervals[jp]):
lcb, ucb = pt - intervals[jp],\
pt + intervals[jp]
# Nonsymmetric interval
else:
lcb, ucb = pt - intervals[jp][0],\
pt + intervals[jp][1]
# Draw the interval
if horizontal:
ax.plot([lcb, ucb], [pos+yo, pos+yo], '-',
transform=trans,
**line_props[styles[jp]])
else:
ax.plot([pos+yo, pos+yo], [lcb, ucb], '-',
transform=trans,
**line_props[styles[jp]])
# Plot the point
sl = styles[jp]
sll = sl if sl not in labeled else None
labeled.add(sl)
if horizontal:
ax.plot([pt,], [pos+yo,], ls='None',
transform=trans, label=sll,
**marker_props[sl])
else:
ax.plot([pos+yo,], [pt,], ls='None',
transform=trans, label=sll,
**marker_props[sl])
if horizontal:
pos -= dpos
else:
pos += dpos
# Set up the axis
if horizontal:
ax.xaxis.set_ticks_position("bottom")
ax.yaxis.set_ticks_position("none")
ax.set_yticklabels([])
ax.spines['left'].set_color('none')
ax.spines['right'].set_color('none')
ax.spines['top'].set_color('none')
ax.spines['bottom'].set_position(('axes', -0.1/aheight))
ax.set_ylim(0, 1)
ax.yaxis.set_ticks(ticks)
ax.autoscale_view(scaley=False, tight=True)
else:
ax.yaxis.set_ticks_position("left")
ax.xaxis.set_ticks_position("none")
ax.set_xticklabels([])
ax.spines['bottom'].set_color('none')
ax.spines['right'].set_color('none')
ax.spines['top'].set_color('none')
ax.spines['left'].set_position(('axes', -0.1/awidth))
ax.set_xlim(0, 1)
ax.xaxis.set_ticks(ticks)
ax.autoscale_view(scalex=False, tight=True)
return fig | Dot plotting (also known as forest and blobbogram).
Produce a dotplot similar in style to those in Cleveland's
"Visualizing Data" book ([1]_). These are also known as "forest plots".
Parameters
----------
points : array_like
The quantitative values to be plotted as markers.
intervals : array_like
The intervals to be plotted around the points. The elements
of `intervals` are either scalars or sequences of length 2. A
scalar indicates the half width of a symmetric interval. A
sequence of length 2 contains the left and right half-widths
(respectively) of a nonsymmetric interval. If None, no
intervals are drawn.
lines : array_like
A grouping variable indicating which points/intervals are
drawn on a common line. If None, each point/interval appears
on its own line.
sections : array_like
A grouping variable indicating which lines are grouped into
sections. If None, everything is drawn in a single section.
styles : array_like
A grouping label defining the plotting style of the markers
and intervals.
marker_props : dict
A dictionary mapping style codes (the values in `styles`) to
dictionaries defining key/value pairs to be passed as keyword
arguments to `plot` when plotting markers. Useful keyword
arguments are "color", "marker", and "ms" (marker size).
line_props : dict
A dictionary mapping style codes (the values in `styles`) to
dictionaries defining key/value pairs to be passed as keyword
arguments to `plot` when plotting interval lines. Useful
keyword arguments are "color", "linestyle", "solid_capstyle",
and "linewidth".
split_names : str
If not None, this is used to split the values of `lines` into
substrings that are drawn in the left and right margins,
respectively. If None, the values of `lines` are drawn in the
left margin.
section_order : array_like
The section labels in the order in which they appear in the
dotplot.
line_order : array_like
The line labels in the order in which they appear in the
dotplot.
stacked : bool
If True, when multiple points or intervals are drawn on the
same line, they are offset from each other.
styles_order : array_like
If stacked=True, this is the order in which the point styles
on a given line are drawn from top to bottom (if horizontal
is True) or from left to right (if horizontal is False). If
None (default), the order is lexical.
striped : bool
If True, every other line is enclosed in a shaded box.
horizontal : bool
If True (default), the lines are drawn horizontally, otherwise
they are drawn vertically.
show_names : str
Determines whether labels (names) are shown in the left and/or
right margins (top/bottom margins if `horizontal` is True).
If `both`, labels are drawn in both margins, if 'left', labels
are drawn in the left or top margin. If `right`, labels are
drawn in the right or bottom margin.
fmt_left_name : callable
The left/top margin names are passed through this function
before drawing on the plot.
fmt_right_name : callable
The right/bottom marginnames are passed through this function
before drawing on the plot.
show_section_titles : bool or None
If None, section titles are drawn only if there is more than
one section. If False/True, section titles are never/always
drawn, respectively.
ax : matplotlib.axes
The axes on which the dotplot is drawn. If None, a new axes
is created.
Returns
-------
fig : Figure
The figure given by `ax.figure` or a new instance.
Notes
-----
`points`, `intervals`, `lines`, `sections`, `styles` must all have
the same length whenever present.
References
----------
.. [1] Cleveland, William S. (1993). "Visualizing Data". Hobart Press.
.. [2] Jacoby, William G. (2006) "The Dot Plot: A Graphical Display
for Labeled Quantitative Values." The Political Methodologist
14(1): 6-14.
Examples
--------
This is a simple dotplot with one point per line:
>>> dot_plot(points=point_values)
This dotplot has labels on the lines (if elements in
`label_values` are repeated, the corresponding points appear on
the same line):
>>> dot_plot(points=point_values, lines=label_values) | dot_plot | python | statsmodels/statsmodels | statsmodels/graphics/dotplots.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/graphics/dotplots.py | BSD-3-Clause |
def interaction_plot(x, trace, response, func="mean", ax=None, plottype='b',
xlabel=None, ylabel=None, colors=None, markers=None,
linestyles=None, legendloc='best', legendtitle=None,
**kwargs):
"""
Interaction plot for factor level statistics.
Note. If categorial factors are supplied levels will be internally
recoded to integers. This ensures matplotlib compatibility. Uses
a DataFrame to calculate an `aggregate` statistic for each level of the
factor or group given by `trace`.
Parameters
----------
x : array_like
The `x` factor levels constitute the x-axis. If a `pandas.Series` is
given its name will be used in `xlabel` if `xlabel` is None.
trace : array_like
The `trace` factor levels will be drawn as lines in the plot.
If `trace` is a `pandas.Series` its name will be used as the
`legendtitle` if `legendtitle` is None.
response : array_like
The reponse or dependent variable. If a `pandas.Series` is given
its name will be used in `ylabel` if `ylabel` is None.
func : function
Anything accepted by `pandas.DataFrame.aggregate`. This is applied to
the response variable grouped by the trace levels.
ax : axes, optional
Matplotlib axes instance
plottype : str {'line', 'scatter', 'both'}, optional
The type of plot to return. Can be 'l', 's', or 'b'
xlabel : str, optional
Label to use for `x`. Default is 'X'. If `x` is a `pandas.Series` it
will use the series names.
ylabel : str, optional
Label to use for `response`. Default is 'func of response'. If
`response` is a `pandas.Series` it will use the series names.
colors : list, optional
If given, must have length == number of levels in trace.
markers : list, optional
If given, must have length == number of levels in trace
linestyles : list, optional
If given, must have length == number of levels in trace.
legendloc : {None, str, int}
Location passed to the legend command.
legendtitle : {None, str}
Title of the legend.
**kwargs
These will be passed to the plot command used either plot or scatter.
If you want to control the overall plotting options, use kwargs.
Returns
-------
Figure
The figure given by `ax.figure` or a new instance.
Examples
--------
>>> import numpy as np
>>> np.random.seed(12345)
>>> weight = np.random.randint(1,4,size=60)
>>> duration = np.random.randint(1,3,size=60)
>>> days = np.log(np.random.randint(1,30, size=60))
>>> fig = interaction_plot(weight, duration, days,
... colors=['red','blue'], markers=['D','^'], ms=10)
>>> import matplotlib.pyplot as plt
>>> plt.show()
.. plot::
import numpy as np
from statsmodels.graphics.factorplots import interaction_plot
np.random.seed(12345)
weight = np.random.randint(1,4,size=60)
duration = np.random.randint(1,3,size=60)
days = np.log(np.random.randint(1,30, size=60))
fig = interaction_plot(weight, duration, days,
colors=['red','blue'], markers=['D','^'], ms=10)
import matplotlib.pyplot as plt
#plt.show()
"""
from pandas import DataFrame
fig, ax = utils.create_mpl_ax(ax)
response_name = ylabel or getattr(response, 'name', 'response')
func_name = getattr(func, "__name__", str(func))
ylabel = f'{func_name} of {response_name}'
xlabel = xlabel or getattr(x, 'name', 'X')
legendtitle = legendtitle or getattr(trace, 'name', 'Trace')
ax.set_ylabel(ylabel)
ax.set_xlabel(xlabel)
x_values = x_levels = None
if isinstance(x[0], str):
x_levels = [val for val in np.unique(x)]
x_values = lrange(len(x_levels))
x = _recode(x, dict(zip(x_levels, x_values)))
data = DataFrame(dict(x=x, trace=trace, response=response))
plot_data = data.groupby(['trace', 'x']).aggregate(func).reset_index()
# return data
# check plot args
n_trace = len(plot_data['trace'].unique())
linestyles = ['-'] * n_trace if linestyles is None else linestyles
markers = ['.'] * n_trace if markers is None else markers
colors = rainbow(n_trace) if colors is None else colors
if len(linestyles) != n_trace:
raise ValueError("Must be a linestyle for each trace level")
if len(markers) != n_trace:
raise ValueError("Must be a marker for each trace level")
if len(colors) != n_trace:
raise ValueError("Must be a color for each trace level")
if plottype == 'both' or plottype == 'b':
for i, (values, group) in enumerate(plot_data.groupby('trace')):
# trace label
label = str(group['trace'].values[0])
ax.plot(group['x'], group['response'], color=colors[i],
marker=markers[i], label=label,
linestyle=linestyles[i], **kwargs)
elif plottype == 'line' or plottype == 'l':
for i, (values, group) in enumerate(plot_data.groupby('trace')):
# trace label
label = str(group['trace'].values[0])
ax.plot(group['x'], group['response'], color=colors[i],
label=label, linestyle=linestyles[i], **kwargs)
elif plottype == 'scatter' or plottype == 's':
for i, (values, group) in enumerate(plot_data.groupby('trace')):
# trace label
label = str(group['trace'].values[0])
ax.scatter(group['x'], group['response'], color=colors[i],
label=label, marker=markers[i], **kwargs)
else:
raise ValueError("Plot type %s not understood" % plottype)
ax.legend(loc=legendloc, title=legendtitle)
ax.margins(.1)
if all([x_levels, x_values]):
ax.set_xticks(x_values)
ax.set_xticklabels(x_levels)
return fig | Interaction plot for factor level statistics.
Note. If categorial factors are supplied levels will be internally
recoded to integers. This ensures matplotlib compatibility. Uses
a DataFrame to calculate an `aggregate` statistic for each level of the
factor or group given by `trace`.
Parameters
----------
x : array_like
The `x` factor levels constitute the x-axis. If a `pandas.Series` is
given its name will be used in `xlabel` if `xlabel` is None.
trace : array_like
The `trace` factor levels will be drawn as lines in the plot.
If `trace` is a `pandas.Series` its name will be used as the
`legendtitle` if `legendtitle` is None.
response : array_like
The reponse or dependent variable. If a `pandas.Series` is given
its name will be used in `ylabel` if `ylabel` is None.
func : function
Anything accepted by `pandas.DataFrame.aggregate`. This is applied to
the response variable grouped by the trace levels.
ax : axes, optional
Matplotlib axes instance
plottype : str {'line', 'scatter', 'both'}, optional
The type of plot to return. Can be 'l', 's', or 'b'
xlabel : str, optional
Label to use for `x`. Default is 'X'. If `x` is a `pandas.Series` it
will use the series names.
ylabel : str, optional
Label to use for `response`. Default is 'func of response'. If
`response` is a `pandas.Series` it will use the series names.
colors : list, optional
If given, must have length == number of levels in trace.
markers : list, optional
If given, must have length == number of levels in trace
linestyles : list, optional
If given, must have length == number of levels in trace.
legendloc : {None, str, int}
Location passed to the legend command.
legendtitle : {None, str}
Title of the legend.
**kwargs
These will be passed to the plot command used either plot or scatter.
If you want to control the overall plotting options, use kwargs.
Returns
-------
Figure
The figure given by `ax.figure` or a new instance.
Examples
--------
>>> import numpy as np
>>> np.random.seed(12345)
>>> weight = np.random.randint(1,4,size=60)
>>> duration = np.random.randint(1,3,size=60)
>>> days = np.log(np.random.randint(1,30, size=60))
>>> fig = interaction_plot(weight, duration, days,
... colors=['red','blue'], markers=['D','^'], ms=10)
>>> import matplotlib.pyplot as plt
>>> plt.show()
.. plot::
import numpy as np
from statsmodels.graphics.factorplots import interaction_plot
np.random.seed(12345)
weight = np.random.randint(1,4,size=60)
duration = np.random.randint(1,3,size=60)
days = np.log(np.random.randint(1,30, size=60))
fig = interaction_plot(weight, duration, days,
colors=['red','blue'], markers=['D','^'], ms=10)
import matplotlib.pyplot as plt
#plt.show() | interaction_plot | python | statsmodels/statsmodels | statsmodels/graphics/factorplots.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/graphics/factorplots.py | BSD-3-Clause |
def _recode(x, levels):
""" Recode categorial data to int factor.
Parameters
----------
x : array_like
array like object supporting with numpy array methods of categorially
coded data.
levels : dict
mapping of labels to integer-codings
Returns
-------
out : instance numpy.ndarray
"""
from pandas import Series
name = None
index = None
if isinstance(x, Series):
name = x.name
index = x.index
x = x.values
if x.dtype.type not in [np.str_, np.object_]:
raise ValueError('This is not a categorial factor.'
' Array of str type required.')
elif not isinstance(levels, dict):
raise ValueError('This is not a valid value for levels.'
' Dict required.')
elif not (np.unique(x) == np.unique(list(levels.keys()))).all():
raise ValueError('The levels do not match the array values.')
else:
out = np.empty(x.shape[0], dtype=int)
for level, coding in levels.items():
out[x == level] = coding
if name:
out = Series(out, name=name, index=index)
return out | Recode categorial data to int factor.
Parameters
----------
x : array_like
array like object supporting with numpy array methods of categorially
coded data.
levels : dict
mapping of labels to integer-codings
Returns
-------
out : instance numpy.ndarray | _recode | python | statsmodels/statsmodels | statsmodels/graphics/factorplots.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/graphics/factorplots.py | BSD-3-Clause |
def plot_acf(
x,
ax=None,
lags=None,
*,
alpha=0.05,
use_vlines=True,
adjusted=False,
fft=False,
missing="none",
title="Autocorrelation",
zero=True,
auto_ylims=False,
bartlett_confint=True,
vlines_kwargs=None,
**kwargs,
):
"""
Plot the autocorrelation function
Plots lags on the horizontal and the correlations on vertical axis.
Parameters
----------
x : array_like
Array of time-series values
ax : AxesSubplot, optional
If given, this subplot is used to plot in instead of a new figure being
created.
lags : {int, array_like}, optional
An int or array of lag values, used on horizontal axis. Uses
np.arange(lags) when lags is an int. If not provided,
``lags=np.arange(len(corr))`` is used.
alpha : scalar, optional
If a number is given, the confidence intervals for the given level are
returned. For instance if alpha=.05, 95 % confidence intervals are
returned where the standard deviation is computed according to
Bartlett's formula. The confidence intervals centered at 0 to simplify
detecting which estaimated autocorrelations are significantly
different from 0. If None, no confidence intervals are plotted.
use_vlines : bool, optional
If True, vertical lines and markers are plotted.
If False, only markers are plotted. The default marker is 'o'; it can
be overridden with a ``marker`` kwarg.
adjusted : bool
If True, then denominators for autocovariance are n-k, otherwise n
fft : bool, optional
If True, computes the ACF via FFT.
missing : str, optional
A string in ['none', 'raise', 'conservative', 'drop'] specifying how
the NaNs are to be treated.
title : str, optional
Title to place on plot. Default is 'Autocorrelation'
zero : bool, optional
Flag indicating whether to include the 0-lag autocorrelation.
Default is True.
auto_ylims : bool, optional
If True, adjusts automatically the y-axis limits to ACF values.
bartlett_confint : bool, default True
Confidence intervals for ACF values are generally placed at 2
standard errors around r_k. The formula used for standard error
depends upon the situation. If the autocorrelations are being used
to test for randomness of residuals as part of the ARIMA routine,
the standard errors are determined assuming the residuals are white
noise. The approximate formula for any lag is that standard error
of each r_k = 1/sqrt(N). See section 9.4 of [1] for more details on
the 1/sqrt(N) result. For more elementary discussion, see section
5.3.2 in [2].
For the ACF of raw data, the standard error at a lag k is
found as if the right model was an MA(k-1). This allows the
possible interpretation that if all autocorrelations past a
certain lag are within the limits, the model might be an MA of
order defined by the last significant autocorrelation. In this
case, a moving average model is assumed for the data and the
standard errors for the confidence intervals should be
generated using Bartlett's formula. For more details on
Bartlett formula result, see section 7.2 in [1].
vlines_kwargs : dict, optional
Optional dictionary of keyword arguments that are passed to vlines.
**kwargs : kwargs, optional
Optional keyword arguments that are directly passed on to the
Matplotlib ``plot`` and ``axhline`` functions.
Returns
-------
Figure
If `ax` is None, the created figure. Otherwise the figure to which
`ax` is connected.
See Also
--------
statsmodels.tsa.stattools.acf
matplotlib.pyplot.xcorr
matplotlib.pyplot.acorr
Notes
-----
Adapted from matplotlib's `xcorr`.
Data are plotted as ``plot(lags, corr, **kwargs)``
kwargs is used to pass matplotlib optional arguments to both the line
tracing the autocorrelations and for the horizontal line at 0. These
options must be valid for a Line2D object.
vlines_kwargs is used to pass additional optional arguments to the
vertical lines connecting each autocorrelation to the axis. These options
must be valid for a LineCollection object.
References
----------
[1] Brockwell and Davis, 1987. Time Series Theory and Methods
[2] Brockwell and Davis, 2010. Introduction to Time Series and
Forecasting, 2nd edition.
Examples
--------
>>> import pandas as pd
>>> import matplotlib.pyplot as plt
>>> import statsmodels.api as sm
>>> dta = sm.datasets.sunspots.load_pandas().data
>>> dta.index = pd.Index(sm.tsa.datetools.dates_from_range('1700', '2008'))
>>> del dta["YEAR"]
>>> sm.graphics.tsa.plot_acf(dta.values.squeeze(), lags=40)
>>> plt.show()
.. plot:: plots/graphics_tsa_plot_acf.py
"""
fig, ax = utils.create_mpl_ax(ax)
lags, nlags, irregular = _prepare_data_corr_plot(x, lags, zero)
vlines_kwargs = {} if vlines_kwargs is None else vlines_kwargs
confint = None
# acf has different return type based on alpha
acf_x = acf(
x,
nlags=nlags,
alpha=alpha,
fft=fft,
bartlett_confint=bartlett_confint,
adjusted=adjusted,
missing=missing,
)
if alpha is not None:
acf_x, confint = acf_x[:2]
_plot_corr(
ax,
title,
acf_x,
confint,
lags,
irregular,
use_vlines,
vlines_kwargs,
auto_ylims=auto_ylims,
**kwargs,
)
return fig | Plot the autocorrelation function
Plots lags on the horizontal and the correlations on vertical axis.
Parameters
----------
x : array_like
Array of time-series values
ax : AxesSubplot, optional
If given, this subplot is used to plot in instead of a new figure being
created.
lags : {int, array_like}, optional
An int or array of lag values, used on horizontal axis. Uses
np.arange(lags) when lags is an int. If not provided,
``lags=np.arange(len(corr))`` is used.
alpha : scalar, optional
If a number is given, the confidence intervals for the given level are
returned. For instance if alpha=.05, 95 % confidence intervals are
returned where the standard deviation is computed according to
Bartlett's formula. The confidence intervals centered at 0 to simplify
detecting which estaimated autocorrelations are significantly
different from 0. If None, no confidence intervals are plotted.
use_vlines : bool, optional
If True, vertical lines and markers are plotted.
If False, only markers are plotted. The default marker is 'o'; it can
be overridden with a ``marker`` kwarg.
adjusted : bool
If True, then denominators for autocovariance are n-k, otherwise n
fft : bool, optional
If True, computes the ACF via FFT.
missing : str, optional
A string in ['none', 'raise', 'conservative', 'drop'] specifying how
the NaNs are to be treated.
title : str, optional
Title to place on plot. Default is 'Autocorrelation'
zero : bool, optional
Flag indicating whether to include the 0-lag autocorrelation.
Default is True.
auto_ylims : bool, optional
If True, adjusts automatically the y-axis limits to ACF values.
bartlett_confint : bool, default True
Confidence intervals for ACF values are generally placed at 2
standard errors around r_k. The formula used for standard error
depends upon the situation. If the autocorrelations are being used
to test for randomness of residuals as part of the ARIMA routine,
the standard errors are determined assuming the residuals are white
noise. The approximate formula for any lag is that standard error
of each r_k = 1/sqrt(N). See section 9.4 of [1] for more details on
the 1/sqrt(N) result. For more elementary discussion, see section
5.3.2 in [2].
For the ACF of raw data, the standard error at a lag k is
found as if the right model was an MA(k-1). This allows the
possible interpretation that if all autocorrelations past a
certain lag are within the limits, the model might be an MA of
order defined by the last significant autocorrelation. In this
case, a moving average model is assumed for the data and the
standard errors for the confidence intervals should be
generated using Bartlett's formula. For more details on
Bartlett formula result, see section 7.2 in [1].
vlines_kwargs : dict, optional
Optional dictionary of keyword arguments that are passed to vlines.
**kwargs : kwargs, optional
Optional keyword arguments that are directly passed on to the
Matplotlib ``plot`` and ``axhline`` functions.
Returns
-------
Figure
If `ax` is None, the created figure. Otherwise the figure to which
`ax` is connected.
See Also
--------
statsmodels.tsa.stattools.acf
matplotlib.pyplot.xcorr
matplotlib.pyplot.acorr
Notes
-----
Adapted from matplotlib's `xcorr`.
Data are plotted as ``plot(lags, corr, **kwargs)``
kwargs is used to pass matplotlib optional arguments to both the line
tracing the autocorrelations and for the horizontal line at 0. These
options must be valid for a Line2D object.
vlines_kwargs is used to pass additional optional arguments to the
vertical lines connecting each autocorrelation to the axis. These options
must be valid for a LineCollection object.
References
----------
[1] Brockwell and Davis, 1987. Time Series Theory and Methods
[2] Brockwell and Davis, 2010. Introduction to Time Series and
Forecasting, 2nd edition.
Examples
--------
>>> import pandas as pd
>>> import matplotlib.pyplot as plt
>>> import statsmodels.api as sm
>>> dta = sm.datasets.sunspots.load_pandas().data
>>> dta.index = pd.Index(sm.tsa.datetools.dates_from_range('1700', '2008'))
>>> del dta["YEAR"]
>>> sm.graphics.tsa.plot_acf(dta.values.squeeze(), lags=40)
>>> plt.show()
.. plot:: plots/graphics_tsa_plot_acf.py | plot_acf | python | statsmodels/statsmodels | statsmodels/graphics/tsaplots.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/graphics/tsaplots.py | BSD-3-Clause |
def plot_pacf(
x,
ax=None,
lags=None,
alpha=0.05,
method="ywm",
use_vlines=True,
title="Partial Autocorrelation",
zero=True,
vlines_kwargs=None,
**kwargs,
):
"""
Plot the partial autocorrelation function
Parameters
----------
x : array_like
Array of time-series values
ax : AxesSubplot, optional
If given, this subplot is used to plot in instead of a new figure being
created.
lags : {int, array_like}, optional
An int or array of lag values, used on horizontal axis. Uses
np.arange(lags) when lags is an int. If not provided,
``lags=np.arange(len(corr))`` is used.
alpha : float, optional
If a number is given, the confidence intervals for the given level are
returned. For instance if alpha=.05, 95 % confidence intervals are
returned where the standard deviation is computed according to
1/sqrt(len(x))
method : str
Specifies which method for the calculations to use:
- "ywm" or "ywmle" : Yule-Walker without adjustment. Default.
- "yw" or "ywadjusted" : Yule-Walker with sample-size adjustment in
denominator for acovf. Default.
- "ols" : regression of time series on lags of it and on constant.
- "ols-inefficient" : regression of time series on lags using a single
common sample to estimate all pacf coefficients.
- "ols-adjusted" : regression of time series on lags with a bias
adjustment.
- "ld" or "ldadjusted" : Levinson-Durbin recursion with bias
correction.
- "ldb" or "ldbiased" : Levinson-Durbin recursion without bias
correction.
use_vlines : bool, optional
If True, vertical lines and markers are plotted.
If False, only markers are plotted. The default marker is 'o'; it can
be overridden with a ``marker`` kwarg.
title : str, optional
Title to place on plot. Default is 'Partial Autocorrelation'
zero : bool, optional
Flag indicating whether to include the 0-lag autocorrelation.
Default is True.
vlines_kwargs : dict, optional
Optional dictionary of keyword arguments that are passed to vlines.
**kwargs : kwargs, optional
Optional keyword arguments that are directly passed on to the
Matplotlib ``plot`` and ``axhline`` functions.
Returns
-------
Figure
If `ax` is None, the created figure. Otherwise the figure to which
`ax` is connected.
See Also
--------
statsmodels.tsa.stattools.pacf
matplotlib.pyplot.xcorr
matplotlib.pyplot.acorr
Notes
-----
Plots lags on the horizontal and the correlations on vertical axis.
Adapted from matplotlib's `xcorr`.
Data are plotted as ``plot(lags, corr, **kwargs)``
kwargs is used to pass matplotlib optional arguments to both the line
tracing the autocorrelations and for the horizontal line at 0. These
options must be valid for a Line2D object.
vlines_kwargs is used to pass additional optional arguments to the
vertical lines connecting each autocorrelation to the axis. These options
must be valid for a LineCollection object.
Examples
--------
>>> import pandas as pd
>>> import matplotlib.pyplot as plt
>>> import statsmodels.api as sm
>>> dta = sm.datasets.sunspots.load_pandas().data
>>> dta.index = pd.Index(sm.tsa.datetools.dates_from_range('1700', '2008'))
>>> del dta["YEAR"]
>>> sm.graphics.tsa.plot_pacf(dta.values.squeeze(), lags=40, method="ywm")
>>> plt.show()
.. plot:: plots/graphics_tsa_plot_pacf.py
"""
fig, ax = utils.create_mpl_ax(ax)
vlines_kwargs = {} if vlines_kwargs is None else vlines_kwargs
lags, nlags, irregular = _prepare_data_corr_plot(x, lags, zero)
confint = None
if alpha is None:
acf_x = pacf(x, nlags=nlags, alpha=alpha, method=method)
else:
acf_x, confint = pacf(x, nlags=nlags, alpha=alpha, method=method)
_plot_corr(
ax,
title,
acf_x,
confint,
lags,
irregular,
use_vlines,
vlines_kwargs,
**kwargs,
)
return fig | Plot the partial autocorrelation function
Parameters
----------
x : array_like
Array of time-series values
ax : AxesSubplot, optional
If given, this subplot is used to plot in instead of a new figure being
created.
lags : {int, array_like}, optional
An int or array of lag values, used on horizontal axis. Uses
np.arange(lags) when lags is an int. If not provided,
``lags=np.arange(len(corr))`` is used.
alpha : float, optional
If a number is given, the confidence intervals for the given level are
returned. For instance if alpha=.05, 95 % confidence intervals are
returned where the standard deviation is computed according to
1/sqrt(len(x))
method : str
Specifies which method for the calculations to use:
- "ywm" or "ywmle" : Yule-Walker without adjustment. Default.
- "yw" or "ywadjusted" : Yule-Walker with sample-size adjustment in
denominator for acovf. Default.
- "ols" : regression of time series on lags of it and on constant.
- "ols-inefficient" : regression of time series on lags using a single
common sample to estimate all pacf coefficients.
- "ols-adjusted" : regression of time series on lags with a bias
adjustment.
- "ld" or "ldadjusted" : Levinson-Durbin recursion with bias
correction.
- "ldb" or "ldbiased" : Levinson-Durbin recursion without bias
correction.
use_vlines : bool, optional
If True, vertical lines and markers are plotted.
If False, only markers are plotted. The default marker is 'o'; it can
be overridden with a ``marker`` kwarg.
title : str, optional
Title to place on plot. Default is 'Partial Autocorrelation'
zero : bool, optional
Flag indicating whether to include the 0-lag autocorrelation.
Default is True.
vlines_kwargs : dict, optional
Optional dictionary of keyword arguments that are passed to vlines.
**kwargs : kwargs, optional
Optional keyword arguments that are directly passed on to the
Matplotlib ``plot`` and ``axhline`` functions.
Returns
-------
Figure
If `ax` is None, the created figure. Otherwise the figure to which
`ax` is connected.
See Also
--------
statsmodels.tsa.stattools.pacf
matplotlib.pyplot.xcorr
matplotlib.pyplot.acorr
Notes
-----
Plots lags on the horizontal and the correlations on vertical axis.
Adapted from matplotlib's `xcorr`.
Data are plotted as ``plot(lags, corr, **kwargs)``
kwargs is used to pass matplotlib optional arguments to both the line
tracing the autocorrelations and for the horizontal line at 0. These
options must be valid for a Line2D object.
vlines_kwargs is used to pass additional optional arguments to the
vertical lines connecting each autocorrelation to the axis. These options
must be valid for a LineCollection object.
Examples
--------
>>> import pandas as pd
>>> import matplotlib.pyplot as plt
>>> import statsmodels.api as sm
>>> dta = sm.datasets.sunspots.load_pandas().data
>>> dta.index = pd.Index(sm.tsa.datetools.dates_from_range('1700', '2008'))
>>> del dta["YEAR"]
>>> sm.graphics.tsa.plot_pacf(dta.values.squeeze(), lags=40, method="ywm")
>>> plt.show()
.. plot:: plots/graphics_tsa_plot_pacf.py | plot_pacf | python | statsmodels/statsmodels | statsmodels/graphics/tsaplots.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/graphics/tsaplots.py | BSD-3-Clause |
def plot_ccf(
x,
y,
*,
ax=None,
lags=None,
negative_lags=False,
alpha=0.05,
use_vlines=True,
adjusted=False,
fft=False,
title="Cross-correlation",
auto_ylims=False,
vlines_kwargs=None,
**kwargs,
):
"""
Plot the cross-correlation function
Correlations between ``x`` and the lags of ``y`` are calculated.
The lags are shown on the horizontal axis and the correlations
on the vertical axis.
Parameters
----------
x, y : array_like
Arrays of time-series values.
ax : AxesSubplot, optional
If given, this subplot is used to plot in, otherwise a new figure with
one subplot is created.
lags : {int, array_like}, optional
An int or array of lag values, used on the horizontal axis. Uses
``np.arange(lags)`` when lags is an int. If not provided,
``lags=np.arange(len(corr))`` is used.
negative_lags: bool, optional
If True, negative lags are shown on the horizontal axis.
alpha : scalar, optional
If a number is given, the confidence intervals for the given level are
plotted, e.g. if alpha=.05, 95 % confidence intervals are shown.
If None, confidence intervals are not shown on the plot.
use_vlines : bool, optional
If True, shows vertical lines and markers for the correlation values.
If False, only shows markers. The default marker is 'o'; it can
be overridden with a ``marker`` kwarg.
adjusted : bool
If True, then denominators for cross-correlations are n-k, otherwise n.
fft : bool, optional
If True, computes the CCF via FFT.
title : str, optional
Title to place on plot. Default is 'Cross-correlation'.
auto_ylims : bool, optional
If True, adjusts automatically the vertical axis limits to CCF values.
vlines_kwargs : dict, optional
Optional dictionary of keyword arguments that are passed to vlines.
**kwargs : kwargs, optional
Optional keyword arguments that are directly passed on to the
Matplotlib ``plot`` and ``axhline`` functions.
Returns
-------
Figure
The figure where the plot is drawn. This is either an existing figure
if the `ax` argument is provided, or a newly created figure
if `ax` is None.
See Also
--------
statsmodels.graphics.tsaplots.plot_acf
Examples
--------
>>> import pandas as pd
>>> import matplotlib.pyplot as plt
>>> import statsmodels.api as sm
>>> dta = sm.datasets.macrodata.load_pandas().data
>>> diffed = dta.diff().dropna()
>>> sm.graphics.tsa.plot_ccf(diffed["unemp"], diffed["infl"])
>>> plt.show()
"""
fig, ax = utils.create_mpl_ax(ax)
lags, nlags, irregular = _prepare_data_corr_plot(x, lags, True)
vlines_kwargs = {} if vlines_kwargs is None else vlines_kwargs
if negative_lags:
lags = -lags
ccf_res = ccf(
x, y, adjusted=adjusted, fft=fft, alpha=alpha, nlags=nlags + 1
)
if alpha is not None:
ccf_xy, confint = ccf_res
else:
ccf_xy = ccf_res
confint = None
_plot_corr(
ax,
title,
ccf_xy,
confint,
lags,
irregular,
use_vlines,
vlines_kwargs,
auto_ylims=auto_ylims,
skip_lag0_confint=False,
**kwargs,
)
return fig | Plot the cross-correlation function
Correlations between ``x`` and the lags of ``y`` are calculated.
The lags are shown on the horizontal axis and the correlations
on the vertical axis.
Parameters
----------
x, y : array_like
Arrays of time-series values.
ax : AxesSubplot, optional
If given, this subplot is used to plot in, otherwise a new figure with
one subplot is created.
lags : {int, array_like}, optional
An int or array of lag values, used on the horizontal axis. Uses
``np.arange(lags)`` when lags is an int. If not provided,
``lags=np.arange(len(corr))`` is used.
negative_lags: bool, optional
If True, negative lags are shown on the horizontal axis.
alpha : scalar, optional
If a number is given, the confidence intervals for the given level are
plotted, e.g. if alpha=.05, 95 % confidence intervals are shown.
If None, confidence intervals are not shown on the plot.
use_vlines : bool, optional
If True, shows vertical lines and markers for the correlation values.
If False, only shows markers. The default marker is 'o'; it can
be overridden with a ``marker`` kwarg.
adjusted : bool
If True, then denominators for cross-correlations are n-k, otherwise n.
fft : bool, optional
If True, computes the CCF via FFT.
title : str, optional
Title to place on plot. Default is 'Cross-correlation'.
auto_ylims : bool, optional
If True, adjusts automatically the vertical axis limits to CCF values.
vlines_kwargs : dict, optional
Optional dictionary of keyword arguments that are passed to vlines.
**kwargs : kwargs, optional
Optional keyword arguments that are directly passed on to the
Matplotlib ``plot`` and ``axhline`` functions.
Returns
-------
Figure
The figure where the plot is drawn. This is either an existing figure
if the `ax` argument is provided, or a newly created figure
if `ax` is None.
See Also
--------
statsmodels.graphics.tsaplots.plot_acf
Examples
--------
>>> import pandas as pd
>>> import matplotlib.pyplot as plt
>>> import statsmodels.api as sm
>>> dta = sm.datasets.macrodata.load_pandas().data
>>> diffed = dta.diff().dropna()
>>> sm.graphics.tsa.plot_ccf(diffed["unemp"], diffed["infl"])
>>> plt.show() | plot_ccf | python | statsmodels/statsmodels | statsmodels/graphics/tsaplots.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/graphics/tsaplots.py | BSD-3-Clause |
def plot_accf_grid(
x,
*,
varnames=None,
fig=None,
lags=None,
negative_lags=True,
alpha=0.05,
use_vlines=True,
adjusted=False,
fft=False,
missing="none",
zero=True,
auto_ylims=False,
bartlett_confint=False,
vlines_kwargs=None,
**kwargs,
):
"""
Plot auto/cross-correlation grid
Plots lags on the horizontal axis and the correlations
on the vertical axis of each graph.
Parameters
----------
x : array_like
2D array of time-series values: rows are observations,
columns are variables.
varnames: sequence of str, optional
Variable names to use in plot titles. If ``x`` is a pandas dataframe
and ``varnames`` is provided, it overrides the column names
of the dataframe. If ``varnames`` is not provided and ``x`` is not
a dataframe, variable names ``x[0]``, ``x[1]``, etc. are generated.
fig : Matplotlib figure instance, optional
If given, this figure is used to plot in, otherwise a new figure
is created.
lags : {int, array_like}, optional
An int or array of lag values, used on horizontal axes. Uses
``np.arange(lags)`` when lags is an int. If not provided,
``lags=np.arange(len(corr))`` is used.
negative_lags: bool, optional
If True, negative lags are shown on the horizontal axes of plots
below the main diagonal.
alpha : scalar, optional
If a number is given, the confidence intervals for the given level are
plotted, e.g. if alpha=.05, 95 % confidence intervals are shown.
If None, confidence intervals are not shown on the plot.
use_vlines : bool, optional
If True, shows vertical lines and markers for the correlation values.
If False, only shows markers. The default marker is 'o'; it can
be overridden with a ``marker`` kwarg.
adjusted : bool
If True, then denominators for correlations are n-k, otherwise n.
fft : bool, optional
If True, computes the ACF via FFT.
missing : str, optional
A string in ['none', 'raise', 'conservative', 'drop'] specifying how
NaNs are to be treated.
zero : bool, optional
Flag indicating whether to include the 0-lag autocorrelations
(which are always equal to 1). Default is True.
auto_ylims : bool, optional
If True, adjusts automatically the vertical axis limits
to correlation values.
bartlett_confint : bool, default False
If True, use Bartlett's formula to calculate confidence intervals
in auto-correlation plots. See the description of ``plot_acf`` for
details. This argument does not affect cross-correlation plots.
vlines_kwargs : dict, optional
Optional dictionary of keyword arguments that are passed to vlines.
**kwargs : kwargs, optional
Optional keyword arguments that are directly passed on to the
Matplotlib ``plot`` and ``axhline`` functions.
Returns
-------
Figure
If `fig` is None, the created figure. Otherwise, `fig` is returned.
Plots on the grid show the cross-correlation of the row variable
with the lags of the column variable.
See Also
--------
statsmodels.graphics.tsaplots.plot_acf
statsmodels.graphics.tsaplots.plot_ccf
Examples
--------
>>> import pandas as pd
>>> import matplotlib.pyplot as plt
>>> import statsmodels.api as sm
>>> dta = sm.datasets.macrodata.load_pandas().data
>>> diffed = dta.diff().dropna()
>>> sm.graphics.tsa.plot_accf_grid(diffed[["unemp", "infl"]])
>>> plt.show()
"""
from statsmodels.tools.data import _is_using_pandas
array_like(x, "x", ndim=2)
m = x.shape[1]
fig = utils.create_mpl_fig(fig)
gs = fig.add_gridspec(m, m)
if _is_using_pandas(x, None):
varnames = varnames or list(x.columns)
def get_var(i):
return x.iloc[:, i]
else:
varnames = varnames or [f'x[{i}]' for i in range(m)]
x = np.asarray(x)
def get_var(i):
return x[:, i]
for i in range(m):
for j in range(m):
ax = fig.add_subplot(gs[i, j])
if i == j:
plot_acf(
get_var(i),
ax=ax,
title=f'ACF({varnames[i]})',
lags=lags,
alpha=alpha,
use_vlines=use_vlines,
adjusted=adjusted,
fft=fft,
missing=missing,
zero=zero,
auto_ylims=auto_ylims,
bartlett_confint=bartlett_confint,
vlines_kwargs=vlines_kwargs,
**kwargs,
)
else:
plot_ccf(
get_var(i),
get_var(j),
ax=ax,
title=f'CCF({varnames[i]}, {varnames[j]})',
lags=lags,
negative_lags=negative_lags and i > j,
alpha=alpha,
use_vlines=use_vlines,
adjusted=adjusted,
fft=fft,
auto_ylims=auto_ylims,
vlines_kwargs=vlines_kwargs,
**kwargs,
)
return fig | Plot auto/cross-correlation grid
Plots lags on the horizontal axis and the correlations
on the vertical axis of each graph.
Parameters
----------
x : array_like
2D array of time-series values: rows are observations,
columns are variables.
varnames: sequence of str, optional
Variable names to use in plot titles. If ``x`` is a pandas dataframe
and ``varnames`` is provided, it overrides the column names
of the dataframe. If ``varnames`` is not provided and ``x`` is not
a dataframe, variable names ``x[0]``, ``x[1]``, etc. are generated.
fig : Matplotlib figure instance, optional
If given, this figure is used to plot in, otherwise a new figure
is created.
lags : {int, array_like}, optional
An int or array of lag values, used on horizontal axes. Uses
``np.arange(lags)`` when lags is an int. If not provided,
``lags=np.arange(len(corr))`` is used.
negative_lags: bool, optional
If True, negative lags are shown on the horizontal axes of plots
below the main diagonal.
alpha : scalar, optional
If a number is given, the confidence intervals for the given level are
plotted, e.g. if alpha=.05, 95 % confidence intervals are shown.
If None, confidence intervals are not shown on the plot.
use_vlines : bool, optional
If True, shows vertical lines and markers for the correlation values.
If False, only shows markers. The default marker is 'o'; it can
be overridden with a ``marker`` kwarg.
adjusted : bool
If True, then denominators for correlations are n-k, otherwise n.
fft : bool, optional
If True, computes the ACF via FFT.
missing : str, optional
A string in ['none', 'raise', 'conservative', 'drop'] specifying how
NaNs are to be treated.
zero : bool, optional
Flag indicating whether to include the 0-lag autocorrelations
(which are always equal to 1). Default is True.
auto_ylims : bool, optional
If True, adjusts automatically the vertical axis limits
to correlation values.
bartlett_confint : bool, default False
If True, use Bartlett's formula to calculate confidence intervals
in auto-correlation plots. See the description of ``plot_acf`` for
details. This argument does not affect cross-correlation plots.
vlines_kwargs : dict, optional
Optional dictionary of keyword arguments that are passed to vlines.
**kwargs : kwargs, optional
Optional keyword arguments that are directly passed on to the
Matplotlib ``plot`` and ``axhline`` functions.
Returns
-------
Figure
If `fig` is None, the created figure. Otherwise, `fig` is returned.
Plots on the grid show the cross-correlation of the row variable
with the lags of the column variable.
See Also
--------
statsmodels.graphics.tsaplots.plot_acf
statsmodels.graphics.tsaplots.plot_ccf
Examples
--------
>>> import pandas as pd
>>> import matplotlib.pyplot as plt
>>> import statsmodels.api as sm
>>> dta = sm.datasets.macrodata.load_pandas().data
>>> diffed = dta.diff().dropna()
>>> sm.graphics.tsa.plot_accf_grid(diffed[["unemp", "infl"]])
>>> plt.show() | plot_accf_grid | python | statsmodels/statsmodels | statsmodels/graphics/tsaplots.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/graphics/tsaplots.py | BSD-3-Clause |
def seasonal_plot(grouped_x, xticklabels, ylabel=None, ax=None):
"""
Consider using one of month_plot or quarter_plot unless you need
irregular plotting.
Parameters
----------
grouped_x : iterable of DataFrames
Should be a GroupBy object (or similar pair of group_names and groups
as DataFrames) with a DatetimeIndex or PeriodIndex
xticklabels : list of str
List of season labels, one for each group.
ylabel : str
Lable for y axis
ax : AxesSubplot, optional
If given, this subplot is used to plot in instead of a new figure being
created.
"""
fig, ax = utils.create_mpl_ax(ax)
start = 0
ticks = []
for season, df in grouped_x:
df = df.copy() # or sort balks for series. may be better way
df.sort_index()
nobs = len(df)
x_plot = np.arange(start, start + nobs)
ticks.append(x_plot.mean())
ax.plot(x_plot, df.values, "k")
ax.hlines(
df.values.mean(), x_plot[0], x_plot[-1], colors="r", linewidth=3
)
start += nobs
ax.set_xticks(ticks)
ax.set_xticklabels(xticklabels)
ax.set_ylabel(ylabel)
ax.margins(0.1, 0.05)
return fig | Consider using one of month_plot or quarter_plot unless you need
irregular plotting.
Parameters
----------
grouped_x : iterable of DataFrames
Should be a GroupBy object (or similar pair of group_names and groups
as DataFrames) with a DatetimeIndex or PeriodIndex
xticklabels : list of str
List of season labels, one for each group.
ylabel : str
Lable for y axis
ax : AxesSubplot, optional
If given, this subplot is used to plot in instead of a new figure being
created. | seasonal_plot | python | statsmodels/statsmodels | statsmodels/graphics/tsaplots.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/graphics/tsaplots.py | BSD-3-Clause |
def month_plot(x, dates=None, ylabel=None, ax=None):
"""
Seasonal plot of monthly data.
Parameters
----------
x : array_like
Seasonal data to plot. If dates is None, x must be a pandas object
with a PeriodIndex or DatetimeIndex with a monthly frequency.
dates : array_like, optional
If `x` is not a pandas object, then dates must be supplied.
ylabel : str, optional
The label for the y-axis. Will attempt to use the `name` attribute
of the Series.
ax : Axes, optional
Existing axes instance.
Returns
-------
Figure
If `ax` is provided, the Figure instance attached to `ax`. Otherwise
a new Figure instance.
Examples
--------
>>> import statsmodels.api as sm
>>> import pandas as pd
>>> dta = sm.datasets.elnino.load_pandas().data
>>> dta['YEAR'] = dta.YEAR.astype(int).astype(str)
>>> dta = dta.set_index('YEAR').T.unstack()
>>> dates = pd.to_datetime(list(map(lambda x: '-'.join(x) + '-1',
... dta.index.values)))
>>> dta.index = pd.DatetimeIndex(dates, freq='MS')
>>> fig = sm.graphics.tsa.month_plot(dta)
.. plot:: plots/graphics_tsa_month_plot.py
"""
if dates is None:
from statsmodels.tools.data import _check_period_index
_check_period_index(x, freq="M")
else:
x = pd.Series(x, index=pd.PeriodIndex(dates, freq="M"))
# there's no zero month
xticklabels = list(calendar.month_abbr)[1:]
return seasonal_plot(
x.groupby(lambda y: y.month), xticklabels, ylabel=ylabel, ax=ax
) | Seasonal plot of monthly data.
Parameters
----------
x : array_like
Seasonal data to plot. If dates is None, x must be a pandas object
with a PeriodIndex or DatetimeIndex with a monthly frequency.
dates : array_like, optional
If `x` is not a pandas object, then dates must be supplied.
ylabel : str, optional
The label for the y-axis. Will attempt to use the `name` attribute
of the Series.
ax : Axes, optional
Existing axes instance.
Returns
-------
Figure
If `ax` is provided, the Figure instance attached to `ax`. Otherwise
a new Figure instance.
Examples
--------
>>> import statsmodels.api as sm
>>> import pandas as pd
>>> dta = sm.datasets.elnino.load_pandas().data
>>> dta['YEAR'] = dta.YEAR.astype(int).astype(str)
>>> dta = dta.set_index('YEAR').T.unstack()
>>> dates = pd.to_datetime(list(map(lambda x: '-'.join(x) + '-1',
... dta.index.values)))
>>> dta.index = pd.DatetimeIndex(dates, freq='MS')
>>> fig = sm.graphics.tsa.month_plot(dta)
.. plot:: plots/graphics_tsa_month_plot.py | month_plot | python | statsmodels/statsmodels | statsmodels/graphics/tsaplots.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/graphics/tsaplots.py | BSD-3-Clause |
def quarter_plot(x, dates=None, ylabel=None, ax=None):
"""
Seasonal plot of quarterly data
Parameters
----------
x : array_like
Seasonal data to plot. If dates is None, x must be a pandas object
with a PeriodIndex or DatetimeIndex with a monthly frequency.
dates : array_like, optional
If `x` is not a pandas object, then dates must be supplied.
ylabel : str, optional
The label for the y-axis. Will attempt to use the `name` attribute
of the Series.
ax : matplotlib.axes, optional
Existing axes instance.
Returns
-------
Figure
If `ax` is provided, the Figure instance attached to `ax`. Otherwise
a new Figure instance.
Examples
--------
>>> import statsmodels.api as sm
>>> import pandas as pd
>>> dta = sm.datasets.elnino.load_pandas().data
>>> dta['YEAR'] = dta.YEAR.astype(int).astype(str)
>>> dta = dta.set_index('YEAR').T.unstack()
>>> dates = pd.to_datetime(list(map(lambda x: '-'.join(x) + '-1',
... dta.index.values)))
>>> dta.index = dates.to_period('Q')
>>> fig = sm.graphics.tsa.quarter_plot(dta)
.. plot:: plots/graphics_tsa_quarter_plot.py
"""
if dates is None:
from statsmodels.tools.data import _check_period_index
_check_period_index(x, freq="Q")
else:
x = pd.Series(x, index=pd.PeriodIndex(dates, freq="Q"))
xticklabels = ["q1", "q2", "q3", "q4"]
return seasonal_plot(
x.groupby(lambda y: y.quarter), xticklabels, ylabel=ylabel, ax=ax
) | Seasonal plot of quarterly data
Parameters
----------
x : array_like
Seasonal data to plot. If dates is None, x must be a pandas object
with a PeriodIndex or DatetimeIndex with a monthly frequency.
dates : array_like, optional
If `x` is not a pandas object, then dates must be supplied.
ylabel : str, optional
The label for the y-axis. Will attempt to use the `name` attribute
of the Series.
ax : matplotlib.axes, optional
Existing axes instance.
Returns
-------
Figure
If `ax` is provided, the Figure instance attached to `ax`. Otherwise
a new Figure instance.
Examples
--------
>>> import statsmodels.api as sm
>>> import pandas as pd
>>> dta = sm.datasets.elnino.load_pandas().data
>>> dta['YEAR'] = dta.YEAR.astype(int).astype(str)
>>> dta = dta.set_index('YEAR').T.unstack()
>>> dates = pd.to_datetime(list(map(lambda x: '-'.join(x) + '-1',
... dta.index.values)))
>>> dta.index = dates.to_period('Q')
>>> fig = sm.graphics.tsa.quarter_plot(dta)
.. plot:: plots/graphics_tsa_quarter_plot.py | quarter_plot | python | statsmodels/statsmodels | statsmodels/graphics/tsaplots.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/graphics/tsaplots.py | BSD-3-Clause |
def plot_predict(
result,
start=None,
end=None,
dynamic=False,
alpha=0.05,
ax=None,
**predict_kwargs,
):
"""
Parameters
----------
result : Result
Any model result supporting ``get_prediction``.
start : int, str, or datetime, optional
Zero-indexed observation number at which to start forecasting,
i.e., the first forecast is start. Can also be a date string to
parse or a datetime type. Default is the the zeroth observation.
end : int, str, or datetime, optional
Zero-indexed observation number at which to end forecasting, i.e.,
the last forecast is end. Can also be a date string to
parse or a datetime type. However, if the dates index does not
have a fixed frequency, end must be an integer index if you
want out of sample prediction. Default is the last observation in
the sample.
dynamic : bool, int, str, or datetime, optional
Integer offset relative to `start` at which to begin dynamic
prediction. Can also be an absolute date string to parse or a
datetime type (these are not interpreted as offsets).
Prior to this observation, true endogenous values will be used for
prediction; starting with this observation and continuing through
the end of prediction, forecasted endogenous values will be used
instead.
alpha : {float, None}
The tail probability not covered by the confidence interval. Must
be in (0, 1). Confidence interval is constructed assuming normally
distributed shocks. If None, figure will not show the confidence
interval.
ax : AxesSubplot
matplotlib Axes instance to use
**predict_kwargs
Any additional keyword arguments to pass to ``result.get_prediction``.
Returns
-------
Figure
matplotlib Figure containing the prediction plot
"""
from statsmodels.graphics.utils import _import_mpl, create_mpl_ax
_ = _import_mpl()
fig, ax = create_mpl_ax(ax)
from statsmodels.tsa.base.prediction import PredictionResults
# use predict so you set dates
pred: PredictionResults = result.get_prediction(
start=start, end=end, dynamic=dynamic, **predict_kwargs
)
mean = pred.predicted_mean
if isinstance(mean, (pd.Series, pd.DataFrame)):
x = mean.index
mean.plot(ax=ax, label="forecast")
else:
x = np.arange(mean.shape[0])
ax.plot(x, mean, label="forecast")
if alpha is not None:
label = f"{1-alpha:.0%} confidence interval"
ci = pred.conf_int(alpha)
conf_int = np.asarray(ci)
ax.fill_between(
x,
conf_int[:, 0],
conf_int[:, 1],
color="gray",
alpha=0.5,
label=label,
)
ax.legend(loc="best")
return fig | Parameters
----------
result : Result
Any model result supporting ``get_prediction``.
start : int, str, or datetime, optional
Zero-indexed observation number at which to start forecasting,
i.e., the first forecast is start. Can also be a date string to
parse or a datetime type. Default is the the zeroth observation.
end : int, str, or datetime, optional
Zero-indexed observation number at which to end forecasting, i.e.,
the last forecast is end. Can also be a date string to
parse or a datetime type. However, if the dates index does not
have a fixed frequency, end must be an integer index if you
want out of sample prediction. Default is the last observation in
the sample.
dynamic : bool, int, str, or datetime, optional
Integer offset relative to `start` at which to begin dynamic
prediction. Can also be an absolute date string to parse or a
datetime type (these are not interpreted as offsets).
Prior to this observation, true endogenous values will be used for
prediction; starting with this observation and continuing through
the end of prediction, forecasted endogenous values will be used
instead.
alpha : {float, None}
The tail probability not covered by the confidence interval. Must
be in (0, 1). Confidence interval is constructed assuming normally
distributed shocks. If None, figure will not show the confidence
interval.
ax : AxesSubplot
matplotlib Axes instance to use
**predict_kwargs
Any additional keyword arguments to pass to ``result.get_prediction``.
Returns
-------
Figure
matplotlib Figure containing the prediction plot | plot_predict | python | statsmodels/statsmodels | statsmodels/graphics/tsaplots.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/graphics/tsaplots.py | BSD-3-Clause |
def add_lowess(ax, lines_idx=0, frac=.2, **lowess_kwargs):
"""
Add Lowess line to a plot.
Parameters
----------
ax : AxesSubplot
The Axes to which to add the plot
lines_idx : int
This is the line on the existing plot to which you want to add
a smoothed lowess line.
frac : float
The fraction of the points to use when doing the lowess fit.
lowess_kwargs
Additional keyword arguments are passes to lowess.
Returns
-------
Figure
The figure that holds the instance.
"""
y0 = ax.get_lines()[lines_idx]._y
x0 = ax.get_lines()[lines_idx]._x
lres = lowess(y0, x0, frac=frac, **lowess_kwargs)
ax.plot(lres[:, 0], lres[:, 1], 'r', lw=1.5)
return ax.figure | Add Lowess line to a plot.
Parameters
----------
ax : AxesSubplot
The Axes to which to add the plot
lines_idx : int
This is the line on the existing plot to which you want to add
a smoothed lowess line.
frac : float
The fraction of the points to use when doing the lowess fit.
lowess_kwargs
Additional keyword arguments are passes to lowess.
Returns
-------
Figure
The figure that holds the instance. | add_lowess | python | statsmodels/statsmodels | statsmodels/graphics/regressionplots.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/graphics/regressionplots.py | BSD-3-Clause |
def plot_fit(results, exog_idx, y_true=None, ax=None, vlines=True, **kwargs):
"""
Plot fit against one regressor.
This creates one graph with the scatterplot of observed values
compared to fitted values.
Parameters
----------
results : Results
A result instance with resid, model.endog and model.exog as
attributes.
exog_idx : {int, str}
Name or index of regressor in exog matrix.
y_true : array_like. optional
If this is not None, then the array is added to the plot.
ax : AxesSubplot, optional
If given, this subplot is used to plot in instead of a new figure being
created.
vlines : bool, optional
If this not True, then the uncertainty (pointwise prediction intervals) of the fit is not
plotted.
**kwargs
The keyword arguments are passed to the plot command for the fitted
values points.
Returns
-------
Figure
If `ax` is None, the created figure. Otherwise the figure to which
`ax` is connected.
Examples
--------
Load the Statewide Crime data set and perform linear regression with
`poverty` and `hs_grad` as variables and `murder` as the response
>>> import statsmodels.api as sm
>>> import matplotlib.pyplot as plt
>>> data = sm.datasets.statecrime.load_pandas().data
>>> murder = data['murder']
>>> X = data[['poverty', 'hs_grad']]
>>> X["constant"] = 1
>>> y = murder
>>> model = sm.OLS(y, X)
>>> results = model.fit()
Create a plot just for the variable 'Poverty.'
Note that vertical bars representing uncertainty are plotted since vlines is true
>>> fig, ax = plt.subplots()
>>> fig = sm.graphics.plot_fit(results, 0, ax=ax)
>>> ax.set_ylabel("Murder Rate")
>>> ax.set_xlabel("Poverty Level")
>>> ax.set_title("Linear Regression")
>>> plt.show()
.. plot:: plots/graphics_plot_fit_ex.py
"""
fig, ax = utils.create_mpl_ax(ax)
exog_name, exog_idx = utils.maybe_name_or_idx(exog_idx, results.model)
results = maybe_unwrap_results(results)
#maybe add option for wendog, wexog
y = results.model.endog
x1 = results.model.exog[:, exog_idx]
x1_argsort = np.argsort(x1)
y = y[x1_argsort]
x1 = x1[x1_argsort]
ax.plot(x1, y, 'bo', label=results.model.endog_names)
if y_true is not None:
ax.plot(x1, y_true[x1_argsort], 'b-', label='True values')
title = 'Fitted values versus %s' % exog_name
ax.plot(x1, results.fittedvalues[x1_argsort], 'D', color='r',
label='fitted', **kwargs)
if vlines is True:
_, iv_l, iv_u = wls_prediction_std(results)
ax.vlines(x1, iv_l[x1_argsort], iv_u[x1_argsort], linewidth=1,
color='k', alpha=.7)
#ax.fill_between(x1, iv_l[x1_argsort], iv_u[x1_argsort], alpha=0.1,
# color='k')
ax.set_title(title)
ax.set_xlabel(exog_name)
ax.set_ylabel(results.model.endog_names)
ax.legend(loc='best', numpoints=1)
return fig | Plot fit against one regressor.
This creates one graph with the scatterplot of observed values
compared to fitted values.
Parameters
----------
results : Results
A result instance with resid, model.endog and model.exog as
attributes.
exog_idx : {int, str}
Name or index of regressor in exog matrix.
y_true : array_like. optional
If this is not None, then the array is added to the plot.
ax : AxesSubplot, optional
If given, this subplot is used to plot in instead of a new figure being
created.
vlines : bool, optional
If this not True, then the uncertainty (pointwise prediction intervals) of the fit is not
plotted.
**kwargs
The keyword arguments are passed to the plot command for the fitted
values points.
Returns
-------
Figure
If `ax` is None, the created figure. Otherwise the figure to which
`ax` is connected.
Examples
--------
Load the Statewide Crime data set and perform linear regression with
`poverty` and `hs_grad` as variables and `murder` as the response
>>> import statsmodels.api as sm
>>> import matplotlib.pyplot as plt
>>> data = sm.datasets.statecrime.load_pandas().data
>>> murder = data['murder']
>>> X = data[['poverty', 'hs_grad']]
>>> X["constant"] = 1
>>> y = murder
>>> model = sm.OLS(y, X)
>>> results = model.fit()
Create a plot just for the variable 'Poverty.'
Note that vertical bars representing uncertainty are plotted since vlines is true
>>> fig, ax = plt.subplots()
>>> fig = sm.graphics.plot_fit(results, 0, ax=ax)
>>> ax.set_ylabel("Murder Rate")
>>> ax.set_xlabel("Poverty Level")
>>> ax.set_title("Linear Regression")
>>> plt.show()
.. plot:: plots/graphics_plot_fit_ex.py | plot_fit | python | statsmodels/statsmodels | statsmodels/graphics/regressionplots.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/graphics/regressionplots.py | BSD-3-Clause |
def plot_regress_exog(results, exog_idx, fig=None):
"""Plot regression results against one regressor.
This plots four graphs in a 2 by 2 figure: 'endog versus exog',
'residuals versus exog', 'fitted versus exog' and
'fitted plus residual versus exog'
Parameters
----------
results : result instance
A result instance with resid, model.endog and model.exog as attributes.
exog_idx : int or str
Name or index of regressor in exog matrix.
fig : Figure, optional
If given, this figure is simply returned. Otherwise a new figure is
created.
Returns
-------
Figure
The value of `fig` if provided. Otherwise a new instance.
Examples
--------
Load the Statewide Crime data set and build a model with regressors
including the rate of high school graduation (hs_grad), population in urban
areas (urban), households below poverty line (poverty), and single person
households (single). Outcome variable is the murder rate (murder).
Build a 2 by 2 figure based on poverty showing fitted versus actual murder
rate, residuals versus the poverty rate, partial regression plot of poverty,
and CCPR plot for poverty rate.
>>> import statsmodels.api as sm
>>> import matplotlib.pyplot as plt
>>> import statsmodels.formula.api as smf
>>> fig = plt.figure(figsize=(8, 6))
>>> crime_data = sm.datasets.statecrime.load_pandas()
>>> results = smf.ols('murder ~ hs_grad + urban + poverty + single',
... data=crime_data.data).fit()
>>> sm.graphics.plot_regress_exog(results, 'poverty', fig=fig)
>>> plt.show()
.. plot:: plots/graphics_regression_regress_exog.py
"""
fig = utils.create_mpl_fig(fig)
exog_name, exog_idx = utils.maybe_name_or_idx(exog_idx, results.model)
results = maybe_unwrap_results(results)
#maybe add option for wendog, wexog
y_name = results.model.endog_names
x1 = results.model.exog[:, exog_idx]
prstd, iv_l, iv_u = wls_prediction_std(results)
ax = fig.add_subplot(2, 2, 1)
ax.plot(x1, results.model.endog, 'o', color='b', alpha=0.9, label=y_name)
ax.plot(x1, results.fittedvalues, 'D', color='r', label='fitted',
alpha=.5)
ax.vlines(x1, iv_l, iv_u, linewidth=1, color='k', alpha=.7)
ax.set_title('Y and Fitted vs. X', fontsize='large')
ax.set_xlabel(exog_name)
ax.set_ylabel(y_name)
ax.legend(loc='best')
ax = fig.add_subplot(2, 2, 2)
ax.plot(x1, results.resid, 'o')
ax.axhline(y=0, color='black')
ax.set_title('Residuals versus %s' % exog_name, fontsize='large')
ax.set_xlabel(exog_name)
ax.set_ylabel("resid")
ax = fig.add_subplot(2, 2, 3)
exog_noti = np.ones(results.model.exog.shape[1], bool)
exog_noti[exog_idx] = False
exog_others = results.model.exog[:, exog_noti]
from pandas import Series
fig = plot_partregress(results.model.data.orig_endog,
Series(x1, name=exog_name,
index=results.model.data.row_labels),
exog_others, obs_labels=False, ax=ax)
ax.set_title('Partial regression plot', fontsize='large')
#ax.set_ylabel("Fitted values")
#ax.set_xlabel(exog_name)
ax = fig.add_subplot(2, 2, 4)
fig = plot_ccpr(results, exog_idx, ax=ax)
ax.set_title('CCPR Plot', fontsize='large')
#ax.set_xlabel(exog_name)
#ax.set_ylabel("Fitted values + resids")
fig.suptitle('Regression Plots for %s' % exog_name, fontsize="large")
fig.tight_layout()
fig.subplots_adjust(top=.90)
return fig | Plot regression results against one regressor.
This plots four graphs in a 2 by 2 figure: 'endog versus exog',
'residuals versus exog', 'fitted versus exog' and
'fitted plus residual versus exog'
Parameters
----------
results : result instance
A result instance with resid, model.endog and model.exog as attributes.
exog_idx : int or str
Name or index of regressor in exog matrix.
fig : Figure, optional
If given, this figure is simply returned. Otherwise a new figure is
created.
Returns
-------
Figure
The value of `fig` if provided. Otherwise a new instance.
Examples
--------
Load the Statewide Crime data set and build a model with regressors
including the rate of high school graduation (hs_grad), population in urban
areas (urban), households below poverty line (poverty), and single person
households (single). Outcome variable is the murder rate (murder).
Build a 2 by 2 figure based on poverty showing fitted versus actual murder
rate, residuals versus the poverty rate, partial regression plot of poverty,
and CCPR plot for poverty rate.
>>> import statsmodels.api as sm
>>> import matplotlib.pyplot as plt
>>> import statsmodels.formula.api as smf
>>> fig = plt.figure(figsize=(8, 6))
>>> crime_data = sm.datasets.statecrime.load_pandas()
>>> results = smf.ols('murder ~ hs_grad + urban + poverty + single',
... data=crime_data.data).fit()
>>> sm.graphics.plot_regress_exog(results, 'poverty', fig=fig)
>>> plt.show()
.. plot:: plots/graphics_regression_regress_exog.py | plot_regress_exog | python | statsmodels/statsmodels | statsmodels/graphics/regressionplots.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/graphics/regressionplots.py | BSD-3-Clause |
def _partial_regression(endog, exog_i, exog_others):
"""Partial regression.
regress endog on exog_i conditional on exog_others
uses OLS
Parameters
----------
endog : array_like
exog : array_like
exog_others : array_like
Returns
-------
res1c : OLS results instance
(res1a, res1b) : tuple of OLS results instances
results from regression of endog on exog_others and of exog_i on
exog_others
"""
#FIXME: This function does not appear to be used.
res1a = OLS(endog, exog_others).fit()
res1b = OLS(exog_i, exog_others).fit()
res1c = OLS(res1a.resid, res1b.resid).fit()
return res1c, (res1a, res1b) | Partial regression.
regress endog on exog_i conditional on exog_others
uses OLS
Parameters
----------
endog : array_like
exog : array_like
exog_others : array_like
Returns
-------
res1c : OLS results instance
(res1a, res1b) : tuple of OLS results instances
results from regression of endog on exog_others and of exog_i on
exog_others | _partial_regression | python | statsmodels/statsmodels | statsmodels/graphics/regressionplots.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/graphics/regressionplots.py | BSD-3-Clause |
def plot_partregress(endog, exog_i, exog_others, data=None,
title_kwargs={}, obs_labels=True, label_kwargs={},
ax=None, ret_coords=False, eval_env=1, **kwargs):
"""Plot partial regression for a single regressor.
Parameters
----------
endog : {ndarray, str}
The endogenous or response variable. If string is given, you can use a
arbitrary translations as with a formula.
exog_i : {ndarray, str}
The exogenous, explanatory variable. If string is given, you can use a
arbitrary translations as with a formula.
exog_others : {ndarray, list[str]}
Any other exogenous, explanatory variables. If a list of strings is
given, each item is a term in formula. You can use a arbitrary
translations as with a formula. The effect of these variables will be
removed by OLS regression.
data : {DataFrame, dict}
Some kind of data structure with names if the other variables are
given as strings.
title_kwargs : dict
Keyword arguments to pass on for the title. The key to control the
fonts is fontdict.
obs_labels : {bool, array_like}
Whether or not to annotate the plot points with their observation
labels. If obs_labels is a boolean, the point labels will try to do
the right thing. First it will try to use the index of data, then
fall back to the index of exog_i. Alternatively, you may give an
array-like object corresponding to the observation numbers.
label_kwargs : dict
Keyword arguments that control annotate for the observation labels.
ax : AxesSubplot, optional
If given, this subplot is used to plot in instead of a new figure being
created.
ret_coords : bool
If True will return the coordinates of the points in the plot. You
can use this to add your own annotations.
eval_env : int
Patsy eval environment if user functions and formulas are used in
defining endog or exog.
**kwargs
The keyword arguments passed to plot for the points.
Returns
-------
fig : Figure
If `ax` is None, the created figure. Otherwise the figure to which
`ax` is connected.
coords : list, optional
If ret_coords is True, return a tuple of arrays (x_coords, y_coords).
See Also
--------
plot_partregress_grid : Plot partial regression for a set of regressors.
Notes
-----
The slope of the fitted line is the that of `exog_i` in the full
multiple regression. The individual points can be used to assess the
influence of points on the estimated coefficient.
Examples
--------
Load the Statewide Crime data set and plot partial regression of the rate
of high school graduation (hs_grad) on the murder rate(murder).
The effects of the percent of the population living in urban areas (urban),
below the poverty line (poverty) , and in a single person household (single)
are removed by OLS regression.
>>> import statsmodels.api as sm
>>> import matplotlib.pyplot as plt
>>> crime_data = sm.datasets.statecrime.load_pandas()
>>> sm.graphics.plot_partregress(endog='murder', exog_i='hs_grad',
... exog_others=['urban', 'poverty', 'single'],
... data=crime_data.data, obs_labels=False)
>>> plt.show()
.. plot:: plots/graphics_regression_partregress.py
More detailed examples can be found in the Regression Plots notebook
on the examples page.
"""
#NOTE: there is no interaction between possible missing data and
#obs_labels yet, so this will need to be tweaked a bit for this case
fig, ax = utils.create_mpl_ax(ax)
# strings, use patsy to transform to data
if isinstance(endog, str):
endog = FormulaManager().get_matrices(endog + "-1", data, eval_env=eval_env, pandas=False)
mgr = FormulaManager()
if isinstance(exog_others, str):
RHS = mgr.get_matrices(exog_others, data, eval_env=eval_env, pandas=False)
elif isinstance(exog_others, list):
RHS = "+".join(exog_others)
RHS = mgr.get_matrices(RHS, data, eval_env=eval_env, pandas=False)
else:
RHS = exog_others
RHS_isemtpy = False
if isinstance(RHS, np.ndarray) and RHS.size==0:
RHS_isemtpy = True
elif isinstance(RHS, pd.DataFrame) and RHS.empty:
RHS_isemtpy = True
if isinstance(exog_i, str):
exog_i = mgr.get_matrices(exog_i + "-1", data, eval_env=eval_env, pandas=False)
# all arrays or pandas-like
if RHS_isemtpy:
endog = np.asarray(endog)
exog_i = np.asarray(exog_i)
ax.plot(endog, exog_i, 'o', **kwargs)
fitted_line = OLS(endog, exog_i).fit()
x_axis_endog_name = 'x' if isinstance(exog_i, np.ndarray) else exog_i.name
y_axis_endog_name = 'y' if isinstance(endog, np.ndarray) else endog.model_spec.column_names[0]
else:
res_yaxis = OLS(endog, RHS).fit()
res_xaxis = OLS(exog_i, RHS).fit()
xaxis_resid = res_xaxis.resid
yaxis_resid = res_yaxis.resid
x_axis_endog_name = res_xaxis.model.endog_names
y_axis_endog_name = res_yaxis.model.endog_names
ax.plot(xaxis_resid, yaxis_resid, 'o', **kwargs)
fitted_line = OLS(yaxis_resid, xaxis_resid).fit()
fig = abline_plot(0, np.asarray(fitted_line.params)[0], color='k', ax=ax)
if x_axis_endog_name == 'y': # for no names regression will just get a y
x_axis_endog_name = 'x' # this is misleading, so use x
ax.set_xlabel("e(%s | X)" % x_axis_endog_name)
ax.set_ylabel("e(%s | X)" % y_axis_endog_name)
ax.set_title('Partial Regression Plot', **title_kwargs)
# NOTE: if we want to get super fancy, we could annotate if a point is
# clicked using this widget
# http://stackoverflow.com/questions/4652439/
# is-there-a-matplotlib-equivalent-of-matlabs-datacursormode/
# 4674445#4674445
if obs_labels is True:
if data is not None:
obs_labels = data.index
elif hasattr(exog_i, "index"):
obs_labels = exog_i.index
else:
obs_labels = res_xaxis.model.data.row_labels
#NOTE: row_labels can be None.
#Maybe we should fix this to never be the case.
if obs_labels is None:
obs_labels = lrange(len(exog_i))
if obs_labels is not False: # could be array_like
if len(obs_labels) != len(exog_i):
raise ValueError("obs_labels does not match length of exog_i")
label_kwargs.update(dict(ha="center", va="bottom"))
ax = utils.annotate_axes(lrange(len(obs_labels)), obs_labels,
lzip(res_xaxis.resid, res_yaxis.resid),
[(0, 5)] * len(obs_labels), "x-large", ax=ax,
**label_kwargs)
if ret_coords:
return fig, (res_xaxis.resid, res_yaxis.resid)
else:
return fig | Plot partial regression for a single regressor.
Parameters
----------
endog : {ndarray, str}
The endogenous or response variable. If string is given, you can use a
arbitrary translations as with a formula.
exog_i : {ndarray, str}
The exogenous, explanatory variable. If string is given, you can use a
arbitrary translations as with a formula.
exog_others : {ndarray, list[str]}
Any other exogenous, explanatory variables. If a list of strings is
given, each item is a term in formula. You can use a arbitrary
translations as with a formula. The effect of these variables will be
removed by OLS regression.
data : {DataFrame, dict}
Some kind of data structure with names if the other variables are
given as strings.
title_kwargs : dict
Keyword arguments to pass on for the title. The key to control the
fonts is fontdict.
obs_labels : {bool, array_like}
Whether or not to annotate the plot points with their observation
labels. If obs_labels is a boolean, the point labels will try to do
the right thing. First it will try to use the index of data, then
fall back to the index of exog_i. Alternatively, you may give an
array-like object corresponding to the observation numbers.
label_kwargs : dict
Keyword arguments that control annotate for the observation labels.
ax : AxesSubplot, optional
If given, this subplot is used to plot in instead of a new figure being
created.
ret_coords : bool
If True will return the coordinates of the points in the plot. You
can use this to add your own annotations.
eval_env : int
Patsy eval environment if user functions and formulas are used in
defining endog or exog.
**kwargs
The keyword arguments passed to plot for the points.
Returns
-------
fig : Figure
If `ax` is None, the created figure. Otherwise the figure to which
`ax` is connected.
coords : list, optional
If ret_coords is True, return a tuple of arrays (x_coords, y_coords).
See Also
--------
plot_partregress_grid : Plot partial regression for a set of regressors.
Notes
-----
The slope of the fitted line is the that of `exog_i` in the full
multiple regression. The individual points can be used to assess the
influence of points on the estimated coefficient.
Examples
--------
Load the Statewide Crime data set and plot partial regression of the rate
of high school graduation (hs_grad) on the murder rate(murder).
The effects of the percent of the population living in urban areas (urban),
below the poverty line (poverty) , and in a single person household (single)
are removed by OLS regression.
>>> import statsmodels.api as sm
>>> import matplotlib.pyplot as plt
>>> crime_data = sm.datasets.statecrime.load_pandas()
>>> sm.graphics.plot_partregress(endog='murder', exog_i='hs_grad',
... exog_others=['urban', 'poverty', 'single'],
... data=crime_data.data, obs_labels=False)
>>> plt.show()
.. plot:: plots/graphics_regression_partregress.py
More detailed examples can be found in the Regression Plots notebook
on the examples page. | plot_partregress | python | statsmodels/statsmodels | statsmodels/graphics/regressionplots.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/graphics/regressionplots.py | BSD-3-Clause |
def plot_partregress_grid(results, exog_idx=None, grid=None, fig=None):
"""
Plot partial regression for a set of regressors.
Parameters
----------
results : Results instance
A regression model results instance.
exog_idx : {None, list[int], list[str]}
The indices or column names of the exog used in the plot, default is
all.
grid : {None, tuple[int]}
If grid is given, then it is used for the arrangement of the subplots.
The format of grid is (nrows, ncols). If grid is None, then ncol is
one, if there are only 2 subplots, and the number of columns is two
otherwise.
fig : Figure, optional
If given, this figure is simply returned. Otherwise a new figure is
created.
Returns
-------
Figure
If `fig` is None, the created figure. Otherwise `fig` itself.
See Also
--------
plot_partregress : Plot partial regression for a single regressor.
plot_ccpr : Plot CCPR against one regressor
Notes
-----
A subplot is created for each explanatory variable given by exog_idx.
The partial regression plot shows the relationship between the response
and the given explanatory variable after removing the effect of all other
explanatory variables in exog.
References
----------
See http://www.itl.nist.gov/div898/software/dataplot/refman1/auxillar/partregr.htm
Examples
--------
Using the state crime dataset separately plot the effect of the each
variable on the on the outcome, murder rate while accounting for the effect
of all other variables in the model visualized with a grid of partial
regression plots.
>>> from statsmodels.graphics.regressionplots import plot_partregress_grid
>>> import statsmodels.api as sm
>>> import matplotlib.pyplot as plt
>>> import statsmodels.formula.api as smf
>>> fig = plt.figure(figsize=(8, 6))
>>> crime_data = sm.datasets.statecrime.load_pandas()
>>> results = smf.ols('murder ~ hs_grad + urban + poverty + single',
... data=crime_data.data).fit()
>>> plot_partregress_grid(results, fig=fig)
>>> plt.show()
.. plot:: plots/graphics_regression_partregress_grid.py
"""
import pandas
fig = utils.create_mpl_fig(fig)
exog_name, exog_idx = utils.maybe_name_or_idx(exog_idx, results.model)
# TODO: maybe add option for using wendog, wexog instead
y = pandas.Series(results.model.endog, name=results.model.endog_names)
exog = results.model.exog
k_vars = exog.shape[1]
# this function does not make sense if k_vars=1
nrows = (len(exog_idx) + 1) // 2
ncols = 1 if nrows == len(exog_idx) else 2
if grid is not None:
nrows, ncols = grid
if ncols > 1:
title_kwargs = {"fontdict": {"fontsize": 'small'}}
# for indexing purposes
other_names = np.array(results.model.exog_names)
for i, idx in enumerate(exog_idx):
others = lrange(k_vars)
others.pop(idx)
exog_others = pandas.DataFrame(exog[:, others],
columns=other_names[others])
ax = fig.add_subplot(nrows, ncols, i + 1)
plot_partregress(y, pandas.Series(exog[:, idx],
name=other_names[idx]),
exog_others, ax=ax, title_kwargs=title_kwargs,
obs_labels=False)
ax.set_title("")
fig.suptitle("Partial Regression Plot", fontsize="large")
fig.tight_layout()
fig.subplots_adjust(top=.95)
return fig | Plot partial regression for a set of regressors.
Parameters
----------
results : Results instance
A regression model results instance.
exog_idx : {None, list[int], list[str]}
The indices or column names of the exog used in the plot, default is
all.
grid : {None, tuple[int]}
If grid is given, then it is used for the arrangement of the subplots.
The format of grid is (nrows, ncols). If grid is None, then ncol is
one, if there are only 2 subplots, and the number of columns is two
otherwise.
fig : Figure, optional
If given, this figure is simply returned. Otherwise a new figure is
created.
Returns
-------
Figure
If `fig` is None, the created figure. Otherwise `fig` itself.
See Also
--------
plot_partregress : Plot partial regression for a single regressor.
plot_ccpr : Plot CCPR against one regressor
Notes
-----
A subplot is created for each explanatory variable given by exog_idx.
The partial regression plot shows the relationship between the response
and the given explanatory variable after removing the effect of all other
explanatory variables in exog.
References
----------
See http://www.itl.nist.gov/div898/software/dataplot/refman1/auxillar/partregr.htm
Examples
--------
Using the state crime dataset separately plot the effect of the each
variable on the on the outcome, murder rate while accounting for the effect
of all other variables in the model visualized with a grid of partial
regression plots.
>>> from statsmodels.graphics.regressionplots import plot_partregress_grid
>>> import statsmodels.api as sm
>>> import matplotlib.pyplot as plt
>>> import statsmodels.formula.api as smf
>>> fig = plt.figure(figsize=(8, 6))
>>> crime_data = sm.datasets.statecrime.load_pandas()
>>> results = smf.ols('murder ~ hs_grad + urban + poverty + single',
... data=crime_data.data).fit()
>>> plot_partregress_grid(results, fig=fig)
>>> plt.show()
.. plot:: plots/graphics_regression_partregress_grid.py | plot_partregress_grid | python | statsmodels/statsmodels | statsmodels/graphics/regressionplots.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/graphics/regressionplots.py | BSD-3-Clause |
def plot_ccpr(results, exog_idx, ax=None):
"""
Plot CCPR against one regressor.
Generates a component and component-plus-residual (CCPR) plot.
Parameters
----------
results : result instance
A regression results instance.
exog_idx : {int, str}
Exogenous, explanatory variable. If string is given, it should
be the variable name that you want to use, and you can use arbitrary
translations as with a formula.
ax : AxesSubplot, optional
If given, it is used to plot in instead of a new figure being
created.
Returns
-------
Figure
If `ax` is None, the created figure. Otherwise the figure to which
`ax` is connected.
See Also
--------
plot_ccpr_grid : Creates CCPR plot for multiple regressors in a plot grid.
Notes
-----
The CCPR plot provides a way to judge the effect of one regressor on the
response variable by taking into account the effects of the other
independent variables. The partial residuals plot is defined as
Residuals + B_i*X_i versus X_i. The component adds the B_i*X_i versus
X_i to show where the fitted line would lie. Care should be taken if X_i
is highly correlated with any of the other independent variables. If this
is the case, the variance evident in the plot will be an underestimate of
the true variance.
References
----------
http://www.itl.nist.gov/div898/software/dataplot/refman1/auxillar/ccpr.htm
Examples
--------
Using the state crime dataset plot the effect of the rate of single
households ('single') on the murder rate while accounting for high school
graduation rate ('hs_grad'), percentage of people in an urban area, and rate
of poverty ('poverty').
>>> import statsmodels.api as sm
>>> import matplotlib.pyplot as plt
>>> import statsmodels.formula.api as smf
>>> crime_data = sm.datasets.statecrime.load_pandas()
>>> results = smf.ols('murder ~ hs_grad + urban + poverty + single',
... data=crime_data.data).fit()
>>> sm.graphics.plot_ccpr(results, 'single')
>>> plt.show()
.. plot:: plots/graphics_regression_ccpr.py
"""
fig, ax = utils.create_mpl_ax(ax)
exog_name, exog_idx = utils.maybe_name_or_idx(exog_idx, results.model)
results = maybe_unwrap_results(results)
x1 = results.model.exog[:, exog_idx]
#namestr = ' for %s' % self.name if self.name else ''
x1beta = x1*results.params[exog_idx]
ax.plot(x1, x1beta + results.resid, 'o')
from statsmodels.tools.tools import add_constant
mod = OLS(x1beta, add_constant(x1)).fit()
params = mod.params
fig = abline_plot(*params, **dict(ax=ax))
#ax.plot(x1, x1beta, '-')
ax.set_title('Component and component plus residual plot')
ax.set_ylabel("Residual + %s*beta_%d" % (exog_name, exog_idx))
ax.set_xlabel("%s" % exog_name)
return fig | Plot CCPR against one regressor.
Generates a component and component-plus-residual (CCPR) plot.
Parameters
----------
results : result instance
A regression results instance.
exog_idx : {int, str}
Exogenous, explanatory variable. If string is given, it should
be the variable name that you want to use, and you can use arbitrary
translations as with a formula.
ax : AxesSubplot, optional
If given, it is used to plot in instead of a new figure being
created.
Returns
-------
Figure
If `ax` is None, the created figure. Otherwise the figure to which
`ax` is connected.
See Also
--------
plot_ccpr_grid : Creates CCPR plot for multiple regressors in a plot grid.
Notes
-----
The CCPR plot provides a way to judge the effect of one regressor on the
response variable by taking into account the effects of the other
independent variables. The partial residuals plot is defined as
Residuals + B_i*X_i versus X_i. The component adds the B_i*X_i versus
X_i to show where the fitted line would lie. Care should be taken if X_i
is highly correlated with any of the other independent variables. If this
is the case, the variance evident in the plot will be an underestimate of
the true variance.
References
----------
http://www.itl.nist.gov/div898/software/dataplot/refman1/auxillar/ccpr.htm
Examples
--------
Using the state crime dataset plot the effect of the rate of single
households ('single') on the murder rate while accounting for high school
graduation rate ('hs_grad'), percentage of people in an urban area, and rate
of poverty ('poverty').
>>> import statsmodels.api as sm
>>> import matplotlib.pyplot as plt
>>> import statsmodels.formula.api as smf
>>> crime_data = sm.datasets.statecrime.load_pandas()
>>> results = smf.ols('murder ~ hs_grad + urban + poverty + single',
... data=crime_data.data).fit()
>>> sm.graphics.plot_ccpr(results, 'single')
>>> plt.show()
.. plot:: plots/graphics_regression_ccpr.py | plot_ccpr | python | statsmodels/statsmodels | statsmodels/graphics/regressionplots.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/graphics/regressionplots.py | BSD-3-Clause |
def plot_ccpr_grid(results, exog_idx=None, grid=None, fig=None):
"""
Generate CCPR plots against a set of regressors, plot in a grid.
Generates a grid of component and component-plus-residual (CCPR) plots.
Parameters
----------
results : result instance
A results instance with exog and params.
exog_idx : None or list of int
The indices or column names of the exog used in the plot.
grid : None or tuple of int (nrows, ncols)
If grid is given, then it is used for the arrangement of the subplots.
If grid is None, then ncol is one, if there are only 2 subplots, and
the number of columns is two otherwise.
fig : Figure, optional
If given, this figure is simply returned. Otherwise a new figure is
created.
Returns
-------
Figure
If `ax` is None, the created figure. Otherwise the figure to which
`ax` is connected.
See Also
--------
plot_ccpr : Creates CCPR plot for a single regressor.
Notes
-----
Partial residual plots are formed as::
Res + Betahat(i)*Xi versus Xi
and CCPR adds::
Betahat(i)*Xi versus Xi
References
----------
See http://www.itl.nist.gov/div898/software/dataplot/refman1/auxillar/ccpr.htm
Examples
--------
Using the state crime dataset separately plot the effect of the each
variable on the on the outcome, murder rate while accounting for the effect
of all other variables in the model.
>>> import statsmodels.api as sm
>>> import matplotlib.pyplot as plt
>>> import statsmodels.formula.api as smf
>>> fig = plt.figure(figsize=(8, 8))
>>> crime_data = sm.datasets.statecrime.load_pandas()
>>> results = smf.ols('murder ~ hs_grad + urban + poverty + single',
... data=crime_data.data).fit()
>>> sm.graphics.plot_ccpr_grid(results, fig=fig)
>>> plt.show()
.. plot:: plots/graphics_regression_ccpr_grid.py
"""
fig = utils.create_mpl_fig(fig)
exog_name, exog_idx = utils.maybe_name_or_idx(exog_idx, results.model)
if grid is not None:
nrows, ncols = grid
else:
if len(exog_idx) > 2:
nrows = int(np.ceil(len(exog_idx)/2.))
ncols = 2
else:
nrows = len(exog_idx)
ncols = 1
seen_constant = 0
for i, idx in enumerate(exog_idx):
if results.model.exog[:, idx].var() == 0:
seen_constant = 1
continue
ax = fig.add_subplot(nrows, ncols, i+1-seen_constant)
fig = plot_ccpr(results, exog_idx=idx, ax=ax)
ax.set_title("")
fig.suptitle("Component-Component Plus Residual Plot", fontsize="large")
fig.tight_layout()
fig.subplots_adjust(top=.95)
return fig | Generate CCPR plots against a set of regressors, plot in a grid.
Generates a grid of component and component-plus-residual (CCPR) plots.
Parameters
----------
results : result instance
A results instance with exog and params.
exog_idx : None or list of int
The indices or column names of the exog used in the plot.
grid : None or tuple of int (nrows, ncols)
If grid is given, then it is used for the arrangement of the subplots.
If grid is None, then ncol is one, if there are only 2 subplots, and
the number of columns is two otherwise.
fig : Figure, optional
If given, this figure is simply returned. Otherwise a new figure is
created.
Returns
-------
Figure
If `ax` is None, the created figure. Otherwise the figure to which
`ax` is connected.
See Also
--------
plot_ccpr : Creates CCPR plot for a single regressor.
Notes
-----
Partial residual plots are formed as::
Res + Betahat(i)*Xi versus Xi
and CCPR adds::
Betahat(i)*Xi versus Xi
References
----------
See http://www.itl.nist.gov/div898/software/dataplot/refman1/auxillar/ccpr.htm
Examples
--------
Using the state crime dataset separately plot the effect of the each
variable on the on the outcome, murder rate while accounting for the effect
of all other variables in the model.
>>> import statsmodels.api as sm
>>> import matplotlib.pyplot as plt
>>> import statsmodels.formula.api as smf
>>> fig = plt.figure(figsize=(8, 8))
>>> crime_data = sm.datasets.statecrime.load_pandas()
>>> results = smf.ols('murder ~ hs_grad + urban + poverty + single',
... data=crime_data.data).fit()
>>> sm.graphics.plot_ccpr_grid(results, fig=fig)
>>> plt.show()
.. plot:: plots/graphics_regression_ccpr_grid.py | plot_ccpr_grid | python | statsmodels/statsmodels | statsmodels/graphics/regressionplots.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/graphics/regressionplots.py | BSD-3-Clause |
def abline_plot(intercept=None, slope=None, horiz=None, vert=None,
model_results=None, ax=None, **kwargs):
"""
Plot a line given an intercept and slope.
Parameters
----------
intercept : float
The intercept of the line.
slope : float
The slope of the line.
horiz : float or array_like
Data for horizontal lines on the y-axis.
vert : array_like
Data for verterical lines on the x-axis.
model_results : statsmodels results instance
Any object that has a two-value `params` attribute. Assumed that it
is (intercept, slope).
ax : axes, optional
Matplotlib axes instance.
**kwargs
Options passed to matplotlib.pyplot.plt.
Returns
-------
Figure
The figure given by `ax.figure` or a new instance.
Examples
--------
>>> import numpy as np
>>> import statsmodels.api as sm
>>> np.random.seed(12345)
>>> X = sm.add_constant(np.random.normal(0, 20, size=30))
>>> y = np.dot(X, [25, 3.5]) + np.random.normal(0, 30, size=30)
>>> mod = sm.OLS(y,X).fit()
>>> fig = sm.graphics.abline_plot(model_results=mod)
>>> ax = fig.axes[0]
>>> ax.scatter(X[:,1], y)
>>> ax.margins(.1)
>>> import matplotlib.pyplot as plt
>>> plt.show()
.. plot:: plots/graphics_regression_abline.py
"""
if ax is not None: # get axis limits first thing, do not change these
x = ax.get_xlim()
else:
x = None
fig, ax = utils.create_mpl_ax(ax)
if model_results:
intercept, slope = model_results.params
if x is None:
x = [model_results.model.exog[:, 1].min(),
model_results.model.exog[:, 1].max()]
else:
if not (intercept is not None and slope is not None):
raise ValueError("specify slope and intercepty or model_results")
if x is None:
x = ax.get_xlim()
data_y = [x[0]*slope+intercept, x[1]*slope+intercept]
ax.set_xlim(x)
#ax.set_ylim(y)
from matplotlib.lines import Line2D
class ABLine2D(Line2D):
def __init__(self, *args, **kwargs):
super().__init__(*args, **kwargs)
self.id_xlim_callback = None
self.id_ylim_callback = None
def remove(self):
ax = self.axes
if self.id_xlim_callback:
ax.callbacks.disconnect(self.id_xlim_callback)
if self.id_ylim_callback:
ax.callbacks.disconnect(self.id_ylim_callback)
super().remove()
def update_datalim(self, ax):
ax.set_autoscale_on(False)
children = ax.get_children()
ablines = [child for child in children if child is self]
abline = ablines[0]
x = ax.get_xlim()
y = [x[0] * slope + intercept, x[1] * slope + intercept]
abline.set_data(x, y)
ax.figure.canvas.draw()
# TODO: how to intercept something like a margins call and adjust?
line = ABLine2D(x, data_y, **kwargs)
ax.add_line(line)
line.id_xlim_callback = ax.callbacks.connect('xlim_changed', line.update_datalim)
line.id_ylim_callback = ax.callbacks.connect('ylim_changed', line.update_datalim)
if horiz:
ax.hline(horiz)
if vert:
ax.vline(vert)
return fig | Plot a line given an intercept and slope.
Parameters
----------
intercept : float
The intercept of the line.
slope : float
The slope of the line.
horiz : float or array_like
Data for horizontal lines on the y-axis.
vert : array_like
Data for verterical lines on the x-axis.
model_results : statsmodels results instance
Any object that has a two-value `params` attribute. Assumed that it
is (intercept, slope).
ax : axes, optional
Matplotlib axes instance.
**kwargs
Options passed to matplotlib.pyplot.plt.
Returns
-------
Figure
The figure given by `ax.figure` or a new instance.
Examples
--------
>>> import numpy as np
>>> import statsmodels.api as sm
>>> np.random.seed(12345)
>>> X = sm.add_constant(np.random.normal(0, 20, size=30))
>>> y = np.dot(X, [25, 3.5]) + np.random.normal(0, 30, size=30)
>>> mod = sm.OLS(y,X).fit()
>>> fig = sm.graphics.abline_plot(model_results=mod)
>>> ax = fig.axes[0]
>>> ax.scatter(X[:,1], y)
>>> ax.margins(.1)
>>> import matplotlib.pyplot as plt
>>> plt.show()
.. plot:: plots/graphics_regression_abline.py | abline_plot | python | statsmodels/statsmodels | statsmodels/graphics/regressionplots.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/graphics/regressionplots.py | BSD-3-Clause |
def ceres_resids(results, focus_exog, frac=0.66, cond_means=None):
"""
Calculate the CERES residuals (Conditional Expectation Partial
Residuals) for a fitted model.
Parameters
----------
results : model results instance
The fitted model for which the CERES residuals are calculated.
focus_exog : int
The column of results.model.exog used as the 'focus variable'.
frac : float, optional
Lowess smoothing parameter for estimating the conditional
means. Not used if `cond_means` is provided.
cond_means : array_like, optional
If provided, the columns of this array are the conditional
means E[exog | focus exog], where exog ranges over some
or all of the columns of exog other than focus exog. If
this is an empty nx0 array, the conditional means are
treated as being zero. If None, the conditional means are
estimated.
Returns
-------
An array containing the CERES residuals.
Notes
-----
If `cond_means` is not provided, it is obtained by smoothing each
column of exog (except the focus column) against the focus column.
Currently only supports GLM, GEE, and OLS models.
"""
model = results.model
if not isinstance(model, (GLM, GEE, OLS)):
raise ValueError("ceres residuals not available for %s" %
model.__class__.__name__)
focus_exog, focus_col = utils.maybe_name_or_idx(focus_exog, model)
# Indices of non-focus columns
ix_nf = range(len(results.params))
ix_nf = list(ix_nf)
ix_nf.pop(focus_col)
nnf = len(ix_nf)
# Estimate the conditional means if not provided.
if cond_means is None:
# Below we calculate E[x | focus] where x is each column other
# than the focus column. We do not want the intercept when we do
# this so we remove it here.
pexog = model.exog[:, ix_nf]
pexog -= pexog.mean(0)
u, s, vt = np.linalg.svd(pexog, 0)
ii = np.flatnonzero(s > 1e-6)
pexog = u[:, ii]
fcol = model.exog[:, focus_col]
cond_means = np.empty((len(fcol), pexog.shape[1]))
for j in range(pexog.shape[1]):
# Get the fitted values for column i given the other
# columns (skip the intercept).
y0 = pexog[:, j]
cf = lowess(y0, fcol, frac=frac, return_sorted=False)
cond_means[:, j] = cf
new_exog = np.concatenate((model.exog[:, ix_nf], cond_means), axis=1)
# Refit the model using the adjusted exog values
klass = model.__class__
init_kwargs = model._get_init_kwds()
new_model = klass(model.endog, new_exog, **init_kwargs)
new_result = new_model.fit()
# The partial residual, with respect to l(x2) (notation of Cook 1998)
presid = model.endog - new_result.fittedvalues
if isinstance(model, (GLM, GEE)):
presid *= model.family.link.deriv(new_result.fittedvalues)
if new_exog.shape[1] > nnf:
presid += np.dot(new_exog[:, nnf:], new_result.params[nnf:])
return presid | Calculate the CERES residuals (Conditional Expectation Partial
Residuals) for a fitted model.
Parameters
----------
results : model results instance
The fitted model for which the CERES residuals are calculated.
focus_exog : int
The column of results.model.exog used as the 'focus variable'.
frac : float, optional
Lowess smoothing parameter for estimating the conditional
means. Not used if `cond_means` is provided.
cond_means : array_like, optional
If provided, the columns of this array are the conditional
means E[exog | focus exog], where exog ranges over some
or all of the columns of exog other than focus exog. If
this is an empty nx0 array, the conditional means are
treated as being zero. If None, the conditional means are
estimated.
Returns
-------
An array containing the CERES residuals.
Notes
-----
If `cond_means` is not provided, it is obtained by smoothing each
column of exog (except the focus column) against the focus column.
Currently only supports GLM, GEE, and OLS models. | ceres_resids | python | statsmodels/statsmodels | statsmodels/graphics/regressionplots.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/graphics/regressionplots.py | BSD-3-Clause |
def partial_resids(results, focus_exog):
"""
Returns partial residuals for a fitted model with respect to a
'focus predictor'.
Parameters
----------
results : results instance
A fitted regression model.
focus col : int
The column index of model.exog with respect to which the
partial residuals are calculated.
Returns
-------
An array of partial residuals.
References
----------
RD Cook and R Croos-Dabrera (1998). Partial residual plots in
generalized linear models. Journal of the American Statistical
Association, 93:442.
"""
# TODO: could be a method of results
# TODO: see Cook et al (1998) for a more general definition
# The calculation follows equation (8) from Cook's paper.
model = results.model
resid = model.endog - results.predict()
if isinstance(model, (GLM, GEE)):
resid *= model.family.link.deriv(results.fittedvalues)
elif isinstance(model, (OLS, GLS, WLS)):
pass # No need to do anything
else:
raise ValueError("Partial residuals for '%s' not implemented."
% type(model))
if type(focus_exog) is str:
focus_col = model.exog_names.index(focus_exog)
else:
focus_col = focus_exog
focus_val = results.params[focus_col] * model.exog[:, focus_col]
return focus_val + resid | Returns partial residuals for a fitted model with respect to a
'focus predictor'.
Parameters
----------
results : results instance
A fitted regression model.
focus col : int
The column index of model.exog with respect to which the
partial residuals are calculated.
Returns
-------
An array of partial residuals.
References
----------
RD Cook and R Croos-Dabrera (1998). Partial residual plots in
generalized linear models. Journal of the American Statistical
Association, 93:442. | partial_resids | python | statsmodels/statsmodels | statsmodels/graphics/regressionplots.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/graphics/regressionplots.py | BSD-3-Clause |
def added_variable_resids(results, focus_exog, resid_type=None,
use_glm_weights=True, fit_kwargs=None):
"""
Residualize the endog variable and a 'focus' exog variable in a
regression model with respect to the other exog variables.
Parameters
----------
results : regression results instance
A fitted model including the focus exog and all other
predictors of interest.
focus_exog : {int, str}
The column of results.model.exog or a variable name that is
to be residualized against the other predictors.
resid_type : str
The type of residuals to use for the dependent variable. If
None, uses `resid_deviance` for GLM/GEE and `resid` otherwise.
use_glm_weights : bool
Only used if the model is a GLM or GEE. If True, the
residuals for the focus predictor are computed using WLS, with
the weights obtained from the IRLS calculations for fitting
the GLM. If False, unweighted regression is used.
fit_kwargs : dict, optional
Keyword arguments to be passed to fit when refitting the
model.
Returns
-------
endog_resid : array_like
The residuals for the original exog
focus_exog_resid : array_like
The residuals for the focus predictor
Notes
-----
The 'focus variable' residuals are always obtained using linear
regression.
Currently only GLM, GEE, and OLS models are supported.
"""
model = results.model
if not isinstance(model, (GEE, GLM, OLS)):
raise ValueError("model type %s not supported for added variable residuals" %
model.__class__.__name__)
exog = model.exog
endog = model.endog
focus_exog, focus_col = utils.maybe_name_or_idx(focus_exog, model)
focus_exog_vals = exog[:, focus_col]
# Default residuals
if resid_type is None:
if isinstance(model, (GEE, GLM)):
resid_type = "resid_deviance"
else:
resid_type = "resid"
ii = range(exog.shape[1])
ii = list(ii)
ii.pop(focus_col)
reduced_exog = exog[:, ii]
start_params = results.params[ii]
klass = model.__class__
kwargs = model._get_init_kwds()
new_model = klass(endog, reduced_exog, **kwargs)
args = {"start_params": start_params}
if fit_kwargs is not None:
args.update(fit_kwargs)
new_result = new_model.fit(**args)
if not getattr(new_result, "converged", True):
raise ValueError("fit did not converge when calculating added variable residuals")
try:
endog_resid = getattr(new_result, resid_type)
except AttributeError:
raise ValueError("'%s' residual type not available" % resid_type)
import statsmodels.regression.linear_model as lm
if isinstance(model, (GLM, GEE)) and use_glm_weights:
weights = model.family.weights(results.fittedvalues)
if hasattr(model, "data_weights"):
weights = weights * model.data_weights
lm_results = lm.WLS(focus_exog_vals, reduced_exog, weights).fit()
else:
lm_results = lm.OLS(focus_exog_vals, reduced_exog).fit()
focus_exog_resid = lm_results.resid
return endog_resid, focus_exog_resid | Residualize the endog variable and a 'focus' exog variable in a
regression model with respect to the other exog variables.
Parameters
----------
results : regression results instance
A fitted model including the focus exog and all other
predictors of interest.
focus_exog : {int, str}
The column of results.model.exog or a variable name that is
to be residualized against the other predictors.
resid_type : str
The type of residuals to use for the dependent variable. If
None, uses `resid_deviance` for GLM/GEE and `resid` otherwise.
use_glm_weights : bool
Only used if the model is a GLM or GEE. If True, the
residuals for the focus predictor are computed using WLS, with
the weights obtained from the IRLS calculations for fitting
the GLM. If False, unweighted regression is used.
fit_kwargs : dict, optional
Keyword arguments to be passed to fit when refitting the
model.
Returns
-------
endog_resid : array_like
The residuals for the original exog
focus_exog_resid : array_like
The residuals for the focus predictor
Notes
-----
The 'focus variable' residuals are always obtained using linear
regression.
Currently only GLM, GEE, and OLS models are supported. | added_variable_resids | python | statsmodels/statsmodels | statsmodels/graphics/regressionplots.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/graphics/regressionplots.py | BSD-3-Clause |
def violinplot(data, ax=None, labels=None, positions=None, side='both',
show_boxplot=True, plot_opts=None):
"""
Make a violin plot of each dataset in the `data` sequence.
A violin plot is a boxplot combined with a kernel density estimate of the
probability density function per point.
Parameters
----------
data : sequence[array_like]
Data arrays, one array per value in `positions`.
ax : AxesSubplot, optional
If given, this subplot is used to plot in instead of a new figure being
created.
labels : list[str], optional
Tick labels for the horizontal axis. If not given, integers
``1..len(data)`` are used.
positions : array_like, optional
Position array, used as the horizontal axis of the plot. If not given,
spacing of the violins will be equidistant.
side : {'both', 'left', 'right'}, optional
How to plot the violin. Default is 'both'. The 'left', 'right'
options can be used to create asymmetric violin plots.
show_boxplot : bool, optional
Whether or not to show normal box plots on top of the violins.
Default is True.
plot_opts : dict, optional
A dictionary with plotting options. Any of the following can be
provided, if not present in `plot_opts` the defaults will be used::
- 'violin_fc', MPL color. Fill color for violins. Default is 'y'.
- 'violin_ec', MPL color. Edge color for violins. Default is 'k'.
- 'violin_lw', scalar. Edge linewidth for violins. Default is 1.
- 'violin_alpha', float. Transparancy of violins. Default is 0.5.
- 'cutoff', bool. If True, limit violin range to data range.
Default is False.
- 'cutoff_val', scalar. Where to cut off violins if `cutoff` is
True. Default is 1.5 standard deviations.
- 'cutoff_type', {'std', 'abs'}. Whether cutoff value is absolute,
or in standard deviations. Default is 'std'.
- 'violin_width' : float. Relative width of violins. Max available
space is 1, default is 0.8.
- 'label_fontsize', MPL fontsize. Adjusts fontsize only if given.
- 'label_rotation', scalar. Adjusts label rotation only if given.
Specify in degrees.
- 'bw_factor', Adjusts the scipy gaussian_kde kernel. default: None.
Options for scalar or callable.
Returns
-------
Figure
If `ax` is None, the created figure. Otherwise the figure to which
`ax` is connected.
See Also
--------
beanplot : Bean plot, builds on `violinplot`.
matplotlib.pyplot.boxplot : Standard boxplot.
Notes
-----
The appearance of violins can be customized with `plot_opts`. If
customization of boxplot elements is required, set `show_boxplot` to False
and plot it on top of the violins by calling the Matplotlib `boxplot`
function directly. For example::
violinplot(data, ax=ax, show_boxplot=False)
ax.boxplot(data, sym='cv', whis=2.5)
It can happen that the axis labels or tick labels fall outside the plot
area, especially with rotated labels on the horizontal axis. With
Matplotlib 1.1 or higher, this can easily be fixed by calling
``ax.tight_layout()``. With older Matplotlib one has to use ``plt.rc`` or
``plt.rcParams`` to fix this, for example::
plt.rc('figure.subplot', bottom=0.25)
violinplot(data, ax=ax)
References
----------
J.L. Hintze and R.D. Nelson, "Violin Plots: A Box Plot-Density Trace
Synergism", The American Statistician, Vol. 52, pp.181-84, 1998.
Examples
--------
We use the American National Election Survey 1996 dataset, which has Party
Identification of respondents as independent variable and (among other
data) age as dependent variable.
>>> data = sm.datasets.anes96.load_pandas()
>>> party_ID = np.arange(7)
>>> labels = ["Strong Democrat", "Weak Democrat", "Independent-Democrat",
... "Independent-Indpendent", "Independent-Republican",
... "Weak Republican", "Strong Republican"]
Group age by party ID, and create a violin plot with it:
>>> plt.rcParams['figure.subplot.bottom'] = 0.23 # keep labels visible
>>> age = [data.exog['age'][data.endog == id] for id in party_ID]
>>> fig = plt.figure()
>>> ax = fig.add_subplot(111)
>>> sm.graphics.violinplot(age, ax=ax, labels=labels,
... plot_opts={'cutoff_val':5, 'cutoff_type':'abs',
... 'label_fontsize':'small',
... 'label_rotation':30})
>>> ax.set_xlabel("Party identification of respondent.")
>>> ax.set_ylabel("Age")
>>> plt.show()
.. plot:: plots/graphics_boxplot_violinplot.py
"""
plot_opts = {} if plot_opts is None else plot_opts
if max([np.size(arr) for arr in data]) == 0:
msg = "No Data to make Violin: Try again!"
raise ValueError(msg)
fig, ax = utils.create_mpl_ax(ax)
data = list(map(np.asarray, data))
if positions is None:
positions = np.arange(len(data)) + 1
# Determine available horizontal space for each individual violin.
pos_span = np.max(positions) - np.min(positions)
width = np.min([0.15 * np.max([pos_span, 1.]),
plot_opts.get('violin_width', 0.8) / 2.])
# Plot violins.
for pos_data, pos in zip(data, positions):
_single_violin(ax, pos, pos_data, width, side, plot_opts)
if show_boxplot:
try:
ax.boxplot(
data, notch=1, positions=positions, orientation='vertical'
)
except TypeError:
# Remove after Matplotlib 3.10 is the minimum
ax.boxplot(data, notch=1, positions=positions, vert=1)
# Set ticks and tick labels of horizontal axis.
_set_ticks_labels(ax, data, labels, positions, plot_opts)
return fig | Make a violin plot of each dataset in the `data` sequence.
A violin plot is a boxplot combined with a kernel density estimate of the
probability density function per point.
Parameters
----------
data : sequence[array_like]
Data arrays, one array per value in `positions`.
ax : AxesSubplot, optional
If given, this subplot is used to plot in instead of a new figure being
created.
labels : list[str], optional
Tick labels for the horizontal axis. If not given, integers
``1..len(data)`` are used.
positions : array_like, optional
Position array, used as the horizontal axis of the plot. If not given,
spacing of the violins will be equidistant.
side : {'both', 'left', 'right'}, optional
How to plot the violin. Default is 'both'. The 'left', 'right'
options can be used to create asymmetric violin plots.
show_boxplot : bool, optional
Whether or not to show normal box plots on top of the violins.
Default is True.
plot_opts : dict, optional
A dictionary with plotting options. Any of the following can be
provided, if not present in `plot_opts` the defaults will be used::
- 'violin_fc', MPL color. Fill color for violins. Default is 'y'.
- 'violin_ec', MPL color. Edge color for violins. Default is 'k'.
- 'violin_lw', scalar. Edge linewidth for violins. Default is 1.
- 'violin_alpha', float. Transparancy of violins. Default is 0.5.
- 'cutoff', bool. If True, limit violin range to data range.
Default is False.
- 'cutoff_val', scalar. Where to cut off violins if `cutoff` is
True. Default is 1.5 standard deviations.
- 'cutoff_type', {'std', 'abs'}. Whether cutoff value is absolute,
or in standard deviations. Default is 'std'.
- 'violin_width' : float. Relative width of violins. Max available
space is 1, default is 0.8.
- 'label_fontsize', MPL fontsize. Adjusts fontsize only if given.
- 'label_rotation', scalar. Adjusts label rotation only if given.
Specify in degrees.
- 'bw_factor', Adjusts the scipy gaussian_kde kernel. default: None.
Options for scalar or callable.
Returns
-------
Figure
If `ax` is None, the created figure. Otherwise the figure to which
`ax` is connected.
See Also
--------
beanplot : Bean plot, builds on `violinplot`.
matplotlib.pyplot.boxplot : Standard boxplot.
Notes
-----
The appearance of violins can be customized with `plot_opts`. If
customization of boxplot elements is required, set `show_boxplot` to False
and plot it on top of the violins by calling the Matplotlib `boxplot`
function directly. For example::
violinplot(data, ax=ax, show_boxplot=False)
ax.boxplot(data, sym='cv', whis=2.5)
It can happen that the axis labels or tick labels fall outside the plot
area, especially with rotated labels on the horizontal axis. With
Matplotlib 1.1 or higher, this can easily be fixed by calling
``ax.tight_layout()``. With older Matplotlib one has to use ``plt.rc`` or
``plt.rcParams`` to fix this, for example::
plt.rc('figure.subplot', bottom=0.25)
violinplot(data, ax=ax)
References
----------
J.L. Hintze and R.D. Nelson, "Violin Plots: A Box Plot-Density Trace
Synergism", The American Statistician, Vol. 52, pp.181-84, 1998.
Examples
--------
We use the American National Election Survey 1996 dataset, which has Party
Identification of respondents as independent variable and (among other
data) age as dependent variable.
>>> data = sm.datasets.anes96.load_pandas()
>>> party_ID = np.arange(7)
>>> labels = ["Strong Democrat", "Weak Democrat", "Independent-Democrat",
... "Independent-Indpendent", "Independent-Republican",
... "Weak Republican", "Strong Republican"]
Group age by party ID, and create a violin plot with it:
>>> plt.rcParams['figure.subplot.bottom'] = 0.23 # keep labels visible
>>> age = [data.exog['age'][data.endog == id] for id in party_ID]
>>> fig = plt.figure()
>>> ax = fig.add_subplot(111)
>>> sm.graphics.violinplot(age, ax=ax, labels=labels,
... plot_opts={'cutoff_val':5, 'cutoff_type':'abs',
... 'label_fontsize':'small',
... 'label_rotation':30})
>>> ax.set_xlabel("Party identification of respondent.")
>>> ax.set_ylabel("Age")
>>> plt.show()
.. plot:: plots/graphics_boxplot_violinplot.py | violinplot | python | statsmodels/statsmodels | statsmodels/graphics/boxplots.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/graphics/boxplots.py | BSD-3-Clause |
def _violin_range(pos_data, plot_opts):
"""Return array with correct range, with which violins can be plotted."""
cutoff = plot_opts.get('cutoff', False)
cutoff_type = plot_opts.get('cutoff_type', 'std')
cutoff_val = plot_opts.get('cutoff_val', 1.5)
s = 0.0
if not cutoff:
if cutoff_type == 'std':
s = cutoff_val * np.std(pos_data)
else:
s = cutoff_val
x_lower = kde.dataset.min() - s
x_upper = kde.dataset.max() + s
return np.linspace(x_lower, x_upper, 100) | Return array with correct range, with which violins can be plotted. | _single_violin._violin_range | python | statsmodels/statsmodels | statsmodels/graphics/boxplots.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/graphics/boxplots.py | BSD-3-Clause |
def _single_violin(ax, pos, pos_data, width, side, plot_opts):
""""""
bw_factor = plot_opts.get('bw_factor', None)
def _violin_range(pos_data, plot_opts):
"""Return array with correct range, with which violins can be plotted."""
cutoff = plot_opts.get('cutoff', False)
cutoff_type = plot_opts.get('cutoff_type', 'std')
cutoff_val = plot_opts.get('cutoff_val', 1.5)
s = 0.0
if not cutoff:
if cutoff_type == 'std':
s = cutoff_val * np.std(pos_data)
else:
s = cutoff_val
x_lower = kde.dataset.min() - s
x_upper = kde.dataset.max() + s
return np.linspace(x_lower, x_upper, 100)
pos_data = np.asarray(pos_data)
# Kernel density estimate for data at this position.
kde = gaussian_kde(pos_data, bw_method=bw_factor)
# Create violin for pos, scaled to the available space.
xvals = _violin_range(pos_data, plot_opts)
violin = kde.evaluate(xvals)
violin = width * violin / violin.max()
if side == 'both':
envelope_l, envelope_r = (-violin + pos, violin + pos)
elif side == 'right':
envelope_l, envelope_r = (pos, violin + pos)
elif side == 'left':
envelope_l, envelope_r = (-violin + pos, pos)
else:
msg = "`side` parameter should be one of {'left', 'right', 'both'}."
raise ValueError(msg)
# Draw the violin.
ax.fill_betweenx(xvals, envelope_l, envelope_r,
facecolor=plot_opts.get('violin_fc', '#66c2a5'),
edgecolor=plot_opts.get('violin_ec', 'k'),
lw=plot_opts.get('violin_lw', 1),
alpha=plot_opts.get('violin_alpha', 0.5))
return xvals, violin | bw_factor = plot_opts.get('bw_factor', None)
def _violin_range(pos_data, plot_opts):
"""Return array with correct range, with which violins can be plotted. | _single_violin | python | statsmodels/statsmodels | statsmodels/graphics/boxplots.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/graphics/boxplots.py | BSD-3-Clause |
def _set_ticks_labels(ax, data, labels, positions, plot_opts):
"""Set ticks and labels on horizontal axis."""
# Set xticks and limits.
ax.set_xlim([np.min(positions) - 0.5, np.max(positions) + 0.5])
ax.set_xticks(positions)
label_fontsize = plot_opts.get('label_fontsize')
label_rotation = plot_opts.get('label_rotation')
if label_fontsize or label_rotation:
from matplotlib.artist import setp
if labels is not None:
if not len(labels) == len(data):
msg = "Length of `labels` should equal length of `data`."
raise ValueError(msg)
xticknames = ax.set_xticklabels(labels)
if label_fontsize:
setp(xticknames, fontsize=label_fontsize)
if label_rotation:
setp(xticknames, rotation=label_rotation)
return | Set ticks and labels on horizontal axis. | _set_ticks_labels | python | statsmodels/statsmodels | statsmodels/graphics/boxplots.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/graphics/boxplots.py | BSD-3-Clause |
def beanplot(data, ax=None, labels=None, positions=None, side='both',
jitter=False, plot_opts={}):
"""
Bean plot of each dataset in a sequence.
A bean plot is a combination of a `violinplot` (kernel density estimate of
the probability density function per point) with a line-scatter plot of all
individual data points.
Parameters
----------
data : sequence[array_like]
Data arrays, one array per value in `positions`.
ax : AxesSubplot
If given, this subplot is used to plot in instead of a new figure being
created.
labels : list[str], optional
Tick labels for the horizontal axis. If not given, integers
``1..len(data)`` are used.
positions : array_like, optional
Position array, used as the horizontal axis of the plot. If not given,
spacing of the violins will be equidistant.
side : {'both', 'left', 'right'}, optional
How to plot the violin. Default is 'both'. The 'left', 'right'
options can be used to create asymmetric violin plots.
jitter : bool, optional
If True, jitter markers within violin instead of plotting regular lines
around the center. This can be useful if the data is very dense.
plot_opts : dict, optional
A dictionary with plotting options. All the options for `violinplot`
can be specified, they will simply be passed to `violinplot`. Options
specific to `beanplot` are:
- 'violin_width' : float. Relative width of violins. Max available
space is 1, default is 0.8.
- 'bean_color', MPL color. Color of bean plot lines. Default is 'k'.
Also used for jitter marker edge color if `jitter` is True.
- 'bean_size', scalar. Line length as a fraction of maximum length.
Default is 0.5.
- 'bean_lw', scalar. Linewidth, default is 0.5.
- 'bean_show_mean', bool. If True (default), show mean as a line.
- 'bean_show_median', bool. If True (default), show median as a
marker.
- 'bean_mean_color', MPL color. Color of mean line. Default is 'b'.
- 'bean_mean_lw', scalar. Linewidth of mean line, default is 2.
- 'bean_mean_size', scalar. Line length as a fraction of maximum length.
Default is 0.5.
- 'bean_median_color', MPL color. Color of median marker. Default
is 'r'.
- 'bean_median_marker', MPL marker. Marker type, default is '+'.
- 'jitter_marker', MPL marker. Marker type for ``jitter=True``.
Default is 'o'.
- 'jitter_marker_size', int. Marker size. Default is 4.
- 'jitter_fc', MPL color. Jitter marker face color. Default is None.
- 'bean_legend_text', str. If given, add a legend with given text.
Returns
-------
Figure
If `ax` is None, the created figure. Otherwise the figure to which
`ax` is connected.
See Also
--------
violinplot : Violin plot, also used internally in `beanplot`.
matplotlib.pyplot.boxplot : Standard boxplot.
References
----------
P. Kampstra, "Beanplot: A Boxplot Alternative for Visual Comparison of
Distributions", J. Stat. Soft., Vol. 28, pp. 1-9, 2008.
Examples
--------
We use the American National Election Survey 1996 dataset, which has Party
Identification of respondents as independent variable and (among other
data) age as dependent variable.
>>> data = sm.datasets.anes96.load_pandas()
>>> party_ID = np.arange(7)
>>> labels = ["Strong Democrat", "Weak Democrat", "Independent-Democrat",
... "Independent-Indpendent", "Independent-Republican",
... "Weak Republican", "Strong Republican"]
Group age by party ID, and create a violin plot with it:
>>> plt.rcParams['figure.subplot.bottom'] = 0.23 # keep labels visible
>>> age = [data.exog['age'][data.endog == id] for id in party_ID]
>>> fig = plt.figure()
>>> ax = fig.add_subplot(111)
>>> sm.graphics.beanplot(age, ax=ax, labels=labels,
... plot_opts={'cutoff_val':5, 'cutoff_type':'abs',
... 'label_fontsize':'small',
... 'label_rotation':30})
>>> ax.set_xlabel("Party identification of respondent.")
>>> ax.set_ylabel("Age")
>>> plt.show()
.. plot:: plots/graphics_boxplot_beanplot.py
"""
fig, ax = utils.create_mpl_ax(ax)
data = list(map(np.asarray, data))
if positions is None:
positions = np.arange(len(data)) + 1
# Determine available horizontal space for each individual violin.
pos_span = np.max(positions) - np.min(positions)
violin_width = np.min([0.15 * np.max([pos_span, 1.]),
plot_opts.get('violin_width', 0.8) / 2.])
bean_width = np.min([0.15 * np.max([pos_span, 1.]),
plot_opts.get('bean_size', 0.5) / 2.])
bean_mean_width = np.min([0.15 * np.max([pos_span, 1.]),
plot_opts.get('bean_mean_size', 0.5) / 2.])
legend_txt = plot_opts.get('bean_legend_text', None)
for pos_data, pos in zip(data, positions):
# Draw violins.
xvals, violin = _single_violin(ax, pos, pos_data, violin_width, side, plot_opts)
if jitter:
# Draw data points at random coordinates within violin envelope.
jitter_coord = pos + _jitter_envelope(pos_data, xvals, violin, side)
ax.plot(jitter_coord, pos_data, ls='',
marker=plot_opts.get('jitter_marker', 'o'),
ms=plot_opts.get('jitter_marker_size', 4),
mec=plot_opts.get('bean_color', 'k'),
mew=1, mfc=plot_opts.get('jitter_fc', 'none'),
label=legend_txt)
else:
# Draw bean lines.
ax.hlines(pos_data, pos - bean_width, pos + bean_width,
lw=plot_opts.get('bean_lw', 0.5),
color=plot_opts.get('bean_color', 'k'),
label=legend_txt)
# Show legend if required.
if legend_txt is not None:
_show_legend(ax)
legend_txt = None # ensure we get one entry per call to beanplot
# Draw mean line.
if plot_opts.get('bean_show_mean', True):
ax.hlines(np.mean(pos_data), pos - bean_mean_width, pos + bean_mean_width,
lw=plot_opts.get('bean_mean_lw', 2.),
color=plot_opts.get('bean_mean_color', 'b'))
# Draw median marker.
if plot_opts.get('bean_show_median', True):
ax.plot(pos, np.median(pos_data),
marker=plot_opts.get('bean_median_marker', '+'),
color=plot_opts.get('bean_median_color', 'r'))
# Set ticks and tick labels of horizontal axis.
_set_ticks_labels(ax, data, labels, positions, plot_opts)
return fig | Bean plot of each dataset in a sequence.
A bean plot is a combination of a `violinplot` (kernel density estimate of
the probability density function per point) with a line-scatter plot of all
individual data points.
Parameters
----------
data : sequence[array_like]
Data arrays, one array per value in `positions`.
ax : AxesSubplot
If given, this subplot is used to plot in instead of a new figure being
created.
labels : list[str], optional
Tick labels for the horizontal axis. If not given, integers
``1..len(data)`` are used.
positions : array_like, optional
Position array, used as the horizontal axis of the plot. If not given,
spacing of the violins will be equidistant.
side : {'both', 'left', 'right'}, optional
How to plot the violin. Default is 'both'. The 'left', 'right'
options can be used to create asymmetric violin plots.
jitter : bool, optional
If True, jitter markers within violin instead of plotting regular lines
around the center. This can be useful if the data is very dense.
plot_opts : dict, optional
A dictionary with plotting options. All the options for `violinplot`
can be specified, they will simply be passed to `violinplot`. Options
specific to `beanplot` are:
- 'violin_width' : float. Relative width of violins. Max available
space is 1, default is 0.8.
- 'bean_color', MPL color. Color of bean plot lines. Default is 'k'.
Also used for jitter marker edge color if `jitter` is True.
- 'bean_size', scalar. Line length as a fraction of maximum length.
Default is 0.5.
- 'bean_lw', scalar. Linewidth, default is 0.5.
- 'bean_show_mean', bool. If True (default), show mean as a line.
- 'bean_show_median', bool. If True (default), show median as a
marker.
- 'bean_mean_color', MPL color. Color of mean line. Default is 'b'.
- 'bean_mean_lw', scalar. Linewidth of mean line, default is 2.
- 'bean_mean_size', scalar. Line length as a fraction of maximum length.
Default is 0.5.
- 'bean_median_color', MPL color. Color of median marker. Default
is 'r'.
- 'bean_median_marker', MPL marker. Marker type, default is '+'.
- 'jitter_marker', MPL marker. Marker type for ``jitter=True``.
Default is 'o'.
- 'jitter_marker_size', int. Marker size. Default is 4.
- 'jitter_fc', MPL color. Jitter marker face color. Default is None.
- 'bean_legend_text', str. If given, add a legend with given text.
Returns
-------
Figure
If `ax` is None, the created figure. Otherwise the figure to which
`ax` is connected.
See Also
--------
violinplot : Violin plot, also used internally in `beanplot`.
matplotlib.pyplot.boxplot : Standard boxplot.
References
----------
P. Kampstra, "Beanplot: A Boxplot Alternative for Visual Comparison of
Distributions", J. Stat. Soft., Vol. 28, pp. 1-9, 2008.
Examples
--------
We use the American National Election Survey 1996 dataset, which has Party
Identification of respondents as independent variable and (among other
data) age as dependent variable.
>>> data = sm.datasets.anes96.load_pandas()
>>> party_ID = np.arange(7)
>>> labels = ["Strong Democrat", "Weak Democrat", "Independent-Democrat",
... "Independent-Indpendent", "Independent-Republican",
... "Weak Republican", "Strong Republican"]
Group age by party ID, and create a violin plot with it:
>>> plt.rcParams['figure.subplot.bottom'] = 0.23 # keep labels visible
>>> age = [data.exog['age'][data.endog == id] for id in party_ID]
>>> fig = plt.figure()
>>> ax = fig.add_subplot(111)
>>> sm.graphics.beanplot(age, ax=ax, labels=labels,
... plot_opts={'cutoff_val':5, 'cutoff_type':'abs',
... 'label_fontsize':'small',
... 'label_rotation':30})
>>> ax.set_xlabel("Party identification of respondent.")
>>> ax.set_ylabel("Age")
>>> plt.show()
.. plot:: plots/graphics_boxplot_beanplot.py | beanplot | python | statsmodels/statsmodels | statsmodels/graphics/boxplots.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/graphics/boxplots.py | BSD-3-Clause |
def _jitter_envelope(pos_data, xvals, violin, side):
"""Determine envelope for jitter markers."""
if side == 'both':
low, high = (-1., 1.)
elif side == 'right':
low, high = (0, 1.)
elif side == 'left':
low, high = (-1., 0)
else:
raise ValueError("`side` input incorrect: %s" % side)
jitter_envelope = np.interp(pos_data, xvals, violin)
jitter_coord = jitter_envelope * np.random.uniform(low=low, high=high,
size=pos_data.size)
return jitter_coord | Determine envelope for jitter markers. | _jitter_envelope | python | statsmodels/statsmodels | statsmodels/graphics/boxplots.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/graphics/boxplots.py | BSD-3-Clause |
def _show_legend(ax):
"""Utility function to show legend."""
leg = ax.legend(loc=1, shadow=True, fancybox=True, labelspacing=0.2,
borderpad=0.15)
ltext = leg.get_texts()
llines = leg.get_lines()
leg.get_frame()
from matplotlib.artist import setp
setp(ltext, fontsize='small')
setp(llines, linewidth=1) | Utility function to show legend. | _show_legend | python | statsmodels/statsmodels | statsmodels/graphics/boxplots.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/graphics/boxplots.py | BSD-3-Clause |
def _normalize_split(proportion):
"""
return a list of proportions of the available space given the division
if only a number is given, it will assume a split in two pieces
"""
if not iterable(proportion):
if proportion == 0:
proportion = array([0.0, 1.0])
elif proportion >= 1:
proportion = array([1.0, 0.0])
elif proportion < 0:
raise ValueError("proportions should be positive,"
"given value: {}".format(proportion))
else:
proportion = array([proportion, 1.0 - proportion])
proportion = np.asarray(proportion, dtype=float)
if np.any(proportion < 0):
raise ValueError("proportions should be positive,"
"given value: {}".format(proportion))
if np.allclose(proportion, 0):
raise ValueError(
"at least one proportion should be greater than zero"
"given value: {}".format(proportion)
)
# ok, data are meaningful, so go on
if len(proportion) < 2:
return array([0.0, 1.0])
left = r_[0, cumsum(proportion)]
left /= left[-1] * 1.0
return left | return a list of proportions of the available space given the division
if only a number is given, it will assume a split in two pieces | _normalize_split | python | statsmodels/statsmodels | statsmodels/graphics/mosaicplot.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/graphics/mosaicplot.py | BSD-3-Clause |
def _split_rect(x, y, width, height, proportion, horizontal=True, gap=0.05):
"""
Split the given rectangle in n segments whose proportion is specified
along the given axis if a gap is inserted, they will be separated by a
certain amount of space, retaining the relative proportion between them
a gap of 1 correspond to a plot that is half void and the remaining half
space is proportionally divided among the pieces.
"""
x, y, w, h = float(x), float(y), float(width), float(height)
if (w < 0) or (h < 0):
raise ValueError("dimension of the square less than"
"zero w={} h={}".format(w, h))
proportions = _normalize_split(proportion)
# extract the starting point and the dimension of each subdivision
# in respect to the unit square
starting = proportions[:-1]
amplitude = proportions[1:] - starting
# how much each extrema is going to be displaced due to gaps
starting += gap * np.arange(len(proportions) - 1)
# how much the squares plus the gaps are extended
extension = starting[-1] + amplitude[-1] - starting[0]
# normalize everything for fit again in the original dimension
starting /= extension
amplitude /= extension
# bring everything to the original square
starting = (x if horizontal else y) + starting * (w if horizontal else h)
amplitude = amplitude * (w if horizontal else h)
# create each 4-tuple for each new block
results = [(s, y, a, h) if horizontal else (x, s, w, a)
for s, a in zip(starting, amplitude)]
return results | Split the given rectangle in n segments whose proportion is specified
along the given axis if a gap is inserted, they will be separated by a
certain amount of space, retaining the relative proportion between them
a gap of 1 correspond to a plot that is half void and the remaining half
space is proportionally divided among the pieces. | _split_rect | python | statsmodels/statsmodels | statsmodels/graphics/mosaicplot.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/graphics/mosaicplot.py | BSD-3-Clause |
def _reduce_dict(count_dict, partial_key):
"""
Make partial sum on a counter dict.
Given a match for the beginning of the category, it will sum each value.
"""
L = len(partial_key)
count = sum(v for k, v in count_dict.items() if k[:L] == partial_key)
return count | Make partial sum on a counter dict.
Given a match for the beginning of the category, it will sum each value. | _reduce_dict | python | statsmodels/statsmodels | statsmodels/graphics/mosaicplot.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/graphics/mosaicplot.py | BSD-3-Clause |
def _key_splitting(rect_dict, keys, values, key_subset, horizontal, gap):
"""
Given a dictionary where each entry is a rectangle, a list of key and
value (count of elements in each category) it split each rect accordingly,
as long as the key start with the tuple key_subset. The other keys are
returned without modification.
"""
result = {}
L = len(key_subset)
for name, (x, y, w, h) in rect_dict.items():
if key_subset == name[:L]:
# split base on the values given
divisions = _split_rect(x, y, w, h, values, horizontal, gap)
for key, rect in zip(keys, divisions):
result[name + (key,)] = rect
else:
result[name] = (x, y, w, h)
return result | Given a dictionary where each entry is a rectangle, a list of key and
value (count of elements in each category) it split each rect accordingly,
as long as the key start with the tuple key_subset. The other keys are
returned without modification. | _key_splitting | python | statsmodels/statsmodels | statsmodels/graphics/mosaicplot.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/graphics/mosaicplot.py | BSD-3-Clause |
def _tuplify(obj):
"""convert an object in a tuple of strings (even if it is not iterable,
like a single integer number, but keep the string healthy)
"""
if np.iterable(obj) and not isinstance(obj, str):
res = tuple(str(o) for o in obj)
else:
res = (str(obj),)
return res | convert an object in a tuple of strings (even if it is not iterable,
like a single integer number, but keep the string healthy) | _tuplify | python | statsmodels/statsmodels | statsmodels/graphics/mosaicplot.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/graphics/mosaicplot.py | BSD-3-Clause |
def _categories_level(keys):
"""use the Ordered dict to implement a simple ordered set
return each level of each category
[[key_1_level_1,key_2_level_1],[key_1_level_2,key_2_level_2]]
"""
res = []
for i in zip(*(keys)):
tuplefied = _tuplify(i)
res.append(list({j: None for j in tuplefied}))
return res | use the Ordered dict to implement a simple ordered set
return each level of each category
[[key_1_level_1,key_2_level_1],[key_1_level_2,key_2_level_2]] | _categories_level | python | statsmodels/statsmodels | statsmodels/graphics/mosaicplot.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/graphics/mosaicplot.py | BSD-3-Clause |
def _hierarchical_split(count_dict, horizontal=True, gap=0.05):
"""
Split a square in a hierarchical way given a contingency table.
Hierarchically split the unit square in alternate directions
in proportion to the subdivision contained in the contingency table
count_dict. This is the function that actually perform the tiling
for the creation of the mosaic plot. If the gap array has been specified
it will insert a corresponding amount of space (proportional to the
unit length), while retaining the proportionality of the tiles.
Parameters
----------
count_dict : dict
Dictionary containing the contingency table.
Each category should contain a non-negative number
with a tuple as index. It expects that all the combination
of keys to be represents; if that is not true, will
automatically consider the missing values as 0
horizontal : bool
The starting direction of the split (by default along
the horizontal axis)
gap : float or array of floats
The list of gaps to be applied on each subdivision.
If the length of the given array is less of the number
of subcategories (or if it's a single number) it will extend
it with exponentially decreasing gaps
Returns
-------
base_rect : dict
A dictionary containing the result of the split.
To each key is associated a 4-tuple of coordinates
that are required to create the corresponding rectangle:
0 - x position of the lower left corner
1 - y position of the lower left corner
2 - width of the rectangle
3 - height of the rectangle
"""
# this is the unit square that we are going to divide
base_rect = dict([(tuple(), (0, 0, 1, 1))])
# get the list of each possible value for each level
categories_levels = _categories_level(list(count_dict.keys()))
L = len(categories_levels)
# recreate the gaps vector starting from an int
if not np.iterable(gap):
gap = [gap / 1.5 ** idx for idx in range(L)]
# extend if it's too short
if len(gap) < L:
last = gap[-1]
gap = list(*gap) + [last / 1.5 ** idx for idx in range(L)]
# trim if it's too long
gap = gap[:L]
# put the count dictionay in order for the keys
# this will allow some code simplification
count_ordered = {k: count_dict[k]
for k in list(product(*categories_levels))}
for cat_idx, cat_enum in enumerate(categories_levels):
# get the partial key up to the actual level
base_keys = list(product(*categories_levels[:cat_idx]))
for key in base_keys:
# for each partial and each value calculate how many
# observation we have in the counting dictionary
part_count = [_reduce_dict(count_ordered, key + (partial,))
for partial in cat_enum]
# reduce the gap for subsequents levels
new_gap = gap[cat_idx]
# split the given subkeys in the rectangle dictionary
base_rect = _key_splitting(base_rect, cat_enum, part_count, key,
horizontal, new_gap)
horizontal = not horizontal
return base_rect | Split a square in a hierarchical way given a contingency table.
Hierarchically split the unit square in alternate directions
in proportion to the subdivision contained in the contingency table
count_dict. This is the function that actually perform the tiling
for the creation of the mosaic plot. If the gap array has been specified
it will insert a corresponding amount of space (proportional to the
unit length), while retaining the proportionality of the tiles.
Parameters
----------
count_dict : dict
Dictionary containing the contingency table.
Each category should contain a non-negative number
with a tuple as index. It expects that all the combination
of keys to be represents; if that is not true, will
automatically consider the missing values as 0
horizontal : bool
The starting direction of the split (by default along
the horizontal axis)
gap : float or array of floats
The list of gaps to be applied on each subdivision.
If the length of the given array is less of the number
of subcategories (or if it's a single number) it will extend
it with exponentially decreasing gaps
Returns
-------
base_rect : dict
A dictionary containing the result of the split.
To each key is associated a 4-tuple of coordinates
that are required to create the corresponding rectangle:
0 - x position of the lower left corner
1 - y position of the lower left corner
2 - width of the rectangle
3 - height of the rectangle | _hierarchical_split | python | statsmodels/statsmodels | statsmodels/graphics/mosaicplot.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/graphics/mosaicplot.py | BSD-3-Clause |
def _single_hsv_to_rgb(hsv):
"""Transform a color from the hsv space to the rgb."""
from matplotlib.colors import hsv_to_rgb
return hsv_to_rgb(array(hsv).reshape(1, 1, 3)).reshape(3) | Transform a color from the hsv space to the rgb. | _single_hsv_to_rgb | python | statsmodels/statsmodels | statsmodels/graphics/mosaicplot.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/graphics/mosaicplot.py | BSD-3-Clause |
def _create_default_properties(data):
""""Create the default properties of the mosaic given the data
first it will varies the color hue (first category) then the color
saturation (second category) and then the color value
(third category). If a fourth category is found, it will put
decoration on the rectangle. Does not manage more than four
level of categories
"""
categories_levels = _categories_level(list(data.keys()))
Nlevels = len(categories_levels)
# first level, the hue
L = len(categories_levels[0])
# hue = np.linspace(1.0, 0.0, L+1)[:-1]
hue = np.linspace(0.0, 1.0, L + 2)[:-2]
# second level, the saturation
L = len(categories_levels[1]) if Nlevels > 1 else 1
saturation = np.linspace(0.5, 1.0, L + 1)[:-1]
# third level, the value
L = len(categories_levels[2]) if Nlevels > 2 else 1
value = np.linspace(0.5, 1.0, L + 1)[:-1]
# fourth level, the hatch
L = len(categories_levels[3]) if Nlevels > 3 else 1
hatch = ['', '/', '-', '|', '+'][:L + 1]
# convert in list and merge with the levels
hue = lzip(list(hue), categories_levels[0])
saturation = lzip(list(saturation),
categories_levels[1] if Nlevels > 1 else [''])
value = lzip(list(value),
categories_levels[2] if Nlevels > 2 else [''])
hatch = lzip(list(hatch),
categories_levels[3] if Nlevels > 3 else [''])
# create the properties dictionary
properties = {}
for h, s, v, t in product(hue, saturation, value, hatch):
hv, hn = h
sv, sn = s
vv, vn = v
tv, tn = t
level = (hn,) + ((sn,) if sn else tuple())
level = level + ((vn,) if vn else tuple())
level = level + ((tn,) if tn else tuple())
hsv = array([hv, sv, vv])
prop = {'color': _single_hsv_to_rgb(hsv), 'hatch': tv, 'lw': 0}
properties[level] = prop
return properties | Create the default properties of the mosaic given the data
first it will varies the color hue (first category) then the color
saturation (second category) and then the color value
(third category). If a fourth category is found, it will put
decoration on the rectangle. Does not manage more than four
level of categories | _create_default_properties | python | statsmodels/statsmodels | statsmodels/graphics/mosaicplot.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/graphics/mosaicplot.py | BSD-3-Clause |
def _normalize_data(data, index):
"""normalize the data to a dict with tuples of strings as keys
right now it works with:
0 - dictionary (or equivalent mappable)
1 - pandas.Series with simple or hierarchical indexes
2 - numpy.ndarrays
3 - everything that can be converted to a numpy array
4 - pandas.DataFrame (via the _normalize_dataframe function)
"""
# if data is a dataframe we need to take a completely new road
# before coming back here. Use the hasattr to avoid importing
# pandas explicitly
if hasattr(data, 'pivot') and hasattr(data, 'groupby'):
data = _normalize_dataframe(data, index)
index = None
# can it be used as a dictionary?
try:
items = list(data.items())
except AttributeError:
# ok, I cannot use the data as a dictionary
# Try to convert it to a numpy array, or die trying
data = np.asarray(data)
temp = {}
for idx in np.ndindex(data.shape):
name = tuple(i for i in idx)
temp[name] = data[idx]
data = temp
items = list(data.items())
# make all the keys a tuple, even if simple numbers
data = {_tuplify(k): v for k, v in items}
categories_levels = _categories_level(list(data.keys()))
# fill the void in the counting dictionary
indexes = product(*categories_levels)
contingency = {k: data.get(k, 0) for k in indexes}
data = contingency
# reorder the keys order according to the one specified by the user
# or if the index is None convert it into a simple list
# right now it does not do any check, but can be modified in the future
index = lrange(len(categories_levels)) if index is None else index
contingency = {}
for key, value in data.items():
new_key = tuple(key[i] for i in index)
contingency[new_key] = value
data = contingency
return data | normalize the data to a dict with tuples of strings as keys
right now it works with:
0 - dictionary (or equivalent mappable)
1 - pandas.Series with simple or hierarchical indexes
2 - numpy.ndarrays
3 - everything that can be converted to a numpy array
4 - pandas.DataFrame (via the _normalize_dataframe function) | _normalize_data | python | statsmodels/statsmodels | statsmodels/graphics/mosaicplot.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/graphics/mosaicplot.py | BSD-3-Clause |
def _normalize_dataframe(dataframe, index):
"""Take a pandas DataFrame and count the element present in the
given columns, return a hierarchical index on those columns
"""
#groupby the given keys, extract the same columns and count the element
# then collapse them with a mean
data = dataframe[index].dropna()
grouped = data.groupby(index, sort=False, observed=False)
counted = grouped[index].count()
averaged = counted.mean(axis=1)
# Fill empty missing with 0, see GH5639
averaged = averaged.fillna(0.0)
return averaged | Take a pandas DataFrame and count the element present in the
given columns, return a hierarchical index on those columns | _normalize_dataframe | python | statsmodels/statsmodels | statsmodels/graphics/mosaicplot.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/graphics/mosaicplot.py | BSD-3-Clause |
def _statistical_coloring(data):
"""evaluate colors from the indipendence properties of the matrix
It will encounter problem if one category has all zeros
"""
data = _normalize_data(data, None)
categories_levels = _categories_level(list(data.keys()))
Nlevels = len(categories_levels)
total = 1.0 * sum(v for v in data.values())
# count the proportion of observation
# for each level that has the given name
# at each level
levels_count = []
for level_idx in range(Nlevels):
proportion = {}
for level in categories_levels[level_idx]:
proportion[level] = 0.0
for key, value in data.items():
if level == key[level_idx]:
proportion[level] += value
proportion[level] /= total
levels_count.append(proportion)
# for each key I obtain the expected value
# and it's standard deviation from a binomial distribution
# under the hipothesys of independence
expected = {}
for key, value in data.items():
base = 1.0
for i, k in enumerate(key):
base *= levels_count[i][k]
expected[key] = base * total, np.sqrt(total * base * (1.0 - base))
# now we have the standard deviation of distance from the
# expected value for each tile. We create the colors from this
sigmas = {k: (data[k] - m) / s for k, (m, s) in expected.items()}
props = {}
for key, dev in sigmas.items():
red = 0.0 if dev < 0 else (dev / (1 + dev))
blue = 0.0 if dev > 0 else (dev / (-1 + dev))
green = (1.0 - red - blue) / 2.0
hatch = 'x' if dev > 2 else 'o' if dev < -2 else ''
props[key] = {'color': [red, green, blue], 'hatch': hatch}
return props | evaluate colors from the indipendence properties of the matrix
It will encounter problem if one category has all zeros | _statistical_coloring | python | statsmodels/statsmodels | statsmodels/graphics/mosaicplot.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/graphics/mosaicplot.py | BSD-3-Clause |
def _create_labels(rects, horizontal, ax, rotation):
"""find the position of the label for each value of each category
right now it supports only up to the four categories
ax: the axis on which the label should be applied
rotation: the rotation list for each side
"""
categories = _categories_level(list(rects.keys()))
if len(categories) > 4:
msg = ("maximum of 4 level supported for axes labeling... and 4"
"is already a lot of levels, are you sure you need them all?")
raise ValueError(msg)
labels = {}
#keep it fixed as will be used a lot of times
items = list(rects.items())
vertical = not horizontal
#get the axis ticks and labels locator to put the correct values!
ax2 = ax.twinx()
ax3 = ax.twiny()
#this is the order of execution for horizontal disposition
ticks_pos = [ax.set_xticks, ax.set_yticks, ax3.set_xticks, ax2.set_yticks]
ticks_lab = [ax.set_xticklabels, ax.set_yticklabels,
ax3.set_xticklabels, ax2.set_yticklabels]
#for the vertical one, rotate it by one
if vertical:
ticks_pos = ticks_pos[1:] + ticks_pos[:1]
ticks_lab = ticks_lab[1:] + ticks_lab[:1]
#clean them
for pos, lab in zip(ticks_pos, ticks_lab):
pos([])
lab([])
#for each level, for each value in the level, take the mean of all
#the sublevel that correspond to that partial key
for level_idx, level in enumerate(categories):
#this dictionary keep the labels only for this level
level_ticks = dict()
for value in level:
#to which level it should refer to get the preceding
#values of labels? it's rather a tricky question...
#this is dependent on the side. It's a very crude management
#but I couldn't think a more general way...
if horizontal:
if level_idx == 3:
index_select = [-1, -1, -1]
else:
index_select = [+0, -1, -1]
else:
if level_idx == 3:
index_select = [+0, -1, +0]
else:
index_select = [-1, -1, -1]
#now I create the base key name and append the current value
#It will search on all the rects to find the corresponding one
#and use them to evaluate the mean position
basekey = tuple(categories[i][index_select[i]]
for i in range(level_idx))
basekey = basekey + (value,)
subset = {k: v for k, v in items
if basekey == k[:level_idx + 1]}
#now I extract the center of all the tiles and make a weighted
#mean of all these center on the area of the tile
#this should give me the (more or less) correct position
#of the center of the category
vals = list(subset.values())
W = sum(w * h for (x, y, w, h) in vals)
x_lab = sum(_get_position(x, w, h, W) for (x, y, w, h) in vals)
y_lab = sum(_get_position(y, h, w, W) for (x, y, w, h) in vals)
#now base on the ordering, select which position to keep
#needs to be written in a more general form of 4 level are enough?
#should give also the horizontal and vertical alignment
side = (level_idx + vertical) % 4
level_ticks[value] = y_lab if side % 2 else x_lab
#now we add the labels of this level to the correct axis
ticks_pos[level_idx](list(level_ticks.values()))
ticks_lab[level_idx](list(level_ticks.keys()),
rotation=rotation[level_idx])
return labels | find the position of the label for each value of each category
right now it supports only up to the four categories
ax: the axis on which the label should be applied
rotation: the rotation list for each side | _create_labels | python | statsmodels/statsmodels | statsmodels/graphics/mosaicplot.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/graphics/mosaicplot.py | BSD-3-Clause |
def mosaic(data, index=None, ax=None, horizontal=True, gap=0.005,
properties=lambda key: None, labelizer=None,
title='', statistic=False, axes_label=True,
label_rotation=0.0):
"""Create a mosaic plot from a contingency table.
It allows to visualize multivariate categorical data in a rigorous
and informative way.
Parameters
----------
data : {dict, Series, ndarray, DataFrame}
The contingency table that contains the data.
Each category should contain a non-negative number
with a tuple as index. It expects that all the combination
of keys to be represents; if that is not true, will
automatically consider the missing values as 0. The order
of the keys will be the same as the one of insertion.
If a dict of a Series (or any other dict like object)
is used, it will take the keys as labels. If a
np.ndarray is provided, it will generate a simple
numerical labels.
index : list, optional
Gives the preferred order for the category ordering. If not specified
will default to the given order. It does not support named indexes
for hierarchical Series. If a DataFrame is provided, it expects
a list with the name of the columns.
ax : Axes, optional
The graph where display the mosaic. If not given, will
create a new figure
horizontal : bool, optional
The starting direction of the split (by default along
the horizontal axis)
gap : {float, sequence[float]}
The list of gaps to be applied on each subdivision.
If the length of the given array is less of the number
of subcategories (or if it's a single number) it will extend
it with exponentially decreasing gaps
properties : dict[str, callable], optional
A function that for each tile in the mosaic take the key
of the tile and returns the dictionary of properties
of the generated Rectangle, like color, hatch or similar.
A default properties set will be provided fot the keys whose
color has not been defined, and will use color variation to help
visually separates the various categories. It should return None
to indicate that it should use the default property for the tile.
A dictionary of the properties for each key can be passed,
and it will be internally converted to the correct function
labelizer : dict[str, callable], optional
A function that generate the text to display at the center of
each tile base on the key of that tile
title : str, optional
The title of the axis
statistic : bool, optional
If true will use a crude statistical model to give colors to the plot.
If the tile has a constraint that is more than 2 standard deviation
from the expected value under independence hypothesis, it will
go from green to red (for positive deviations, blue otherwise) and
will acquire an hatching when crosses the 3 sigma.
axes_label : bool, optional
Show the name of each value of each category
on the axis (default) or hide them.
label_rotation : {float, list[float]}
The rotation of the axis label (if present). If a list is given
each axis can have a different rotation
Returns
-------
fig : Figure
The figure containing the plot.
rects : dict
A dictionary that has the same keys of the original
dataset, that holds a reference to the coordinates of the
tile and the Rectangle that represent it.
References
----------
A Brief History of the Mosaic Display
Michael Friendly, York University, Psychology Department
Journal of Computational and Graphical Statistics, 2001
Mosaic Displays for Loglinear Models.
Michael Friendly, York University, Psychology Department
Proceedings of the Statistical Graphics Section, 1992, 61-68.
Mosaic displays for multi-way contingency tables.
Michael Friendly, York University, Psychology Department
Journal of the american statistical association
March 1994, Vol. 89, No. 425, Theory and Methods
Examples
--------
>>> import numpy as np
>>> import pandas as pd
>>> import matplotlib.pyplot as plt
>>> from statsmodels.graphics.mosaicplot import mosaic
The most simple use case is to take a dictionary and plot the result
>>> data = {'a': 10, 'b': 15, 'c': 16}
>>> mosaic(data, title='basic dictionary')
>>> plt.show()
A more useful example is given by a dictionary with multiple indices.
In this case we use a wider gap to a better visual separation of the
resulting plot
>>> data = {('a', 'b'): 1, ('a', 'c'): 2, ('d', 'b'): 3, ('d', 'c'): 4}
>>> mosaic(data, gap=0.05, title='complete dictionary')
>>> plt.show()
The same data can be given as a simple or hierarchical indexed Series
>>> rand = np.random.random
>>> from itertools import product
>>> tuples = list(product(['bar', 'baz', 'foo', 'qux'], ['one', 'two']))
>>> index = pd.MultiIndex.from_tuples(tuples, names=['first', 'second'])
>>> data = pd.Series(rand(8), index=index)
>>> mosaic(data, title='hierarchical index series')
>>> plt.show()
The third accepted data structure is the np array, for which a
very simple index will be created.
>>> rand = np.random.random
>>> data = 1+rand((2,2))
>>> mosaic(data, title='random non-labeled array')
>>> plt.show()
If you need to modify the labeling and the coloring you can give
a function tocreate the labels and one with the graphical properties
starting from the key tuple
>>> data = {'a': 10, 'b': 15, 'c': 16}
>>> props = lambda key: {'color': 'r' if 'a' in key else 'gray'}
>>> labelizer = lambda k: {('a',): 'first', ('b',): 'second',
... ('c',): 'third'}[k]
>>> mosaic(data, title='colored dictionary', properties=props,
... labelizer=labelizer)
>>> plt.show()
Using a DataFrame as source, specifying the name of the columns of interest
>>> gender = ['male', 'male', 'male', 'female', 'female', 'female']
>>> pet = ['cat', 'dog', 'dog', 'cat', 'dog', 'cat']
>>> data = pd.DataFrame({'gender': gender, 'pet': pet})
>>> mosaic(data, ['pet', 'gender'], title='DataFrame as Source')
>>> plt.show()
.. plot :: plots/graphics_mosaicplot_mosaic.py
"""
if isinstance(data, DataFrame) and index is None:
raise ValueError("You must pass an index if data is a DataFrame."
" See examples.")
from matplotlib.patches import Rectangle
#from pylab import Rectangle
fig, ax = utils.create_mpl_ax(ax)
# normalize the data to a dict with tuple of strings as keys
data = _normalize_data(data, index)
# split the graph into different areas
rects = _hierarchical_split(data, horizontal=horizontal, gap=gap)
# if there is no specified way to create the labels
# create a default one
if labelizer is None:
def labelizer(k):
return "\n".join(k)
if statistic:
default_props = _statistical_coloring(data)
else:
default_props = _create_default_properties(data)
if isinstance(properties, dict):
color_dict = properties
def properties(key):
return color_dict.get(key, None)
for k, v in rects.items():
# create each rectangle and put a label on it
x, y, w, h = v
conf = properties(k)
props = conf if conf else default_props[k]
text = labelizer(k)
Rect = Rectangle((x, y), w, h, label=text, **props)
ax.add_patch(Rect)
ax.text(x + w / 2, y + h / 2, text, ha='center',
va='center', size='smaller')
#creating the labels on the axis
#o clearing it
if axes_label:
if np.iterable(label_rotation):
rotation = label_rotation
else:
rotation = [label_rotation] * 4
_create_labels(rects, horizontal, ax, rotation)
else:
ax.set_xticks([])
ax.set_xticklabels([])
ax.set_yticks([])
ax.set_yticklabels([])
ax.set_title(title)
return fig, rects | Create a mosaic plot from a contingency table.
It allows to visualize multivariate categorical data in a rigorous
and informative way.
Parameters
----------
data : {dict, Series, ndarray, DataFrame}
The contingency table that contains the data.
Each category should contain a non-negative number
with a tuple as index. It expects that all the combination
of keys to be represents; if that is not true, will
automatically consider the missing values as 0. The order
of the keys will be the same as the one of insertion.
If a dict of a Series (or any other dict like object)
is used, it will take the keys as labels. If a
np.ndarray is provided, it will generate a simple
numerical labels.
index : list, optional
Gives the preferred order for the category ordering. If not specified
will default to the given order. It does not support named indexes
for hierarchical Series. If a DataFrame is provided, it expects
a list with the name of the columns.
ax : Axes, optional
The graph where display the mosaic. If not given, will
create a new figure
horizontal : bool, optional
The starting direction of the split (by default along
the horizontal axis)
gap : {float, sequence[float]}
The list of gaps to be applied on each subdivision.
If the length of the given array is less of the number
of subcategories (or if it's a single number) it will extend
it with exponentially decreasing gaps
properties : dict[str, callable], optional
A function that for each tile in the mosaic take the key
of the tile and returns the dictionary of properties
of the generated Rectangle, like color, hatch or similar.
A default properties set will be provided fot the keys whose
color has not been defined, and will use color variation to help
visually separates the various categories. It should return None
to indicate that it should use the default property for the tile.
A dictionary of the properties for each key can be passed,
and it will be internally converted to the correct function
labelizer : dict[str, callable], optional
A function that generate the text to display at the center of
each tile base on the key of that tile
title : str, optional
The title of the axis
statistic : bool, optional
If true will use a crude statistical model to give colors to the plot.
If the tile has a constraint that is more than 2 standard deviation
from the expected value under independence hypothesis, it will
go from green to red (for positive deviations, blue otherwise) and
will acquire an hatching when crosses the 3 sigma.
axes_label : bool, optional
Show the name of each value of each category
on the axis (default) or hide them.
label_rotation : {float, list[float]}
The rotation of the axis label (if present). If a list is given
each axis can have a different rotation
Returns
-------
fig : Figure
The figure containing the plot.
rects : dict
A dictionary that has the same keys of the original
dataset, that holds a reference to the coordinates of the
tile and the Rectangle that represent it.
References
----------
A Brief History of the Mosaic Display
Michael Friendly, York University, Psychology Department
Journal of Computational and Graphical Statistics, 2001
Mosaic Displays for Loglinear Models.
Michael Friendly, York University, Psychology Department
Proceedings of the Statistical Graphics Section, 1992, 61-68.
Mosaic displays for multi-way contingency tables.
Michael Friendly, York University, Psychology Department
Journal of the american statistical association
March 1994, Vol. 89, No. 425, Theory and Methods
Examples
--------
>>> import numpy as np
>>> import pandas as pd
>>> import matplotlib.pyplot as plt
>>> from statsmodels.graphics.mosaicplot import mosaic
The most simple use case is to take a dictionary and plot the result
>>> data = {'a': 10, 'b': 15, 'c': 16}
>>> mosaic(data, title='basic dictionary')
>>> plt.show()
A more useful example is given by a dictionary with multiple indices.
In this case we use a wider gap to a better visual separation of the
resulting plot
>>> data = {('a', 'b'): 1, ('a', 'c'): 2, ('d', 'b'): 3, ('d', 'c'): 4}
>>> mosaic(data, gap=0.05, title='complete dictionary')
>>> plt.show()
The same data can be given as a simple or hierarchical indexed Series
>>> rand = np.random.random
>>> from itertools import product
>>> tuples = list(product(['bar', 'baz', 'foo', 'qux'], ['one', 'two']))
>>> index = pd.MultiIndex.from_tuples(tuples, names=['first', 'second'])
>>> data = pd.Series(rand(8), index=index)
>>> mosaic(data, title='hierarchical index series')
>>> plt.show()
The third accepted data structure is the np array, for which a
very simple index will be created.
>>> rand = np.random.random
>>> data = 1+rand((2,2))
>>> mosaic(data, title='random non-labeled array')
>>> plt.show()
If you need to modify the labeling and the coloring you can give
a function tocreate the labels and one with the graphical properties
starting from the key tuple
>>> data = {'a': 10, 'b': 15, 'c': 16}
>>> props = lambda key: {'color': 'r' if 'a' in key else 'gray'}
>>> labelizer = lambda k: {('a',): 'first', ('b',): 'second',
... ('c',): 'third'}[k]
>>> mosaic(data, title='colored dictionary', properties=props,
... labelizer=labelizer)
>>> plt.show()
Using a DataFrame as source, specifying the name of the columns of interest
>>> gender = ['male', 'male', 'male', 'female', 'female', 'female']
>>> pet = ['cat', 'dog', 'dog', 'cat', 'dog', 'cat']
>>> data = pd.DataFrame({'gender': gender, 'pet': pet})
>>> mosaic(data, ['pet', 'gender'], title='DataFrame as Source')
>>> plt.show()
.. plot :: plots/graphics_mosaicplot_mosaic.py | mosaic | python | statsmodels/statsmodels | statsmodels/graphics/mosaicplot.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/graphics/mosaicplot.py | BSD-3-Clause |
def mean_diff_plot(
m1,
m2,
sd_limit=1.96,
ax=None,
scatter_kwds=None,
mean_line_kwds=None,
limit_lines_kwds=None,
):
"""
Construct a Tukey/Bland-Altman Mean Difference Plot.
Tukey's Mean Difference Plot (also known as a Bland-Altman plot) is a
graphical method to analyze the differences between two methods of
measurement. The mean of the measures is plotted against their difference.
For more information see
https://en.wikipedia.org/wiki/Bland-Altman_plot
Parameters
----------
m1 : array_like
A 1-d array.
m2 : array_like
A 1-d array.
sd_limit : float
The limit of agreements expressed in terms of the standard deviation of
the differences. If `md` is the mean of the differences, and `sd` is
the standard deviation of those differences, then the limits of
agreement that will be plotted are md +/- sd_limit * sd.
The default of 1.96 will produce 95% confidence intervals for the means
of the differences. If sd_limit = 0, no limits will be plotted, and
the ylimit of the plot defaults to 3 standard deviations on either
side of the mean.
ax : AxesSubplot
If `ax` is None, then a figure is created. If an axis instance is
given, the mean difference plot is drawn on the axis.
scatter_kwds : dict
Options to to style the scatter plot. Accepts any keywords for the
matplotlib Axes.scatter plotting method
mean_line_kwds : dict
Options to to style the scatter plot. Accepts any keywords for the
matplotlib Axes.axhline plotting method
limit_lines_kwds : dict
Options to to style the scatter plot. Accepts any keywords for the
matplotlib Axes.axhline plotting method
Returns
-------
Figure
If `ax` is None, the created figure. Otherwise the figure to which
`ax` is connected.
References
----------
Bland JM, Altman DG (1986). "Statistical methods for assessing agreement
between two methods of clinical measurement"
Examples
--------
Load relevant libraries.
>>> import statsmodels.api as sm
>>> import numpy as np
>>> import matplotlib.pyplot as plt
Making a mean difference plot.
>>> # Seed the random number generator.
>>> # This ensures that the results below are reproducible.
>>> np.random.seed(9999)
>>> m1 = np.random.random(20)
>>> m2 = np.random.random(20)
>>> f, ax = plt.subplots(1, figsize = (8,5))
>>> sm.graphics.mean_diff_plot(m1, m2, ax = ax)
>>> plt.show()
.. plot:: plots/graphics-mean_diff_plot.py
"""
fig, ax = utils.create_mpl_ax(ax)
if len(m1) != len(m2):
raise ValueError("m1 does not have the same length as m2.")
if sd_limit < 0:
raise ValueError(f"sd_limit ({sd_limit}) is less than 0.")
means = np.mean([m1, m2], axis=0)
diffs = m1 - m2
mean_diff = np.mean(diffs)
std_diff = np.std(diffs, axis=0)
scatter_kwds = scatter_kwds or {}
if "s" not in scatter_kwds:
scatter_kwds["s"] = 20
mean_line_kwds = mean_line_kwds or {}
limit_lines_kwds = limit_lines_kwds or {}
for kwds in [mean_line_kwds, limit_lines_kwds]:
if "color" not in kwds:
kwds["color"] = "gray"
if "linewidth" not in kwds:
kwds["linewidth"] = 1
if "linestyle" not in mean_line_kwds:
kwds["linestyle"] = "--"
if "linestyle" not in limit_lines_kwds:
kwds["linestyle"] = ":"
ax.scatter(means, diffs, **scatter_kwds) # Plot the means against the diffs.
ax.axhline(mean_diff, **mean_line_kwds) # draw mean line.
# Annotate mean line with mean difference.
ax.annotate(
f"mean diff:\n{mean_diff:0.3g}",
xy=(0.99, 0.5),
horizontalalignment="right",
verticalalignment="center",
fontsize=14,
xycoords="axes fraction",
)
if sd_limit > 0:
half_ylim = (1.5 * sd_limit) * std_diff
ax.set_ylim(mean_diff - half_ylim, mean_diff + half_ylim)
limit_of_agreement = sd_limit * std_diff
lower = mean_diff - limit_of_agreement
upper = mean_diff + limit_of_agreement
for j, lim in enumerate([lower, upper]):
ax.axhline(lim, **limit_lines_kwds)
ax.annotate(
f"-{sd_limit} SD: {lower:0.2g}",
xy=(0.99, 0.07),
horizontalalignment="right",
verticalalignment="bottom",
fontsize=14,
xycoords="axes fraction",
)
ax.annotate(
f"+{sd_limit} SD: {upper:0.2g}",
xy=(0.99, 0.92),
horizontalalignment="right",
fontsize=14,
xycoords="axes fraction",
)
elif sd_limit == 0:
half_ylim = 3 * std_diff
ax.set_ylim(mean_diff - half_ylim, mean_diff + half_ylim)
ax.set_ylabel("Difference", fontsize=15)
ax.set_xlabel("Means", fontsize=15)
ax.tick_params(labelsize=13)
fig.tight_layout()
return fig | Construct a Tukey/Bland-Altman Mean Difference Plot.
Tukey's Mean Difference Plot (also known as a Bland-Altman plot) is a
graphical method to analyze the differences between two methods of
measurement. The mean of the measures is plotted against their difference.
For more information see
https://en.wikipedia.org/wiki/Bland-Altman_plot
Parameters
----------
m1 : array_like
A 1-d array.
m2 : array_like
A 1-d array.
sd_limit : float
The limit of agreements expressed in terms of the standard deviation of
the differences. If `md` is the mean of the differences, and `sd` is
the standard deviation of those differences, then the limits of
agreement that will be plotted are md +/- sd_limit * sd.
The default of 1.96 will produce 95% confidence intervals for the means
of the differences. If sd_limit = 0, no limits will be plotted, and
the ylimit of the plot defaults to 3 standard deviations on either
side of the mean.
ax : AxesSubplot
If `ax` is None, then a figure is created. If an axis instance is
given, the mean difference plot is drawn on the axis.
scatter_kwds : dict
Options to to style the scatter plot. Accepts any keywords for the
matplotlib Axes.scatter plotting method
mean_line_kwds : dict
Options to to style the scatter plot. Accepts any keywords for the
matplotlib Axes.axhline plotting method
limit_lines_kwds : dict
Options to to style the scatter plot. Accepts any keywords for the
matplotlib Axes.axhline plotting method
Returns
-------
Figure
If `ax` is None, the created figure. Otherwise the figure to which
`ax` is connected.
References
----------
Bland JM, Altman DG (1986). "Statistical methods for assessing agreement
between two methods of clinical measurement"
Examples
--------
Load relevant libraries.
>>> import statsmodels.api as sm
>>> import numpy as np
>>> import matplotlib.pyplot as plt
Making a mean difference plot.
>>> # Seed the random number generator.
>>> # This ensures that the results below are reproducible.
>>> np.random.seed(9999)
>>> m1 = np.random.random(20)
>>> m2 = np.random.random(20)
>>> f, ax = plt.subplots(1, figsize = (8,5))
>>> sm.graphics.mean_diff_plot(m1, m2, ax = ax)
>>> plt.show()
.. plot:: plots/graphics-mean_diff_plot.py | mean_diff_plot | python | statsmodels/statsmodels | statsmodels/graphics/agreement.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/graphics/agreement.py | BSD-3-Clause |
def theoretical_percentiles(self):
"""Theoretical percentiles"""
return plotting_pos(self.nobs, self.a) | Theoretical percentiles | theoretical_percentiles | python | statsmodels/statsmodels | statsmodels/graphics/gofplots.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/graphics/gofplots.py | BSD-3-Clause |
def theoretical_quantiles(self):
"""Theoretical quantiles"""
try:
return self.dist.ppf(self.theoretical_percentiles)
except TypeError:
msg = f"{self.dist.name} requires more parameters to compute ppf"
raise TypeError(msg)
except Exception as exc:
msg = f"failed to compute the ppf of {self.dist.name}"
raise type(exc)(msg) | Theoretical quantiles | theoretical_quantiles | python | statsmodels/statsmodels | statsmodels/graphics/gofplots.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/graphics/gofplots.py | BSD-3-Clause |
def sorted_data(self):
"""sorted data"""
sorted_data = np.sort(np.array(self.data))
sorted_data.sort()
return sorted_data | sorted data | sorted_data | python | statsmodels/statsmodels | statsmodels/graphics/gofplots.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/graphics/gofplots.py | BSD-3-Clause |
def sample_quantiles(self):
"""sample quantiles"""
if self.fit and self.loc != 0 and self.scale != 1:
return (self.sorted_data - self.loc) / self.scale
else:
return self.sorted_data | sample quantiles | sample_quantiles | python | statsmodels/statsmodels | statsmodels/graphics/gofplots.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/graphics/gofplots.py | BSD-3-Clause |
def sample_percentiles(self):
"""Sample percentiles"""
_check_for(self.dist, "cdf")
if self._is_frozen:
return self.dist.cdf(self.sorted_data)
quantiles = (self.sorted_data - self.fit_params[-2]) / self.fit_params[-1]
return self.dist.cdf(quantiles) | Sample percentiles | sample_percentiles | python | statsmodels/statsmodels | statsmodels/graphics/gofplots.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/graphics/gofplots.py | BSD-3-Clause |
def ppplot(
self,
xlabel=None,
ylabel=None,
line=None,
other=None,
ax=None,
**plotkwargs,
):
"""
Plot of the percentiles of x versus the percentiles of a distribution.
Parameters
----------
xlabel : str or None, optional
User-provided labels for the x-axis. If None (default),
other values are used depending on the status of the kwarg `other`.
ylabel : str or None, optional
User-provided labels for the y-axis. If None (default),
other values are used depending on the status of the kwarg `other`.
line : {None, "45", "s", "r", q"}, optional
Options for the reference line to which the data is compared:
- "45": 45-degree line
- "s": standardized line, the expected order statistics are
scaled by the standard deviation of the given sample and have
the mean added to them
- "r": A regression line is fit
- "q": A line is fit through the quartiles.
- None: by default no reference line is added to the plot.
other : ProbPlot, array_like, or None, optional
If provided, ECDF(x) will be plotted against p(x) where x are
sorted samples from `self`. ECDF is an empirical cumulative
distribution function estimated from `other` and
p(x) = 0.5/n, 1.5/n, ..., (n-0.5)/n where n is the number of
samples in `self`. If an array-object is provided, it will be
turned into a `ProbPlot` instance default parameters. If not
provided (default), `self.dist(x)` is be plotted against p(x).
ax : AxesSubplot, optional
If given, this subplot is used to plot in instead of a new figure
being created.
**plotkwargs
Additional arguments to be passed to the `plot` command.
Returns
-------
Figure
If `ax` is None, the created figure. Otherwise the figure to which
`ax` is connected.
"""
if other is not None:
check_other = isinstance(other, ProbPlot)
if not check_other:
other = ProbPlot(other)
p_x = self.theoretical_percentiles
ecdf_x = ECDF(other.sample_quantiles)(self.sample_quantiles)
fig, ax = _do_plot(p_x, ecdf_x, self.dist, ax=ax, line=line, **plotkwargs)
if xlabel is None:
xlabel = "Probabilities of 2nd Sample"
if ylabel is None:
ylabel = "Probabilities of 1st Sample"
else:
fig, ax = _do_plot(
self.theoretical_percentiles,
self.sample_percentiles,
self.dist,
ax=ax,
line=line,
**plotkwargs,
)
if xlabel is None:
xlabel = "Theoretical Probabilities"
if ylabel is None:
ylabel = "Sample Probabilities"
ax.set_xlabel(xlabel)
ax.set_ylabel(ylabel)
ax.set_xlim([0.0, 1.0])
ax.set_ylim([0.0, 1.0])
return fig | Plot of the percentiles of x versus the percentiles of a distribution.
Parameters
----------
xlabel : str or None, optional
User-provided labels for the x-axis. If None (default),
other values are used depending on the status of the kwarg `other`.
ylabel : str or None, optional
User-provided labels for the y-axis. If None (default),
other values are used depending on the status of the kwarg `other`.
line : {None, "45", "s", "r", q"}, optional
Options for the reference line to which the data is compared:
- "45": 45-degree line
- "s": standardized line, the expected order statistics are
scaled by the standard deviation of the given sample and have
the mean added to them
- "r": A regression line is fit
- "q": A line is fit through the quartiles.
- None: by default no reference line is added to the plot.
other : ProbPlot, array_like, or None, optional
If provided, ECDF(x) will be plotted against p(x) where x are
sorted samples from `self`. ECDF is an empirical cumulative
distribution function estimated from `other` and
p(x) = 0.5/n, 1.5/n, ..., (n-0.5)/n where n is the number of
samples in `self`. If an array-object is provided, it will be
turned into a `ProbPlot` instance default parameters. If not
provided (default), `self.dist(x)` is be plotted against p(x).
ax : AxesSubplot, optional
If given, this subplot is used to plot in instead of a new figure
being created.
**plotkwargs
Additional arguments to be passed to the `plot` command.
Returns
-------
Figure
If `ax` is None, the created figure. Otherwise the figure to which
`ax` is connected. | ppplot | python | statsmodels/statsmodels | statsmodels/graphics/gofplots.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/graphics/gofplots.py | BSD-3-Clause |
def qqplot(
self,
xlabel=None,
ylabel=None,
line=None,
other=None,
ax=None,
swap: bool = False,
**plotkwargs,
):
"""
Plot of the quantiles of x versus the quantiles/ppf of a distribution.
Can also be used to plot against the quantiles of another `ProbPlot`
instance.
Parameters
----------
xlabel : {None, str}
User-provided labels for the x-axis. If None (default),
other values are used depending on the status of the kwarg `other`.
ylabel : {None, str}
User-provided labels for the y-axis. If None (default),
other values are used depending on the status of the kwarg `other`.
line : {None, "45", "s", "r", q"}, optional
Options for the reference line to which the data is compared:
- "45" - 45-degree line
- "s" - standardized line, the expected order statistics are scaled
by the standard deviation of the given sample and have the mean
added to them
- "r" - A regression line is fit
- "q" - A line is fit through the quartiles.
- None - by default no reference line is added to the plot.
other : {ProbPlot, array_like, None}, optional
If provided, the sample quantiles of this `ProbPlot` instance are
plotted against the sample quantiles of the `other` `ProbPlot`
instance. Sample size of `other` must be equal or larger than
this `ProbPlot` instance. If the sample size is larger, sample
quantiles of `other` will be interpolated to match the sample size
of this `ProbPlot` instance. If an array-like object is provided,
it will be turned into a `ProbPlot` instance using default
parameters. If not provided (default), the theoretical quantiles
are used.
ax : AxesSubplot, optional
If given, this subplot is used to plot in instead of a new figure
being created.
swap : bool, optional
Flag indicating to swap the x and y labels.
**plotkwargs
Additional arguments to be passed to the `plot` command.
Returns
-------
Figure
If `ax` is None, the created figure. Otherwise the figure to which
`ax` is connected.
"""
if other is not None:
check_other = isinstance(other, ProbPlot)
if not check_other:
other = ProbPlot(other)
s_self = self.sample_quantiles
s_other = other.sample_quantiles
if len(s_self) > len(s_other):
raise ValueError(
"Sample size of `other` must be equal or "
+ "larger than this `ProbPlot` instance"
)
elif len(s_self) < len(s_other):
# Use quantiles of the smaller set and interpolate quantiles of
# the larger data set
p = plotting_pos(self.nobs, self.a)
s_other = stats.mstats.mquantiles(s_other, p)
fig, ax = _do_plot(
s_other, s_self, self.dist, ax=ax, line=line, **plotkwargs
)
if xlabel is None:
xlabel = "Quantiles of 2nd Sample"
if ylabel is None:
ylabel = "Quantiles of 1st Sample"
if swap:
xlabel, ylabel = ylabel, xlabel
else:
fig, ax = _do_plot(
self.theoretical_quantiles,
self.sample_quantiles,
self.dist,
ax=ax,
line=line,
**plotkwargs,
)
if xlabel is None:
xlabel = "Theoretical Quantiles"
if ylabel is None:
ylabel = "Sample Quantiles"
ax.set_xlabel(xlabel)
ax.set_ylabel(ylabel)
return fig | Plot of the quantiles of x versus the quantiles/ppf of a distribution.
Can also be used to plot against the quantiles of another `ProbPlot`
instance.
Parameters
----------
xlabel : {None, str}
User-provided labels for the x-axis. If None (default),
other values are used depending on the status of the kwarg `other`.
ylabel : {None, str}
User-provided labels for the y-axis. If None (default),
other values are used depending on the status of the kwarg `other`.
line : {None, "45", "s", "r", q"}, optional
Options for the reference line to which the data is compared:
- "45" - 45-degree line
- "s" - standardized line, the expected order statistics are scaled
by the standard deviation of the given sample and have the mean
added to them
- "r" - A regression line is fit
- "q" - A line is fit through the quartiles.
- None - by default no reference line is added to the plot.
other : {ProbPlot, array_like, None}, optional
If provided, the sample quantiles of this `ProbPlot` instance are
plotted against the sample quantiles of the `other` `ProbPlot`
instance. Sample size of `other` must be equal or larger than
this `ProbPlot` instance. If the sample size is larger, sample
quantiles of `other` will be interpolated to match the sample size
of this `ProbPlot` instance. If an array-like object is provided,
it will be turned into a `ProbPlot` instance using default
parameters. If not provided (default), the theoretical quantiles
are used.
ax : AxesSubplot, optional
If given, this subplot is used to plot in instead of a new figure
being created.
swap : bool, optional
Flag indicating to swap the x and y labels.
**plotkwargs
Additional arguments to be passed to the `plot` command.
Returns
-------
Figure
If `ax` is None, the created figure. Otherwise the figure to which
`ax` is connected. | qqplot | python | statsmodels/statsmodels | statsmodels/graphics/gofplots.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/graphics/gofplots.py | BSD-3-Clause |
def probplot(
self,
xlabel=None,
ylabel=None,
line=None,
exceed=False,
ax=None,
**plotkwargs,
):
"""
Plot of unscaled quantiles of x against the prob of a distribution.
The x-axis is scaled linearly with the quantiles, but the probabilities
are used to label the axis.
Parameters
----------
xlabel : {None, str}, optional
User-provided labels for the x-axis. If None (default),
other values are used depending on the status of the kwarg `other`.
ylabel : {None, str}, optional
User-provided labels for the y-axis. If None (default),
other values are used depending on the status of the kwarg `other`.
line : {None, "45", "s", "r", q"}, optional
Options for the reference line to which the data is compared:
- "45" - 45-degree line
- "s" - standardized line, the expected order statistics are scaled
by the standard deviation of the given sample and have the mean
added to them
- "r" - A regression line is fit
- "q" - A line is fit through the quartiles.
- None - by default no reference line is added to the plot.
exceed : bool, optional
If False (default) the raw sample quantiles are plotted against
the theoretical quantiles, show the probability that a sample will
not exceed a given value. If True, the theoretical quantiles are
flipped such that the figure displays the probability that a
sample will exceed a given value.
ax : AxesSubplot, optional
If given, this subplot is used to plot in instead of a new figure
being created.
**plotkwargs
Additional arguments to be passed to the `plot` command.
Returns
-------
Figure
If `ax` is None, the created figure. Otherwise the figure to which
`ax` is connected.
"""
if exceed:
fig, ax = _do_plot(
self.theoretical_quantiles[::-1],
self.sorted_data,
self.dist,
ax=ax,
line=line,
**plotkwargs,
)
if xlabel is None:
xlabel = "Probability of Exceedance (%)"
else:
fig, ax = _do_plot(
self.theoretical_quantiles,
self.sorted_data,
self.dist,
ax=ax,
line=line,
**plotkwargs,
)
if xlabel is None:
xlabel = "Non-exceedance Probability (%)"
if ylabel is None:
ylabel = "Sample Quantiles"
ax.set_xlabel(xlabel)
ax.set_ylabel(ylabel)
_fmt_probplot_axis(ax, self.dist, self.nobs)
return fig | Plot of unscaled quantiles of x against the prob of a distribution.
The x-axis is scaled linearly with the quantiles, but the probabilities
are used to label the axis.
Parameters
----------
xlabel : {None, str}, optional
User-provided labels for the x-axis. If None (default),
other values are used depending on the status of the kwarg `other`.
ylabel : {None, str}, optional
User-provided labels for the y-axis. If None (default),
other values are used depending on the status of the kwarg `other`.
line : {None, "45", "s", "r", q"}, optional
Options for the reference line to which the data is compared:
- "45" - 45-degree line
- "s" - standardized line, the expected order statistics are scaled
by the standard deviation of the given sample and have the mean
added to them
- "r" - A regression line is fit
- "q" - A line is fit through the quartiles.
- None - by default no reference line is added to the plot.
exceed : bool, optional
If False (default) the raw sample quantiles are plotted against
the theoretical quantiles, show the probability that a sample will
not exceed a given value. If True, the theoretical quantiles are
flipped such that the figure displays the probability that a
sample will exceed a given value.
ax : AxesSubplot, optional
If given, this subplot is used to plot in instead of a new figure
being created.
**plotkwargs
Additional arguments to be passed to the `plot` command.
Returns
-------
Figure
If `ax` is None, the created figure. Otherwise the figure to which
`ax` is connected. | probplot | python | statsmodels/statsmodels | statsmodels/graphics/gofplots.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/graphics/gofplots.py | BSD-3-Clause |
def qqplot(
data,
dist=stats.norm,
distargs=(),
a=0,
loc=0,
scale=1,
fit=False,
line=None,
ax=None,
**plotkwargs,
):
"""
Q-Q plot of the quantiles of x versus the quantiles/ppf of a distribution.
Can take arguments specifying the parameters for dist or fit them
automatically. (See fit under Parameters.)
Parameters
----------
data : array_like
A 1d data array.
dist : callable
Comparison distribution. The default is
scipy.stats.distributions.norm (a standard normal).
distargs : tuple
A tuple of arguments passed to dist to specify it fully
so dist.ppf may be called.
a : float
Offset for the plotting position of an expected order statistic, for
example. The plotting positions are given by (i - a)/(nobs - 2*a + 1)
for i in range(0,nobs+1)
loc : float
Location parameter for dist
scale : float
Scale parameter for dist
fit : bool
If fit is false, loc, scale, and distargs are passed to the
distribution. If fit is True then the parameters for dist
are fit automatically using dist.fit. The quantiles are formed
from the standardized data, after subtracting the fitted loc
and dividing by the fitted scale.
line : {None, "45", "s", "r", "q"}
Options for the reference line to which the data is compared:
- "45" - 45-degree line
- "s" - standardized line, the expected order statistics are scaled
by the standard deviation of the given sample and have the mean
added to them
- "r" - A regression line is fit
- "q" - A line is fit through the quartiles.
- None - by default no reference line is added to the plot.
ax : AxesSubplot, optional
If given, this subplot is used to plot in instead of a new figure being
created.
**plotkwargs
Additional matplotlib arguments to be passed to the `plot` command.
Returns
-------
Figure
If `ax` is None, the created figure. Otherwise the figure to which
`ax` is connected.
See Also
--------
scipy.stats.probplot
Notes
-----
Depends on matplotlib. If `fit` is True then the parameters are fit using
the distribution's fit() method.
Examples
--------
>>> import statsmodels.api as sm
>>> from matplotlib import pyplot as plt
>>> data = sm.datasets.longley.load()
>>> exog = sm.add_constant(data.exog)
>>> mod_fit = sm.OLS(data.endog, exog).fit()
>>> res = mod_fit.resid # residuals
>>> fig = sm.qqplot(res)
>>> plt.show()
qqplot of the residuals against quantiles of t-distribution with 4 degrees
of freedom:
>>> import scipy.stats as stats
>>> fig = sm.qqplot(res, stats.t, distargs=(4,))
>>> plt.show()
qqplot against same as above, but with mean 3 and std 10:
>>> fig = sm.qqplot(res, stats.t, distargs=(4,), loc=3, scale=10)
>>> plt.show()
Automatically determine parameters for t distribution including the
loc and scale:
>>> fig = sm.qqplot(res, stats.t, fit=True, line="45")
>>> plt.show()
The following plot displays some options, follow the link to see the code.
.. plot:: plots/graphics_gofplots_qqplot.py
"""
probplot = ProbPlot(
data, dist=dist, distargs=distargs, fit=fit, a=a, loc=loc, scale=scale
)
fig = probplot.qqplot(ax=ax, line=line, **plotkwargs)
return fig | Q-Q plot of the quantiles of x versus the quantiles/ppf of a distribution.
Can take arguments specifying the parameters for dist or fit them
automatically. (See fit under Parameters.)
Parameters
----------
data : array_like
A 1d data array.
dist : callable
Comparison distribution. The default is
scipy.stats.distributions.norm (a standard normal).
distargs : tuple
A tuple of arguments passed to dist to specify it fully
so dist.ppf may be called.
a : float
Offset for the plotting position of an expected order statistic, for
example. The plotting positions are given by (i - a)/(nobs - 2*a + 1)
for i in range(0,nobs+1)
loc : float
Location parameter for dist
scale : float
Scale parameter for dist
fit : bool
If fit is false, loc, scale, and distargs are passed to the
distribution. If fit is True then the parameters for dist
are fit automatically using dist.fit. The quantiles are formed
from the standardized data, after subtracting the fitted loc
and dividing by the fitted scale.
line : {None, "45", "s", "r", "q"}
Options for the reference line to which the data is compared:
- "45" - 45-degree line
- "s" - standardized line, the expected order statistics are scaled
by the standard deviation of the given sample and have the mean
added to them
- "r" - A regression line is fit
- "q" - A line is fit through the quartiles.
- None - by default no reference line is added to the plot.
ax : AxesSubplot, optional
If given, this subplot is used to plot in instead of a new figure being
created.
**plotkwargs
Additional matplotlib arguments to be passed to the `plot` command.
Returns
-------
Figure
If `ax` is None, the created figure. Otherwise the figure to which
`ax` is connected.
See Also
--------
scipy.stats.probplot
Notes
-----
Depends on matplotlib. If `fit` is True then the parameters are fit using
the distribution's fit() method.
Examples
--------
>>> import statsmodels.api as sm
>>> from matplotlib import pyplot as plt
>>> data = sm.datasets.longley.load()
>>> exog = sm.add_constant(data.exog)
>>> mod_fit = sm.OLS(data.endog, exog).fit()
>>> res = mod_fit.resid # residuals
>>> fig = sm.qqplot(res)
>>> plt.show()
qqplot of the residuals against quantiles of t-distribution with 4 degrees
of freedom:
>>> import scipy.stats as stats
>>> fig = sm.qqplot(res, stats.t, distargs=(4,))
>>> plt.show()
qqplot against same as above, but with mean 3 and std 10:
>>> fig = sm.qqplot(res, stats.t, distargs=(4,), loc=3, scale=10)
>>> plt.show()
Automatically determine parameters for t distribution including the
loc and scale:
>>> fig = sm.qqplot(res, stats.t, fit=True, line="45")
>>> plt.show()
The following plot displays some options, follow the link to see the code.
.. plot:: plots/graphics_gofplots_qqplot.py | qqplot | python | statsmodels/statsmodels | statsmodels/graphics/gofplots.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/graphics/gofplots.py | BSD-3-Clause |
def qqplot_2samples(data1, data2, xlabel=None, ylabel=None, line=None, ax=None):
"""
Q-Q Plot of two samples' quantiles.
Can take either two `ProbPlot` instances or two array-like objects. In the
case of the latter, both inputs will be converted to `ProbPlot` instances
using only the default values - so use `ProbPlot` instances if
finer-grained control of the quantile computations is required.
Parameters
----------
data1 : {array_like, ProbPlot}
Data to plot along x axis. If the sample sizes are unequal, the longer
series is always plotted along the x-axis.
data2 : {array_like, ProbPlot}
Data to plot along y axis. Does not need to have the same number of
observations as data 1. If the sample sizes are unequal, the longer
series is always plotted along the x-axis.
xlabel : {None, str}
User-provided labels for the x-axis. If None (default),
other values are used.
ylabel : {None, str}
User-provided labels for the y-axis. If None (default),
other values are used.
line : {None, "45", "s", "r", q"}
Options for the reference line to which the data is compared:
- "45" - 45-degree line
- "s" - standardized line, the expected order statistics are scaled
by the standard deviation of the given sample and have the mean
added to them
- "r" - A regression line is fit
- "q" - A line is fit through the quartiles.
- None - by default no reference line is added to the plot.
ax : AxesSubplot, optional
If given, this subplot is used to plot in instead of a new figure being
created.
Returns
-------
Figure
If `ax` is None, the created figure. Otherwise the figure to which
`ax` is connected.
See Also
--------
scipy.stats.probplot
Notes
-----
1) Depends on matplotlib.
2) If `data1` and `data2` are not `ProbPlot` instances, instances will be
created using the default parameters. Therefore, it is recommended to use
`ProbPlot` instance if fine-grained control is needed in the computation
of the quantiles.
Examples
--------
>>> import statsmodels.api as sm
>>> import numpy as np
>>> import matplotlib.pyplot as plt
>>> from statsmodels.graphics.gofplots import qqplot_2samples
>>> x = np.random.normal(loc=8.5, scale=2.5, size=37)
>>> y = np.random.normal(loc=8.0, scale=3.0, size=37)
>>> pp_x = sm.ProbPlot(x)
>>> pp_y = sm.ProbPlot(y)
>>> qqplot_2samples(pp_x, pp_y)
>>> plt.show()
.. plot:: plots/graphics_gofplots_qqplot_2samples.py
>>> fig = qqplot_2samples(pp_x, pp_y, xlabel=None, ylabel=None,
... line=None, ax=None)
"""
if not isinstance(data1, ProbPlot):
data1 = ProbPlot(data1)
if not isinstance(data2, ProbPlot):
data2 = ProbPlot(data2)
if data2.data.shape[0] > data1.data.shape[0]:
fig = data1.qqplot(xlabel=xlabel, ylabel=ylabel, line=line, other=data2, ax=ax)
else:
fig = data2.qqplot(
xlabel=ylabel,
ylabel=xlabel,
line=line,
other=data1,
ax=ax,
swap=True,
)
return fig | Q-Q Plot of two samples' quantiles.
Can take either two `ProbPlot` instances or two array-like objects. In the
case of the latter, both inputs will be converted to `ProbPlot` instances
using only the default values - so use `ProbPlot` instances if
finer-grained control of the quantile computations is required.
Parameters
----------
data1 : {array_like, ProbPlot}
Data to plot along x axis. If the sample sizes are unequal, the longer
series is always plotted along the x-axis.
data2 : {array_like, ProbPlot}
Data to plot along y axis. Does not need to have the same number of
observations as data 1. If the sample sizes are unequal, the longer
series is always plotted along the x-axis.
xlabel : {None, str}
User-provided labels for the x-axis. If None (default),
other values are used.
ylabel : {None, str}
User-provided labels for the y-axis. If None (default),
other values are used.
line : {None, "45", "s", "r", q"}
Options for the reference line to which the data is compared:
- "45" - 45-degree line
- "s" - standardized line, the expected order statistics are scaled
by the standard deviation of the given sample and have the mean
added to them
- "r" - A regression line is fit
- "q" - A line is fit through the quartiles.
- None - by default no reference line is added to the plot.
ax : AxesSubplot, optional
If given, this subplot is used to plot in instead of a new figure being
created.
Returns
-------
Figure
If `ax` is None, the created figure. Otherwise the figure to which
`ax` is connected.
See Also
--------
scipy.stats.probplot
Notes
-----
1) Depends on matplotlib.
2) If `data1` and `data2` are not `ProbPlot` instances, instances will be
created using the default parameters. Therefore, it is recommended to use
`ProbPlot` instance if fine-grained control is needed in the computation
of the quantiles.
Examples
--------
>>> import statsmodels.api as sm
>>> import numpy as np
>>> import matplotlib.pyplot as plt
>>> from statsmodels.graphics.gofplots import qqplot_2samples
>>> x = np.random.normal(loc=8.5, scale=2.5, size=37)
>>> y = np.random.normal(loc=8.0, scale=3.0, size=37)
>>> pp_x = sm.ProbPlot(x)
>>> pp_y = sm.ProbPlot(y)
>>> qqplot_2samples(pp_x, pp_y)
>>> plt.show()
.. plot:: plots/graphics_gofplots_qqplot_2samples.py
>>> fig = qqplot_2samples(pp_x, pp_y, xlabel=None, ylabel=None,
... line=None, ax=None) | qqplot_2samples | python | statsmodels/statsmodels | statsmodels/graphics/gofplots.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/graphics/gofplots.py | BSD-3-Clause |
def qqline(ax, line, x=None, y=None, dist=None, fmt="r-", **lineoptions):
"""
Plot a reference line for a qqplot.
Parameters
----------
ax : matplotlib axes instance
The axes on which to plot the line
line : str {"45","r","s","q"}
Options for the reference line to which the data is compared.:
- "45" - 45-degree line
- "s" - standardized line, the expected order statistics are scaled by
the standard deviation of the given sample and have the mean
added to them
- "r" - A regression line is fit
- "q" - A line is fit through the quartiles.
- None - By default no reference line is added to the plot.
x : ndarray
X data for plot. Not needed if line is "45".
y : ndarray
Y data for plot. Not needed if line is "45".
dist : scipy.stats.distribution
A scipy.stats distribution, needed if line is "q".
fmt : str, optional
Line format string passed to `plot`.
**lineoptions
Additional arguments to be passed to the `plot` command.
Notes
-----
There is no return value. The line is plotted on the given `ax`.
Examples
--------
Import the food expenditure dataset. Plot annual food expenditure on x-axis
and household income on y-axis. Use qqline to add regression line into the
plot.
>>> import statsmodels.api as sm
>>> import numpy as np
>>> import matplotlib.pyplot as plt
>>> from statsmodels.graphics.gofplots import qqline
>>> foodexp = sm.datasets.engel.load()
>>> x = foodexp.exog
>>> y = foodexp.endog
>>> ax = plt.subplot(111)
>>> plt.scatter(x, y)
>>> ax.set_xlabel(foodexp.exog_name[0])
>>> ax.set_ylabel(foodexp.endog_name)
>>> qqline(ax, "r", x, y)
>>> plt.show()
.. plot:: plots/graphics_gofplots_qqplot_qqline.py
"""
lineoptions = lineoptions.copy()
for ls in ("-", "--", "-.", ":"):
if ls in fmt:
lineoptions.setdefault("linestyle", ls)
fmt = fmt.replace(ls, "")
break
for marker in (
".",
",",
"o",
"v",
"^",
"<",
">",
"1",
"2",
"3",
"4",
"8",
"s",
"p",
"P",
"*",
"h",
"H",
"+",
"x",
"X",
"D",
"d",
"|",
"_",
):
if marker in fmt:
lineoptions.setdefault("marker", marker)
fmt = fmt.replace(marker, "")
break
if fmt:
lineoptions.setdefault("color", fmt)
if line == "45":
end_pts = lzip(ax.get_xlim(), ax.get_ylim())
end_pts[0] = min(end_pts[0])
end_pts[1] = max(end_pts[1])
ax.plot(end_pts, end_pts, **lineoptions)
ax.set_xlim(end_pts)
ax.set_ylim(end_pts)
return # does this have any side effects?
if x is None or y is None:
raise ValueError("If line is not 45, x and y cannot be None.")
x = np.array(x)
y = np.array(y)
if line == "r":
# could use ax.lines[0].get_xdata(), get_ydata(),
# but don't know axes are "clean"
y = OLS(y, add_constant(x)).fit().fittedvalues
ax.plot(x, y, **lineoptions)
elif line == "s":
m, b = np.std(y), np.mean(y)
ref_line = x * m + b
ax.plot(x, ref_line, **lineoptions)
elif line == "q":
_check_for(dist, "ppf")
q25 = stats.scoreatpercentile(y, 25)
q75 = stats.scoreatpercentile(y, 75)
theoretical_quartiles = dist.ppf([0.25, 0.75])
m = (q75 - q25) / np.diff(theoretical_quartiles)
b = q25 - m * theoretical_quartiles[0]
ax.plot(x, m * x + b, **lineoptions) | Plot a reference line for a qqplot.
Parameters
----------
ax : matplotlib axes instance
The axes on which to plot the line
line : str {"45","r","s","q"}
Options for the reference line to which the data is compared.:
- "45" - 45-degree line
- "s" - standardized line, the expected order statistics are scaled by
the standard deviation of the given sample and have the mean
added to them
- "r" - A regression line is fit
- "q" - A line is fit through the quartiles.
- None - By default no reference line is added to the plot.
x : ndarray
X data for plot. Not needed if line is "45".
y : ndarray
Y data for plot. Not needed if line is "45".
dist : scipy.stats.distribution
A scipy.stats distribution, needed if line is "q".
fmt : str, optional
Line format string passed to `plot`.
**lineoptions
Additional arguments to be passed to the `plot` command.
Notes
-----
There is no return value. The line is plotted on the given `ax`.
Examples
--------
Import the food expenditure dataset. Plot annual food expenditure on x-axis
and household income on y-axis. Use qqline to add regression line into the
plot.
>>> import statsmodels.api as sm
>>> import numpy as np
>>> import matplotlib.pyplot as plt
>>> from statsmodels.graphics.gofplots import qqline
>>> foodexp = sm.datasets.engel.load()
>>> x = foodexp.exog
>>> y = foodexp.endog
>>> ax = plt.subplot(111)
>>> plt.scatter(x, y)
>>> ax.set_xlabel(foodexp.exog_name[0])
>>> ax.set_ylabel(foodexp.endog_name)
>>> qqline(ax, "r", x, y)
>>> plt.show()
.. plot:: plots/graphics_gofplots_qqplot_qqline.py | qqline | python | statsmodels/statsmodels | statsmodels/graphics/gofplots.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/graphics/gofplots.py | BSD-3-Clause |
def plotting_pos(nobs, a=0.0, b=None):
"""
Generates sequence of plotting positions
Parameters
----------
nobs : int
Number of probability points to plot
a : float, default 0.0
alpha parameter for the plotting position of an expected order
statistic
b : float, default None
beta parameter for the plotting position of an expected order
statistic. If None, then b is set to a.
Returns
-------
ndarray
The plotting positions
Notes
-----
The plotting positions are given by (i - a)/(nobs + 1 - a - b) for i in
range(1, nobs+1)
See Also
--------
scipy.stats.mstats.plotting_positions
Additional information on alpha and beta
"""
b = a if b is None else b
return (np.arange(1.0, nobs + 1) - a) / (nobs + 1 - a - b) | Generates sequence of plotting positions
Parameters
----------
nobs : int
Number of probability points to plot
a : float, default 0.0
alpha parameter for the plotting position of an expected order
statistic
b : float, default None
beta parameter for the plotting position of an expected order
statistic. If None, then b is set to a.
Returns
-------
ndarray
The plotting positions
Notes
-----
The plotting positions are given by (i - a)/(nobs + 1 - a - b) for i in
range(1, nobs+1)
See Also
--------
scipy.stats.mstats.plotting_positions
Additional information on alpha and beta | plotting_pos | python | statsmodels/statsmodels | statsmodels/graphics/gofplots.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/graphics/gofplots.py | BSD-3-Clause |
def _fmt_probplot_axis(ax, dist, nobs):
"""
Formats a theoretical quantile axis to display the corresponding
probabilities on the quantiles' scale.
Parameters
----------
ax : AxesSubplot, optional
The axis to be formatted
nobs : scalar
Number of observations in the sample
dist : scipy.stats.distribution
A scipy.stats distribution sufficiently specified to implement its
ppf() method.
Returns
-------
There is no return value. This operates on `ax` in place
"""
_check_for(dist, "ppf")
axis_probs = np.linspace(10, 90, 9, dtype=float)
small = np.array([1.0, 2, 5])
axis_probs = np.r_[small, axis_probs, 100 - small[::-1]]
if nobs >= 50:
axis_probs = np.r_[small / 10, axis_probs, 100 - small[::-1] / 10]
if nobs >= 500:
axis_probs = np.r_[small / 100, axis_probs, 100 - small[::-1] / 100]
axis_probs /= 100.0
axis_qntls = dist.ppf(axis_probs)
ax.set_xticks(axis_qntls)
ax.set_xticklabels(
[str(lbl) for lbl in (axis_probs * 100)],
rotation=45,
rotation_mode="anchor",
horizontalalignment="right",
verticalalignment="center",
)
ax.set_xlim([axis_qntls.min(), axis_qntls.max()]) | Formats a theoretical quantile axis to display the corresponding
probabilities on the quantiles' scale.
Parameters
----------
ax : AxesSubplot, optional
The axis to be formatted
nobs : scalar
Number of observations in the sample
dist : scipy.stats.distribution
A scipy.stats distribution sufficiently specified to implement its
ppf() method.
Returns
-------
There is no return value. This operates on `ax` in place | _fmt_probplot_axis | python | statsmodels/statsmodels | statsmodels/graphics/gofplots.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/graphics/gofplots.py | BSD-3-Clause |
def _do_plot(x, y, dist=None, line=None, ax=None, fmt="b", step=False, **kwargs):
"""
Boiler plate plotting function for the `ppplot`, `qqplot`, and
`probplot` methods of the `ProbPlot` class
Parameters
----------
x : array_like
X-axis data to be plotted
y : array_like
Y-axis data to be plotted
dist : scipy.stats.distribution
A scipy.stats distribution, needed if `line` is "q".
line : {"45", "s", "r", "q", None}, default None
Options for the reference line to which the data is compared.
ax : AxesSubplot, optional
If given, this subplot is used to plot in instead of a new figure being
created.
fmt : str, optional
matplotlib-compatible formatting string for the data markers
kwargs : keywords
These are passed to matplotlib.plot
Returns
-------
fig : Figure
The figure containing `ax`.
ax : AxesSubplot
The original axes if provided. Otherwise a new instance.
"""
plot_style = {
"marker": "o",
"markerfacecolor": "C0",
"markeredgecolor": "C0",
"linestyle": "none",
}
plot_style.update(**kwargs)
where = plot_style.pop("where", "pre")
fig, ax = utils.create_mpl_ax(ax)
ax.set_xmargin(0.02)
if step:
ax.step(x, y, fmt, where=where, **plot_style)
else:
ax.plot(x, y, fmt, **plot_style)
if line:
if line not in ["r", "q", "45", "s"]:
msg = "%s option for line not understood" % line
raise ValueError(msg)
qqline(ax, line, x=x, y=y, dist=dist)
return fig, ax | Boiler plate plotting function for the `ppplot`, `qqplot`, and
`probplot` methods of the `ProbPlot` class
Parameters
----------
x : array_like
X-axis data to be plotted
y : array_like
Y-axis data to be plotted
dist : scipy.stats.distribution
A scipy.stats distribution, needed if `line` is "q".
line : {"45", "s", "r", "q", None}, default None
Options for the reference line to which the data is compared.
ax : AxesSubplot, optional
If given, this subplot is used to plot in instead of a new figure being
created.
fmt : str, optional
matplotlib-compatible formatting string for the data markers
kwargs : keywords
These are passed to matplotlib.plot
Returns
-------
fig : Figure
The figure containing `ax`.
ax : AxesSubplot
The original axes if provided. Otherwise a new instance. | _do_plot | python | statsmodels/statsmodels | statsmodels/graphics/gofplots.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/graphics/gofplots.py | BSD-3-Clause |
def plot_corr(dcorr, xnames=None, ynames=None, title=None, normcolor=False,
ax=None, cmap='RdYlBu_r'):
"""Plot correlation of many variables in a tight color grid.
Parameters
----------
dcorr : ndarray
Correlation matrix, square 2-D array.
xnames : list[str], optional
Labels for the horizontal axis. If not given (None), then the
matplotlib defaults (integers) are used. If it is an empty list, [],
then no ticks and labels are added.
ynames : list[str], optional
Labels for the vertical axis. Works the same way as `xnames`.
If not given, the same names as for `xnames` are re-used.
title : str, optional
The figure title. If None, the default ('Correlation Matrix') is used.
If ``title=''``, then no title is added.
normcolor : bool or tuple of scalars, optional
If False (default), then the color coding range corresponds to the
range of `dcorr`. If True, then the color range is normalized to
(-1, 1). If this is a tuple of two numbers, then they define the range
for the color bar.
ax : AxesSubplot, optional
If `ax` is None, then a figure is created. If an axis instance is
given, then only the main plot but not the colorbar is created.
cmap : str or Matplotlib Colormap instance, optional
The colormap for the plot. Can be any valid Matplotlib Colormap
instance or name.
Returns
-------
Figure
If `ax` is None, the created figure. Otherwise the figure to which
`ax` is connected.
Examples
--------
>>> import numpy as np
>>> import matplotlib.pyplot as plt
>>> import statsmodels.graphics.api as smg
>>> hie_data = sm.datasets.randhie.load_pandas()
>>> corr_matrix = np.corrcoef(hie_data.data.T)
>>> smg.plot_corr(corr_matrix, xnames=hie_data.names)
>>> plt.show()
.. plot:: plots/graphics_correlation_plot_corr.py
"""
if ax is None:
create_colorbar = True
else:
create_colorbar = False
fig, ax = utils.create_mpl_ax(ax)
nvars = dcorr.shape[0]
if ynames is None:
ynames = xnames
if title is None:
title = 'Correlation Matrix'
if isinstance(normcolor, tuple):
vmin, vmax = normcolor
elif normcolor:
vmin, vmax = -1.0, 1.0
else:
vmin, vmax = None, None
axim = ax.imshow(dcorr, cmap=cmap, interpolation='nearest',
extent=(0,nvars,0,nvars), vmin=vmin, vmax=vmax)
# create list of label positions
labelPos = np.arange(0, nvars) + 0.5
if isinstance(ynames, list) and len(ynames) == 0:
ax.set_yticks([])
elif ynames is not None:
ax.set_yticks(labelPos)
ax.set_yticks(labelPos[:-1]+0.5, minor=True)
ax.set_yticklabels(ynames[::-1], fontsize='small',
horizontalalignment='right')
if isinstance(xnames, list) and len(xnames) == 0:
ax.set_xticks([])
elif xnames is not None:
ax.set_xticks(labelPos)
ax.set_xticks(labelPos[:-1]+0.5, minor=True)
ax.set_xticklabels(xnames, fontsize='small', rotation=45,
horizontalalignment='right')
if not title == '':
ax.set_title(title)
if create_colorbar:
fig.colorbar(axim, use_gridspec=True)
fig.tight_layout()
ax.tick_params(which='minor', length=0)
ax.tick_params(direction='out', top=False, right=False)
try:
ax.grid(True, which='minor', linestyle='-', color='w', lw=1)
except AttributeError:
# Seems to fail for axes created with AxesGrid. MPL bug?
pass
return fig | Plot correlation of many variables in a tight color grid.
Parameters
----------
dcorr : ndarray
Correlation matrix, square 2-D array.
xnames : list[str], optional
Labels for the horizontal axis. If not given (None), then the
matplotlib defaults (integers) are used. If it is an empty list, [],
then no ticks and labels are added.
ynames : list[str], optional
Labels for the vertical axis. Works the same way as `xnames`.
If not given, the same names as for `xnames` are re-used.
title : str, optional
The figure title. If None, the default ('Correlation Matrix') is used.
If ``title=''``, then no title is added.
normcolor : bool or tuple of scalars, optional
If False (default), then the color coding range corresponds to the
range of `dcorr`. If True, then the color range is normalized to
(-1, 1). If this is a tuple of two numbers, then they define the range
for the color bar.
ax : AxesSubplot, optional
If `ax` is None, then a figure is created. If an axis instance is
given, then only the main plot but not the colorbar is created.
cmap : str or Matplotlib Colormap instance, optional
The colormap for the plot. Can be any valid Matplotlib Colormap
instance or name.
Returns
-------
Figure
If `ax` is None, the created figure. Otherwise the figure to which
`ax` is connected.
Examples
--------
>>> import numpy as np
>>> import matplotlib.pyplot as plt
>>> import statsmodels.graphics.api as smg
>>> hie_data = sm.datasets.randhie.load_pandas()
>>> corr_matrix = np.corrcoef(hie_data.data.T)
>>> smg.plot_corr(corr_matrix, xnames=hie_data.names)
>>> plt.show()
.. plot:: plots/graphics_correlation_plot_corr.py | plot_corr | python | statsmodels/statsmodels | statsmodels/graphics/correlation.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/graphics/correlation.py | BSD-3-Clause |
def plot_corr_grid(dcorrs, titles=None, ncols=None, normcolor=False, xnames=None,
ynames=None, fig=None, cmap='RdYlBu_r'):
"""
Create a grid of correlation plots.
The individual correlation plots are assumed to all have the same
variables, axis labels can be specified only once.
Parameters
----------
dcorrs : list or iterable of ndarrays
List of correlation matrices.
titles : list[str], optional
List of titles for the subplots. By default no title are shown.
ncols : int, optional
Number of columns in the subplot grid. If not given, the number of
columns is determined automatically.
normcolor : bool or tuple, optional
If False (default), then the color coding range corresponds to the
range of `dcorr`. If True, then the color range is normalized to
(-1, 1). If this is a tuple of two numbers, then they define the range
for the color bar.
xnames : list[str], optional
Labels for the horizontal axis. If not given (None), then the
matplotlib defaults (integers) are used. If it is an empty list, [],
then no ticks and labels are added.
ynames : list[str], optional
Labels for the vertical axis. Works the same way as `xnames`.
If not given, the same names as for `xnames` are re-used.
fig : Figure, optional
If given, this figure is simply returned. Otherwise a new figure is
created.
cmap : str or Matplotlib Colormap instance, optional
The colormap for the plot. Can be any valid Matplotlib Colormap
instance or name.
Returns
-------
Figure
If `ax` is None, the created figure. Otherwise the figure to which
`ax` is connected.
Examples
--------
>>> import numpy as np
>>> import matplotlib.pyplot as plt
>>> import statsmodels.api as sm
In this example we just reuse the same correlation matrix several times.
Of course in reality one would show a different correlation (measuring a
another type of correlation, for example Pearson (linear) and Spearman,
Kendall (nonlinear) correlations) for the same variables.
>>> hie_data = sm.datasets.randhie.load_pandas()
>>> corr_matrix = np.corrcoef(hie_data.data.T)
>>> sm.graphics.plot_corr_grid([corr_matrix] * 8, xnames=hie_data.names)
>>> plt.show()
.. plot:: plots/graphics_correlation_plot_corr_grid.py
"""
if ynames is None:
ynames = xnames
if not titles:
titles = ['']*len(dcorrs)
n_plots = len(dcorrs)
if ncols is not None:
nrows = int(np.ceil(n_plots / float(ncols)))
else:
# Determine number of rows and columns, square if possible, otherwise
# prefer a wide (more columns) over a high layout.
if n_plots < 4:
nrows, ncols = 1, n_plots
else:
nrows = int(np.sqrt(n_plots))
ncols = int(np.ceil(n_plots / float(nrows)))
# Create a figure with the correct size
aspect = min(ncols / float(nrows), 1.8)
vsize = np.sqrt(nrows) * 5
fig = utils.create_mpl_fig(fig, figsize=(vsize * aspect + 1, vsize))
for i, c in enumerate(dcorrs):
ax = fig.add_subplot(nrows, ncols, i+1)
# Ensure to only plot labels on bottom row and left column
_xnames = xnames if nrows * ncols - (i+1) < ncols else []
_ynames = ynames if (i+1) % ncols == 1 else []
plot_corr(c, xnames=_xnames, ynames=_ynames, title=titles[i],
normcolor=normcolor, ax=ax, cmap=cmap)
# Adjust figure margins and add a colorbar
fig.subplots_adjust(bottom=0.1, left=0.09, right=0.9, top=0.9)
cax = fig.add_axes([0.92, 0.1, 0.025, 0.8])
fig.colorbar(fig.axes[0].images[0], cax=cax)
return fig | Create a grid of correlation plots.
The individual correlation plots are assumed to all have the same
variables, axis labels can be specified only once.
Parameters
----------
dcorrs : list or iterable of ndarrays
List of correlation matrices.
titles : list[str], optional
List of titles for the subplots. By default no title are shown.
ncols : int, optional
Number of columns in the subplot grid. If not given, the number of
columns is determined automatically.
normcolor : bool or tuple, optional
If False (default), then the color coding range corresponds to the
range of `dcorr`. If True, then the color range is normalized to
(-1, 1). If this is a tuple of two numbers, then they define the range
for the color bar.
xnames : list[str], optional
Labels for the horizontal axis. If not given (None), then the
matplotlib defaults (integers) are used. If it is an empty list, [],
then no ticks and labels are added.
ynames : list[str], optional
Labels for the vertical axis. Works the same way as `xnames`.
If not given, the same names as for `xnames` are re-used.
fig : Figure, optional
If given, this figure is simply returned. Otherwise a new figure is
created.
cmap : str or Matplotlib Colormap instance, optional
The colormap for the plot. Can be any valid Matplotlib Colormap
instance or name.
Returns
-------
Figure
If `ax` is None, the created figure. Otherwise the figure to which
`ax` is connected.
Examples
--------
>>> import numpy as np
>>> import matplotlib.pyplot as plt
>>> import statsmodels.api as sm
In this example we just reuse the same correlation matrix several times.
Of course in reality one would show a different correlation (measuring a
another type of correlation, for example Pearson (linear) and Spearman,
Kendall (nonlinear) correlations) for the same variables.
>>> hie_data = sm.datasets.randhie.load_pandas()
>>> corr_matrix = np.corrcoef(hie_data.data.T)
>>> sm.graphics.plot_corr_grid([corr_matrix] * 8, xnames=hie_data.names)
>>> plt.show()
.. plot:: plots/graphics_correlation_plot_corr_grid.py | plot_corr_grid | python | statsmodels/statsmodels | statsmodels/graphics/correlation.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/graphics/correlation.py | BSD-3-Clause |
def _make_ellipse(mean, cov, ax, level=0.95, color=None):
"""Support function for scatter_ellipse."""
from matplotlib.patches import Ellipse
v, w = np.linalg.eigh(cov)
u = w[0] / np.linalg.norm(w[0])
angle = np.arctan(u[1]/u[0])
angle = 180 * angle / np.pi # convert to degrees
v = 2 * np.sqrt(v * stats.chi2.ppf(level, 2)) #get size corresponding to level
ell = Ellipse(mean[:2], v[0], v[1], angle=180 + angle, facecolor='none',
edgecolor=color,
#ls='dashed', #for debugging
lw=1.5)
ell.set_clip_box(ax.bbox)
ell.set_alpha(0.5)
ax.add_artist(ell) | Support function for scatter_ellipse. | _make_ellipse | python | statsmodels/statsmodels | statsmodels/graphics/plot_grids.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/graphics/plot_grids.py | BSD-3-Clause |
def scatter_ellipse(data, level=0.9, varnames=None, ell_kwds=None,
plot_kwds=None, add_titles=False, keep_ticks=False,
fig=None):
"""Create a grid of scatter plots with confidence ellipses.
ell_kwds, plot_kdes not used yet
looks ok with 5 or 6 variables, too crowded with 8, too empty with 1
Parameters
----------
data : array_like
Input data.
level : scalar, optional
Default is 0.9.
varnames : list[str], optional
Variable names. Used for y-axis labels, and if `add_titles` is True
also for titles. If not given, integers 1..data.shape[1] are used.
ell_kwds : dict, optional
UNUSED
plot_kwds : dict, optional
UNUSED
add_titles : bool, optional
Whether or not to add titles to each subplot. Default is False.
Titles are constructed from `varnames`.
keep_ticks : bool, optional
If False (default), remove all axis ticks.
fig : Figure, optional
If given, this figure is simply returned. Otherwise a new figure is
created.
Returns
-------
Figure
If `fig` is None, the created figure. Otherwise `fig` itself.
Examples
--------
>>> import statsmodels.api as sm
>>> import matplotlib.pyplot as plt
>>> import numpy as np
>>> from statsmodels.graphics.plot_grids import scatter_ellipse
>>> data = sm.datasets.statecrime.load_pandas().data
>>> fig = plt.figure(figsize=(8,8))
>>> scatter_ellipse(data, varnames=data.columns, fig=fig)
>>> plt.show()
.. plot:: plots/graphics_plot_grids_scatter_ellipse.py
"""
fig = utils.create_mpl_fig(fig)
import matplotlib.ticker as mticker
data = np.asanyarray(data) #needs mean and cov
nvars = data.shape[1]
if varnames is None:
#assuming single digit, nvars<=10 else use 'var%2d'
varnames = ['var%d' % i for i in range(nvars)]
plot_kwds_ = dict(ls='none', marker='.', color='k', alpha=0.5)
if plot_kwds:
plot_kwds_.update(plot_kwds)
ell_kwds_= dict(color='k')
if ell_kwds:
ell_kwds_.update(ell_kwds)
dmean = data.mean(0)
dcov = np.cov(data, rowvar=0)
for i in range(1, nvars):
for j in range(i):
ax = fig.add_subplot(nvars-1, nvars-1, (i-1)*(nvars-1)+j+1)
## #sharey=ax_last) #sharey does not allow empty ticks?
## if j == 0:
## ax_last = ax
## ax.set_ylabel(varnames[i])
#TODO: make sure we have same xlim and ylim
formatter = mticker.FormatStrFormatter('% 3.1f')
ax.yaxis.set_major_formatter(formatter)
ax.xaxis.set_major_formatter(formatter)
idx = np.array([j,i])
ax.plot(*data[:,idx].T, **plot_kwds_)
if np.isscalar(level):
level = [level]
for alpha in level:
_make_ellipse(dmean[idx], dcov[idx[:,None], idx], ax, level=alpha,
**ell_kwds_)
if add_titles:
ax.set_title(f'{varnames[i]}-{varnames[j]}')
if not ax.get_subplotspec().is_first_col():
if not keep_ticks:
ax.set_yticks([])
else:
ax.yaxis.set_major_locator(mticker.MaxNLocator(3))
else:
ax.set_ylabel(varnames[i])
if ax.get_subplotspec().is_last_row():
ax.set_xlabel(varnames[j])
else:
if not keep_ticks:
ax.set_xticks([])
else:
ax.xaxis.set_major_locator(mticker.MaxNLocator(3))
dcorr = np.corrcoef(data, rowvar=0)
dc = dcorr[idx[:,None], idx]
xlim = ax.get_xlim()
ylim = ax.get_ylim()
## xt = xlim[0] + 0.1 * (xlim[1] - xlim[0])
## yt = ylim[0] + 0.1 * (ylim[1] - ylim[0])
## if dc[1,0] < 0 :
## yt = ylim[0] + 0.1 * (ylim[1] - ylim[0])
## else:
## yt = ylim[1] - 0.2 * (ylim[1] - ylim[0])
yrangeq = ylim[0] + 0.4 * (ylim[1] - ylim[0])
if dc[1,0] < -0.25 or (dc[1,0] < 0.25 and dmean[idx][1] > yrangeq):
yt = ylim[0] + 0.1 * (ylim[1] - ylim[0])
else:
yt = ylim[1] - 0.2 * (ylim[1] - ylim[0])
xt = xlim[0] + 0.1 * (xlim[1] - xlim[0])
ax.text(xt, yt, '$\\rho=%0.2f$'% dc[1,0])
for ax in fig.axes:
if ax.get_subplotspec().is_last_row(): # or ax.is_first_col():
ax.xaxis.set_major_locator(mticker.MaxNLocator(3))
if ax.get_subplotspec().is_first_col():
ax.yaxis.set_major_locator(mticker.MaxNLocator(3))
return fig | Create a grid of scatter plots with confidence ellipses.
ell_kwds, plot_kdes not used yet
looks ok with 5 or 6 variables, too crowded with 8, too empty with 1
Parameters
----------
data : array_like
Input data.
level : scalar, optional
Default is 0.9.
varnames : list[str], optional
Variable names. Used for y-axis labels, and if `add_titles` is True
also for titles. If not given, integers 1..data.shape[1] are used.
ell_kwds : dict, optional
UNUSED
plot_kwds : dict, optional
UNUSED
add_titles : bool, optional
Whether or not to add titles to each subplot. Default is False.
Titles are constructed from `varnames`.
keep_ticks : bool, optional
If False (default), remove all axis ticks.
fig : Figure, optional
If given, this figure is simply returned. Otherwise a new figure is
created.
Returns
-------
Figure
If `fig` is None, the created figure. Otherwise `fig` itself.
Examples
--------
>>> import statsmodels.api as sm
>>> import matplotlib.pyplot as plt
>>> import numpy as np
>>> from statsmodels.graphics.plot_grids import scatter_ellipse
>>> data = sm.datasets.statecrime.load_pandas().data
>>> fig = plt.figure(figsize=(8,8))
>>> scatter_ellipse(data, varnames=data.columns, fig=fig)
>>> plt.show()
.. plot:: plots/graphics_plot_grids_scatter_ellipse.py | scatter_ellipse | python | statsmodels/statsmodels | statsmodels/graphics/plot_grids.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/graphics/plot_grids.py | BSD-3-Clause |
def harmfunc(t):
"""Test function, combination of a few harmonic terms."""
# Constant, 0 with p=0.9, 1 with p=1 - for creating outliers
ci = int(np.random.random() > 0.9)
a1i = np.random.random() * 0.05
a2i = np.random.random() * 0.05
b1i = (0.15 - 0.1) * np.random.random() + 0.1
b2i = (0.15 - 0.1) * np.random.random() + 0.1
func = (1 - ci) * (a1i * np.sin(t) + a2i * np.cos(t)) + \
ci * (b1i * np.sin(t) + b2i * np.cos(t))
return func | Test function, combination of a few harmonic terms. | test_fboxplot_rainbowplot.harmfunc | python | statsmodels/statsmodels | statsmodels/graphics/tests/test_functional.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/graphics/tests/test_functional.py | BSD-3-Clause |
def test_fboxplot_rainbowplot(close_figures):
# Test fboxplot and rainbowplot together, is much faster.
def harmfunc(t):
"""Test function, combination of a few harmonic terms."""
# Constant, 0 with p=0.9, 1 with p=1 - for creating outliers
ci = int(np.random.random() > 0.9)
a1i = np.random.random() * 0.05
a2i = np.random.random() * 0.05
b1i = (0.15 - 0.1) * np.random.random() + 0.1
b2i = (0.15 - 0.1) * np.random.random() + 0.1
func = (1 - ci) * (a1i * np.sin(t) + a2i * np.cos(t)) + \
ci * (b1i * np.sin(t) + b2i * np.cos(t))
return func
np.random.seed(1234567)
# Some basic test data, Model 6 from Sun and Genton.
t = np.linspace(0, 2 * np.pi, 250)
data = [harmfunc(t) for _ in range(20)]
# fboxplot test
fig = plt.figure()
ax = fig.add_subplot(111)
_, depth, ix_depth, ix_outliers = fboxplot(data, wfactor=2, ax=ax)
ix_expected = np.array([13, 4, 15, 19, 8, 6, 3, 16, 9, 7, 1, 5, 2,
12, 17, 11, 14, 10, 0, 18])
assert_equal(ix_depth, ix_expected)
ix_expected2 = np.array([2, 11, 17, 18])
assert_equal(ix_outliers, ix_expected2)
# rainbowplot test (re-uses depth variable)
xdata = np.arange(data[0].size)
fig = rainbowplot(data, xdata=xdata, depth=depth, cmap=plt.cm.rainbow) | Test function, combination of a few harmonic terms. | test_fboxplot_rainbowplot | python | statsmodels/statsmodels | statsmodels/graphics/tests/test_functional.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/graphics/tests/test_functional.py | BSD-3-Clause |
def _var_normal(norm):
"""Variance factor for asymptotic relative efficiency of mean M-estimator.
The reference distribution is the standard normal distribution.
This assumes that the psi function is continuous.
Relative efficiency is 1 / var_normal
Parameters
----------
norm : instance of a RobustNorm subclass.
Norm for which variance for relative efficiency is computed.
Returns
-------
Variance factor.
Notes
-----
This function does not verify that the assumption on the psi function and
it's derivative hold.
Examples
--------
The following computes the relative efficiency of an M-estimator for the
mean using HuberT norm. At the default tuning parameter, the relative
efficiency is 95%.
>>> import statsmodels.robust import norms
>>> v = _var_normal(norms.HuberT())
>>> eff = 1 / v
>>> v, eff
(1.0526312909084732, 0.9500002599551741)
Notes
-----
S-estimator for mean and regression also have the same variance and
efficiency computation as M-estimators. Therefore, this function can
be used also for S-estimators and other estimators that .
Reference
---------
Menenez et al., but it's also in all text books for robust statistics.
"""
num = stats.norm.expect(lambda x: norm.psi(x) ** 2)
denom = stats.norm.expect(lambda x: norm.psi_deriv(x))**2
return num / denom | Variance factor for asymptotic relative efficiency of mean M-estimator.
The reference distribution is the standard normal distribution.
This assumes that the psi function is continuous.
Relative efficiency is 1 / var_normal
Parameters
----------
norm : instance of a RobustNorm subclass.
Norm for which variance for relative efficiency is computed.
Returns
-------
Variance factor.
Notes
-----
This function does not verify that the assumption on the psi function and
it's derivative hold.
Examples
--------
The following computes the relative efficiency of an M-estimator for the
mean using HuberT norm. At the default tuning parameter, the relative
efficiency is 95%.
>>> import statsmodels.robust import norms
>>> v = _var_normal(norms.HuberT())
>>> eff = 1 / v
>>> v, eff
(1.0526312909084732, 0.9500002599551741)
Notes
-----
S-estimator for mean and regression also have the same variance and
efficiency computation as M-estimators. Therefore, this function can
be used also for S-estimators and other estimators that .
Reference
---------
Menenez et al., but it's also in all text books for robust statistics. | _var_normal | python | statsmodels/statsmodels | statsmodels/robust/tools.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/robust/tools.py | BSD-3-Clause |
def _var_normal_jump(norm):
"""Variance factor for asymptotic relative efficiency of mean M-estimator.
The reference distribution is the standard normal distribution.
This allows for the case when the psi function is not continuous, i.e.
has jumps as in TrimmedMean norm.
Relative efficiency is 1 / var_normal
Parameters
----------
norm : instance of a RobustNorm subclass.
Norm for which variance for relative efficiency is computed.
Returns
-------
Variance factor.
Notes
-----
This function does not verify that the assumption on the psi function and
it's derivative hold.
Examples
--------
>>> import statsmodels.robust import norms
>>> v = _var_normal_jump(norms.HuberT())
>>> eff = 1 / v
>>> v, eff
(1.0526312908510451, 0.950000260007003)
Reference
---------
Menenez et al., but it's also in all text books for robust statistics.
"""
num = stats.norm.expect(lambda x: norm.psi(x)**2)
def func(x):
# derivative normal pdf
# d/dx(exp(-x^2/2)/sqrt(2 π)) = -(e^(-x^2/2) x)/sqrt(2 π)
return norm.psi(x) * (- x * np.exp(-x**2/2) / np.sqrt(2 * np.pi))
denom = integrate.quad(func, -np.inf, np.inf)[0]
return num / denom**2 | Variance factor for asymptotic relative efficiency of mean M-estimator.
The reference distribution is the standard normal distribution.
This allows for the case when the psi function is not continuous, i.e.
has jumps as in TrimmedMean norm.
Relative efficiency is 1 / var_normal
Parameters
----------
norm : instance of a RobustNorm subclass.
Norm for which variance for relative efficiency is computed.
Returns
-------
Variance factor.
Notes
-----
This function does not verify that the assumption on the psi function and
it's derivative hold.
Examples
--------
>>> import statsmodels.robust import norms
>>> v = _var_normal_jump(norms.HuberT())
>>> eff = 1 / v
>>> v, eff
(1.0526312908510451, 0.950000260007003)
Reference
---------
Menenez et al., but it's also in all text books for robust statistics. | _var_normal_jump | python | statsmodels/statsmodels | statsmodels/robust/tools.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/robust/tools.py | BSD-3-Clause |
def _get_tuning_param(norm, eff, kwd="c", kwargs=None, use_jump=False,
bracket=None,
):
"""Tuning parameter for RLM norms for required relative efficiency.
Parameters
----------
norm : instance of RobustNorm subclass
eff : float in (0, 1)
Required asymptotic relative efficiency compared to least squares
at the normal reference distribution. For example, ``eff=0.95`` for
95% efficiency.
kwd : str
Name of keyword for tuning parameter.
kwargs : dict or None
Dict for other keyword parameters.
use_jump : bool
If False (default), then use computation that require continuous
psi function.
If True, then use computation then the psi function can have jump
discontinuities.
bracket : None or tuple
Bracket with lower and upper bounds to use for scipy.optimize.brentq.
If None, than a default bracket, currently [0.1, 10], is used.
Returns
-------
Float : Value of tuning parameter to achieve asymptotic relative
efficiency.
"""
if bracket is None:
bracket = [0.1, 10]
if not use_jump:
def func(c):
# kwds.update({kwd: c})
# return _var_normal(norm(**kwds)) - 1 / eff
norm._set_tuning_param(c, inplace=True)
return _var_normal(norm) - 1 / eff
else:
def func(c):
norm._set_tuning_param(c, inplace=True)
return _var_normal_jump(norm) - 1 / eff
res = optimize.brentq(func, *bracket)
return res | Tuning parameter for RLM norms for required relative efficiency.
Parameters
----------
norm : instance of RobustNorm subclass
eff : float in (0, 1)
Required asymptotic relative efficiency compared to least squares
at the normal reference distribution. For example, ``eff=0.95`` for
95% efficiency.
kwd : str
Name of keyword for tuning parameter.
kwargs : dict or None
Dict for other keyword parameters.
use_jump : bool
If False (default), then use computation that require continuous
psi function.
If True, then use computation then the psi function can have jump
discontinuities.
bracket : None or tuple
Bracket with lower and upper bounds to use for scipy.optimize.brentq.
If None, than a default bracket, currently [0.1, 10], is used.
Returns
-------
Float : Value of tuning parameter to achieve asymptotic relative
efficiency. | _get_tuning_param | python | statsmodels/statsmodels | statsmodels/robust/tools.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/robust/tools.py | BSD-3-Clause |
def tuning_s_estimator_mean(norm, breakdown=None):
"""Tuning parameter and scale bias correction for S-estimators of mean.
The reference distribution is the normal distribution.
This requires a (hard) redescending norm, i.e. with finite max rho.
Parameters
----------
norm : instance of RobustNorm subclass
breakdown : float or iterable of float in (0, 0.5]
Desired breakdown point between 0 and 0.5.
Default if breakdown is None is a list of breakdown points.
Returns
-------
Holder instance with the following attributes :
- `breakdown` : breakdown point
- `eff` : relative efficiency
- `param` : tuning parameter for norm
- `scale_bias` : correction term for Fisher consistency.
Notes
-----
Based on Rousseeuw and Leroy (1987). See table 19, p. 142 that can be
replicated by this function for TukeyBiweight norm.
Note, the results of this function are based computation without rounding
to decimal precision, and differ in some cases in the last digit from
the table by Rousseeuw and Leroy.
Numerical expectation and root finding based on scipy integrate and
optimize.
TODO: more options for details, numeric approximation and root finding.
There is currently no feasibility check in functions.
Reference
---------
Rousseeuw and Leroy book
"""
if breakdown is None:
bps = [0.5, 0.45, 0.40, 0.35, 0.30, 0.25, 0.20, 0.15, 0.1, 0.05]
else:
# allow for scalar bp
try:
_ = iter(breakdown)
bps = breakdown
except TypeError:
bps = [breakdown]
def func(c):
norm_ = norm
norm_._set_tuning_param(c, inplace=True)
bp = stats.norm.expect(lambda x: norm_.rho(x)) / norm_.max_rho()
return bp
res = []
for bp in bps:
c_bp = optimize.brentq(lambda c0: func(c0) - bp, 0.1, 10)
norm._set_tuning_param(c_bp, inplace=True) # inplace modification
eff = 1 / _var_normal(norm)
b = stats.norm.expect(lambda x : norm.rho(x))
res.append([bp, eff, c_bp, b])
if np.size(bps) > 1:
res = np.asarray(res).T
else:
# use one list
res = res[0]
res2 = Holder(
breakdown=res[0],
eff=res[1],
param=res[2],
scale_bias=res[3],
all=res,
)
return res2 | Tuning parameter and scale bias correction for S-estimators of mean.
The reference distribution is the normal distribution.
This requires a (hard) redescending norm, i.e. with finite max rho.
Parameters
----------
norm : instance of RobustNorm subclass
breakdown : float or iterable of float in (0, 0.5]
Desired breakdown point between 0 and 0.5.
Default if breakdown is None is a list of breakdown points.
Returns
-------
Holder instance with the following attributes :
- `breakdown` : breakdown point
- `eff` : relative efficiency
- `param` : tuning parameter for norm
- `scale_bias` : correction term for Fisher consistency.
Notes
-----
Based on Rousseeuw and Leroy (1987). See table 19, p. 142 that can be
replicated by this function for TukeyBiweight norm.
Note, the results of this function are based computation without rounding
to decimal precision, and differ in some cases in the last digit from
the table by Rousseeuw and Leroy.
Numerical expectation and root finding based on scipy integrate and
optimize.
TODO: more options for details, numeric approximation and root finding.
There is currently no feasibility check in functions.
Reference
---------
Rousseeuw and Leroy book | tuning_s_estimator_mean | python | statsmodels/statsmodels | statsmodels/robust/tools.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/robust/tools.py | BSD-3-Clause |
def scale_bias_cov_biw(c, k_vars):
"""Multivariate scale bias correction for TukeyBiweight norm.
This uses the chisquare distribution as reference distribution for the
squared Mahalanobis distance.
"""
p = k_vars # alias for formula
chip, chip2, chip4, chip6 = stats.chi2.cdf(c**2, [p, p + 2, p + 4, p + 6])
b = p / 2 * chip2 - p * (p + 2) / (2 * c**2) * chip4
b += p * (p + 2) * (p + 4) / (6 * c**4) * chip6 + c**2 / 6 * (1 - chip)
return b, b / (c**2 / 6) | Multivariate scale bias correction for TukeyBiweight norm.
This uses the chisquare distribution as reference distribution for the
squared Mahalanobis distance. | scale_bias_cov_biw | python | statsmodels/statsmodels | statsmodels/robust/tools.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/robust/tools.py | BSD-3-Clause |
def scale_bias_cov(norm, k_vars):
"""Multivariate scale bias correction.
Parameter
---------
norm : norm instance
The rho function of the norm is used in the moment condition for
estimating scale.
k_vars : int
Number of random variables in the multivariate data.
Returns
-------
scale_bias: float
breakdown_point : float
Breakdown point computed as scale bias divided by max rho.
"""
def rho(x):
return norm.rho(np.sqrt(x))
scale_bias = stats.chi2.expect(rho, args=(k_vars,))
return scale_bias, scale_bias / norm.max_rho() | Multivariate scale bias correction.
Parameter
---------
norm : norm instance
The rho function of the norm is used in the moment condition for
estimating scale.
k_vars : int
Number of random variables in the multivariate data.
Returns
-------
scale_bias: float
breakdown_point : float
Breakdown point computed as scale bias divided by max rho. | scale_bias_cov | python | statsmodels/statsmodels | statsmodels/robust/tools.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/robust/tools.py | BSD-3-Clause |
def tuning_s_cov(norm, k_vars, breakdown_point=0.5, limits=()):
"""Tuning parameter for multivariate S-estimator given breakdown point.
"""
from .norms import TukeyBiweight # avoid circular import
if not limits:
limits = (0.5, 30)
if isinstance(norm, TukeyBiweight):
def func(c):
return scale_bias_cov_biw(c, k_vars)[1] - breakdown_point
else:
norm = norm._set_tuning_param(2., inplace=False) # create copy
def func(c):
norm._set_tuning_param(c, inplace=True)
return scale_bias_cov(norm, k_vars)[1] - breakdown_point
p_tune = optimize.brentq(func, limits[0], limits[1])
return p_tune | Tuning parameter for multivariate S-estimator given breakdown point. | tuning_s_cov | python | statsmodels/statsmodels | statsmodels/robust/tools.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/robust/tools.py | BSD-3-Clause |
def eff_mvmean(norm, k_vars):
"""Efficiency for M-estimator of multivariate mean at normal distribution.
This also applies to estimators that are locally equivalent to an
M-estimator such as S- and MM-estimators.
Parameters
----------
norm : instance of norm class
k_vars : int
Number of variables in multivariate random variable, i.e. dimension.
Returns
-------
eff : float
Asymptotic relative efficiency of mean at normal distribution.
alpha : float
Numerical integral. Efficiency is beta**2 / alpha
beta : float
Numerical integral.
Notes
-----
This implements equ. (5.3) p. 1671 in Lopuhaä 1989
References
----------
.. [1] Lopuhaä, Hendrik P. 1989. “On the Relation between S-Estimators
and M-Estimators of Multivariate Location and Covariance.”
The Annals of Statistics 17 (4): 1662–83.
"""
k = k_vars # shortcut
def f_alpha(d):
return norm.psi(d) ** 2 / k
def f_beta(d):
return (1 - 1 / k) * norm.weights(d) + 1 / k * norm.psi_deriv(d)
alpha = stats.chi(k).expect(f_alpha)
beta = stats.chi(k).expect(f_beta)
return beta**2 / alpha, alpha, beta | Efficiency for M-estimator of multivariate mean at normal distribution.
This also applies to estimators that are locally equivalent to an
M-estimator such as S- and MM-estimators.
Parameters
----------
norm : instance of norm class
k_vars : int
Number of variables in multivariate random variable, i.e. dimension.
Returns
-------
eff : float
Asymptotic relative efficiency of mean at normal distribution.
alpha : float
Numerical integral. Efficiency is beta**2 / alpha
beta : float
Numerical integral.
Notes
-----
This implements equ. (5.3) p. 1671 in Lopuhaä 1989
References
----------
.. [1] Lopuhaä, Hendrik P. 1989. “On the Relation between S-Estimators
and M-Estimators of Multivariate Location and Covariance.”
The Annals of Statistics 17 (4): 1662–83. | eff_mvmean | python | statsmodels/statsmodels | statsmodels/robust/tools.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/robust/tools.py | BSD-3-Clause |
def eff_mvshape(norm, k_vars):
"""Efficiency of M-estimator of multivariate shape at normal distribution.
This also applies to estimators that are locally equivalent to an
M-estimator such as S- and MM-estimators.
Parameters
----------
norm : instance of norm class
k_vars : int
Number of variables in multivariate random variable, i.e. dimension.
Returns
-------
eff : float
Asymptotic relative efficiency of mean at normal distribution.
alpha : float
Numerical integral. Efficiency is beta**2 / alpha
beta : float
Numerical integral.
Notes
-----
This implements sigma_1 in equ. (5.5) p. 1671 in Lopuhaä 1989.
Efficiency of shape is approximately 1 / sigma1.
References
----------
.. [1] Lopuhaä, Hendrik P. 1989. “On the Relation between S-Estimators
and M-Estimators of Multivariate Location and Covariance.”
The Annals of Statistics 17 (4): 1662–83.
"""
k = k_vars # shortcut
def f_a(d):
return k * (k + 2) * norm.psi(d) ** 2 * d**2
def f_b(d):
return norm.psi_deriv(d) * d**2 + (k + 1) * norm.psi(d) * d
a = stats.chi(k).expect(f_a)
b = stats.chi(k).expect(f_b)
return b**2 / a, a, b | Efficiency of M-estimator of multivariate shape at normal distribution.
This also applies to estimators that are locally equivalent to an
M-estimator such as S- and MM-estimators.
Parameters
----------
norm : instance of norm class
k_vars : int
Number of variables in multivariate random variable, i.e. dimension.
Returns
-------
eff : float
Asymptotic relative efficiency of mean at normal distribution.
alpha : float
Numerical integral. Efficiency is beta**2 / alpha
beta : float
Numerical integral.
Notes
-----
This implements sigma_1 in equ. (5.5) p. 1671 in Lopuhaä 1989.
Efficiency of shape is approximately 1 / sigma1.
References
----------
.. [1] Lopuhaä, Hendrik P. 1989. “On the Relation between S-Estimators
and M-Estimators of Multivariate Location and Covariance.”
The Annals of Statistics 17 (4): 1662–83. | eff_mvshape | python | statsmodels/statsmodels | statsmodels/robust/tools.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/robust/tools.py | BSD-3-Clause |
def tuning_m_cov_eff(norm, k_vars, efficiency=0.95, eff_mean=True, limits=()):
"""Tuning parameter for multivariate M-estimator given efficiency.
This also applies to estimators that are locally equivalent to an
M-estimator such as S- and MM-estimators.
Parameters
----------
norm : instance of norm class
k_vars : int
Number of variables in multivariate random variable, i.e. dimension.
efficiency : float < 1
Desired asymptotic relative efficiency of mean estimator.
Default is 0.95.
eff_mean : bool
If eff_mean is true (default), then tuning parameter is to achieve
efficiency of mean estimate.
If eff_mean is fale, then tuning parameter is to achieve efficiency
of shape estimate.
limits : tuple
Limits for rootfinding with scipy.optimize.brentq.
In some cases the interval limits for rootfinding can be too small
and not cover the root. Current default limits are (0.5, 30).
Returns
-------
float : Tuning parameter for the norm to achieve desired efficiency.
Asymptotic relative efficiency of mean at normal distribution.
Notes
-----
This uses numerical integration and rootfinding and will be
relatively slow.
"""
if not limits:
limits = (0.5, 30)
# make copy of norm
norm = norm._set_tuning_param(1, inplace=False)
if eff_mean:
def func(c):
norm._set_tuning_param(c, inplace=True)
return eff_mvmean(norm, k_vars)[0] - efficiency
else:
def func(c):
norm._set_tuning_param(c, inplace=True)
return eff_mvshape(norm, k_vars)[0] - efficiency
p_tune = optimize.brentq(func, limits[0], limits[1])
return p_tune | Tuning parameter for multivariate M-estimator given efficiency.
This also applies to estimators that are locally equivalent to an
M-estimator such as S- and MM-estimators.
Parameters
----------
norm : instance of norm class
k_vars : int
Number of variables in multivariate random variable, i.e. dimension.
efficiency : float < 1
Desired asymptotic relative efficiency of mean estimator.
Default is 0.95.
eff_mean : bool
If eff_mean is true (default), then tuning parameter is to achieve
efficiency of mean estimate.
If eff_mean is fale, then tuning parameter is to achieve efficiency
of shape estimate.
limits : tuple
Limits for rootfinding with scipy.optimize.brentq.
In some cases the interval limits for rootfinding can be too small
and not cover the root. Current default limits are (0.5, 30).
Returns
-------
float : Tuning parameter for the norm to achieve desired efficiency.
Asymptotic relative efficiency of mean at normal distribution.
Notes
-----
This uses numerical integration and rootfinding and will be
relatively slow. | tuning_m_cov_eff | python | statsmodels/statsmodels | statsmodels/robust/tools.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/robust/tools.py | BSD-3-Clause |
def tukeybiweight_mvmean_eff(k, eff, eff_mean=True):
"""tuning parameter for biweight norm to achieve efficiency for mv-mean.
Uses values from precomputed table if available, otherwise computes it
numerically and adds it to the module global dict.
"""
if eff_mean:
table_dict = tukeybiweight_mvmean_eff_d
else:
table_dict = tukeybiweight_mvshape_eff_d
try:
tp = table_dict[(k, eff)]
except KeyError:
# compute and cache
from .norms import TukeyBiweight # avoid circular import
norm = TukeyBiweight(c=1)
tp = tuning_m_cov_eff(norm, k, efficiency=eff, eff_mean=eff_mean)
table_dict[(k, eff)] = tp
return tp | tuning parameter for biweight norm to achieve efficiency for mv-mean.
Uses values from precomputed table if available, otherwise computes it
numerically and adds it to the module global dict. | tukeybiweight_mvmean_eff | python | statsmodels/statsmodels | statsmodels/robust/tools.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/robust/tools.py | BSD-3-Clause |
def _cabs(x):
"""absolute value function that changes complex sign based on real sign
This could be useful for complex step derivatives of functions that
need abs. Not yet used.
"""
sign = (x.real >= 0) * 2 - 1
return sign * x | absolute value function that changes complex sign based on real sign
This could be useful for complex step derivatives of functions that
need abs. Not yet used. | _cabs | python | statsmodels/statsmodels | statsmodels/robust/norms.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/robust/norms.py | BSD-3-Clause |
def rho(self, z):
"""
The robust criterion estimator function.
Abstract method:
-2 loglike used in M-estimator
"""
raise NotImplementedError | The robust criterion estimator function.
Abstract method:
-2 loglike used in M-estimator | rho | python | statsmodels/statsmodels | statsmodels/robust/norms.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/robust/norms.py | BSD-3-Clause |
def psi(self, z):
"""
Derivative of rho. Sometimes referred to as the influence function.
Abstract method:
psi = rho'
"""
raise NotImplementedError | Derivative of rho. Sometimes referred to as the influence function.
Abstract method:
psi = rho' | psi | python | statsmodels/statsmodels | statsmodels/robust/norms.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/robust/norms.py | BSD-3-Clause |
def weights(self, z):
"""
Returns the value of psi(z) / z
Abstract method:
psi(z) / z
"""
raise NotImplementedError | Returns the value of psi(z) / z
Abstract method:
psi(z) / z | weights | python | statsmodels/statsmodels | statsmodels/robust/norms.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/robust/norms.py | BSD-3-Clause |
def psi_deriv(self, z):
"""
Derivative of psi. Used to obtain robust covariance matrix.
See statsmodels.rlm for more information.
Abstract method:
psi_derive = psi'
"""
raise NotImplementedError | Derivative of psi. Used to obtain robust covariance matrix.
See statsmodels.rlm for more information.
Abstract method:
psi_derive = psi' | psi_deriv | python | statsmodels/statsmodels | statsmodels/robust/norms.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/robust/norms.py | BSD-3-Clause |
def __call__(self, z):
"""
Returns the value of estimator rho applied to an input
"""
return self.rho(z) | Returns the value of estimator rho applied to an input | __call__ | python | statsmodels/statsmodels | statsmodels/robust/norms.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/robust/norms.py | BSD-3-Clause |
def rho(self, z):
"""
The least squares estimator rho function
Parameters
----------
z : ndarray
1d array
Returns
-------
rho : ndarray
rho(z) = (1/2.)*z**2
"""
return z**2 * 0.5 | The least squares estimator rho function
Parameters
----------
z : ndarray
1d array
Returns
-------
rho : ndarray
rho(z) = (1/2.)*z**2 | rho | python | statsmodels/statsmodels | statsmodels/robust/norms.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/robust/norms.py | BSD-3-Clause |
def psi(self, z):
"""
The psi function for the least squares estimator
The analytic derivative of rho
Parameters
----------
z : array_like
1d array
Returns
-------
psi : ndarray
psi(z) = z
"""
return np.asarray(z) | The psi function for the least squares estimator
The analytic derivative of rho
Parameters
----------
z : array_like
1d array
Returns
-------
psi : ndarray
psi(z) = z | psi | python | statsmodels/statsmodels | statsmodels/robust/norms.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/robust/norms.py | BSD-3-Clause |
def weights(self, z):
"""
The least squares estimator weighting function for the IRLS algorithm.
The psi function scaled by the input z
Parameters
----------
z : array_like
1d array
Returns
-------
weights : ndarray
weights(z) = np.ones(z.shape)
"""
z = np.asarray(z)
return np.ones(z.shape, np.float64) | The least squares estimator weighting function for the IRLS algorithm.
The psi function scaled by the input z
Parameters
----------
z : array_like
1d array
Returns
-------
weights : ndarray
weights(z) = np.ones(z.shape) | weights | python | statsmodels/statsmodels | statsmodels/robust/norms.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/robust/norms.py | BSD-3-Clause |
def psi_deriv(self, z):
"""
The derivative of the least squares psi function.
Returns
-------
psi_deriv : ndarray
ones(z.shape)
Notes
-----
Used to estimate the robust covariance matrix.
"""
z = np.asarray(z)
return np.ones(z.shape, np.float64) | The derivative of the least squares psi function.
Returns
-------
psi_deriv : ndarray
ones(z.shape)
Notes
-----
Used to estimate the robust covariance matrix. | psi_deriv | python | statsmodels/statsmodels | statsmodels/robust/norms.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/robust/norms.py | BSD-3-Clause |
def _set_tuning_param(self, c, inplace=False):
"""Set and change the tuning parameter of the Norm.
Warning: this needs to wipe cached attributes that depend on the param.
"""
if inplace:
self.t = c
return self
else:
return self.__class__(t=c) | Set and change the tuning parameter of the Norm.
Warning: this needs to wipe cached attributes that depend on the param. | _set_tuning_param | python | statsmodels/statsmodels | statsmodels/robust/norms.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/robust/norms.py | BSD-3-Clause |
def _subset(self, z):
"""
Huber's T is defined piecewise over the range for z
"""
z = np.asarray(z)
return np.less_equal(np.abs(z), self.t) | Huber's T is defined piecewise over the range for z | _subset | python | statsmodels/statsmodels | statsmodels/robust/norms.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/robust/norms.py | BSD-3-Clause |
def psi_deriv(self, z):
"""
The derivative of Huber's t psi function
Notes
-----
Used to estimate the robust covariance matrix.
"""
return np.less_equal(np.abs(z), self.t).astype(float) | The derivative of Huber's t psi function
Notes
-----
Used to estimate the robust covariance matrix. | psi_deriv | python | statsmodels/statsmodels | statsmodels/robust/norms.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/robust/norms.py | BSD-3-Clause |
def _set_tuning_param(self, c, inplace=False):
"""Set and change the tuning parameter of the Norm.
Warning: this needs to wipe cached attributes that depend on the param.
"""
# todo : change default to inplace=False, when tools are fixed
if inplace:
self.a = c
return self
else:
return self.__class__(a=c) | Set and change the tuning parameter of the Norm.
Warning: this needs to wipe cached attributes that depend on the param. | _set_tuning_param | python | statsmodels/statsmodels | statsmodels/robust/norms.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/robust/norms.py | BSD-3-Clause |
def psi_deriv(self, z):
"""
The derivative of Ramsay's Ea psi function.
Notes
-----
Used to estimate the robust covariance matrix.
"""
a = self.a
x = np.exp(-a * np.abs(z))
dx = -a * x * np.sign(z)
y = z
dy = 1
return x * dy + y * dx | The derivative of Ramsay's Ea psi function.
Notes
-----
Used to estimate the robust covariance matrix. | psi_deriv | python | statsmodels/statsmodels | statsmodels/robust/norms.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/robust/norms.py | BSD-3-Clause |
def _set_tuning_param(self, c, inplace=False):
"""Set and change the tuning parameter of the Norm.
Warning: this needs to wipe cached attributes that depend on the param.
"""
if inplace:
self.a = c
return self
else:
return self.__class__(a=c) | Set and change the tuning parameter of the Norm.
Warning: this needs to wipe cached attributes that depend on the param. | _set_tuning_param | python | statsmodels/statsmodels | statsmodels/robust/norms.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/robust/norms.py | BSD-3-Clause |
def _subset(self, z):
"""
Andrew's wave is defined piecewise over the range of z.
"""
z = np.asarray(z)
return np.less_equal(np.abs(z), self.a * np.pi) | Andrew's wave is defined piecewise over the range of z. | _subset | python | statsmodels/statsmodels | statsmodels/robust/norms.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/robust/norms.py | BSD-3-Clause |
def psi_deriv(self, z):
"""
The derivative of Andrew's wave psi function
Notes
-----
Used to estimate the robust covariance matrix.
"""
test = self._subset(z)
return test * np.cos(z / self.a) | The derivative of Andrew's wave psi function
Notes
-----
Used to estimate the robust covariance matrix. | psi_deriv | python | statsmodels/statsmodels | statsmodels/robust/norms.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/robust/norms.py | BSD-3-Clause |
def _set_tuning_param(self, c, inplace=False):
"""Set and change the tuning parameter of the Norm.
Warning: this needs to wipe cached attributes that depend on the param.
"""
if inplace:
self.c = c
return self
else:
return self.__class__(c=c) | Set and change the tuning parameter of the Norm.
Warning: this needs to wipe cached attributes that depend on the param. | _set_tuning_param | python | statsmodels/statsmodels | statsmodels/robust/norms.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/robust/norms.py | BSD-3-Clause |
def _subset(self, z):
"""
Least trimmed mean is defined piecewise over the range of z.
"""
z = np.asarray(z)
return np.less_equal(np.abs(z), self.c) | Least trimmed mean is defined piecewise over the range of z. | _subset | python | statsmodels/statsmodels | statsmodels/robust/norms.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/robust/norms.py | BSD-3-Clause |
def psi_deriv(self, z):
"""
The derivative of least trimmed mean psi function
Notes
-----
Used to estimate the robust covariance matrix.
"""
test = self._subset(z)
return test | The derivative of least trimmed mean psi function
Notes
-----
Used to estimate the robust covariance matrix. | psi_deriv | python | statsmodels/statsmodels | statsmodels/robust/norms.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/robust/norms.py | BSD-3-Clause |
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