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def quantile(self, probs, return_pandas=True):
"""
Compute quantiles for a weighted sample.
Parameters
----------
probs : array_like
A vector of probability points at which to calculate the
quantiles. Each element of `probs` should fall in [0, 1].
return_pandas : bool
If True, return value is a Pandas DataFrame or Series.
Otherwise returns a ndarray.
Returns
-------
quantiles : Series, DataFrame, or ndarray
If `return_pandas` = True, returns one of the following:
* data are 1d, `return_pandas` = True: a Series indexed by
the probability points.
* data are 2d, `return_pandas` = True: a DataFrame with
the probability points as row index and the variables
as column index.
If `return_pandas` = False, returns an ndarray containing the
same values as the Series/DataFrame.
Notes
-----
To compute the quantiles, first, the weights are summed over
exact ties yielding distinct data values y_1 < y_2 < ..., and
corresponding weights w_1, w_2, .... Let s_j denote the sum
of the first j weights, and let W denote the sum of all the
weights. For a probability point p, if pW falls strictly
between s_j and s_{j+1} then the estimated quantile is
y_{j+1}. If pW = s_j then the estimated quantile is (y_j +
y_{j+1})/2. If pW < p_1 then the estimated quantile is y_1.
References
----------
SAS documentation for weighted quantiles:
https://support.sas.com/documentation/cdl/en/procstat/63104/HTML/default/viewer.htm#procstat_univariate_sect028.htm
"""
import pandas as pd
probs = np.asarray(probs)
probs = np.atleast_1d(probs)
if self.data.ndim == 1:
rslt = self._quantile(self.data, probs)
if return_pandas:
rslt = pd.Series(rslt, index=probs)
else:
rslt = []
for vec in self.data.T:
rslt.append(self._quantile(vec, probs))
rslt = np.column_stack(rslt)
if return_pandas:
columns = ["col%d" % (j + 1) for j in range(rslt.shape[1])]
rslt = pd.DataFrame(data=rslt, columns=columns, index=probs)
if return_pandas:
rslt.index.name = "p"
return rslt | Compute quantiles for a weighted sample.
Parameters
----------
probs : array_like
A vector of probability points at which to calculate the
quantiles. Each element of `probs` should fall in [0, 1].
return_pandas : bool
If True, return value is a Pandas DataFrame or Series.
Otherwise returns a ndarray.
Returns
-------
quantiles : Series, DataFrame, or ndarray
If `return_pandas` = True, returns one of the following:
* data are 1d, `return_pandas` = True: a Series indexed by
the probability points.
* data are 2d, `return_pandas` = True: a DataFrame with
the probability points as row index and the variables
as column index.
If `return_pandas` = False, returns an ndarray containing the
same values as the Series/DataFrame.
Notes
-----
To compute the quantiles, first, the weights are summed over
exact ties yielding distinct data values y_1 < y_2 < ..., and
corresponding weights w_1, w_2, .... Let s_j denote the sum
of the first j weights, and let W denote the sum of all the
weights. For a probability point p, if pW falls strictly
between s_j and s_{j+1} then the estimated quantile is
y_{j+1}. If pW = s_j then the estimated quantile is (y_j +
y_{j+1})/2. If pW < p_1 then the estimated quantile is y_1.
References
----------
SAS documentation for weighted quantiles:
https://support.sas.com/documentation/cdl/en/procstat/63104/HTML/default/viewer.htm#procstat_univariate_sect028.htm | quantile | python | statsmodels/statsmodels | statsmodels/stats/weightstats.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/stats/weightstats.py | BSD-3-Clause |
def tconfint_mean(self, alpha=0.05, alternative="two-sided"):
"""two-sided confidence interval for weighted mean of data
If the data is 2d, then these are separate confidence intervals
for each column.
Parameters
----------
alpha : float
significance level for the confidence interval, coverage is
``1-alpha``
alternative : str
This specifies the alternative hypothesis for the test that
corresponds to the confidence interval.
The alternative hypothesis, H1, has to be one of the following
'two-sided': H1: mean not equal to value (default)
'larger' : H1: mean larger than value
'smaller' : H1: mean smaller than value
Returns
-------
lower, upper : floats or ndarrays
lower and upper bound of confidence interval
Notes
-----
In a previous version, statsmodels 0.4, alpha was the confidence
level, e.g. 0.95
"""
# TODO: add asymmetric
dof = self.sum_weights - 1
ci = _tconfint_generic(
self.mean, self.std_mean, dof, alpha, alternative
)
return ci | two-sided confidence interval for weighted mean of data
If the data is 2d, then these are separate confidence intervals
for each column.
Parameters
----------
alpha : float
significance level for the confidence interval, coverage is
``1-alpha``
alternative : str
This specifies the alternative hypothesis for the test that
corresponds to the confidence interval.
The alternative hypothesis, H1, has to be one of the following
'two-sided': H1: mean not equal to value (default)
'larger' : H1: mean larger than value
'smaller' : H1: mean smaller than value
Returns
-------
lower, upper : floats or ndarrays
lower and upper bound of confidence interval
Notes
-----
In a previous version, statsmodels 0.4, alpha was the confidence
level, e.g. 0.95 | tconfint_mean | python | statsmodels/statsmodels | statsmodels/stats/weightstats.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/stats/weightstats.py | BSD-3-Clause |
def zconfint_mean(self, alpha=0.05, alternative="two-sided"):
"""two-sided confidence interval for weighted mean of data
Confidence interval is based on normal distribution.
If the data is 2d, then these are separate confidence intervals
for each column.
Parameters
----------
alpha : float
significance level for the confidence interval, coverage is
``1-alpha``
alternative : str
This specifies the alternative hypothesis for the test that
corresponds to the confidence interval.
The alternative hypothesis, H1, has to be one of the following
'two-sided': H1: mean not equal to value (default)
'larger' : H1: mean larger than value
'smaller' : H1: mean smaller than value
Returns
-------
lower, upper : floats or ndarrays
lower and upper bound of confidence interval
Notes
-----
In a previous version, statsmodels 0.4, alpha was the confidence
level, e.g. 0.95
"""
return _zconfint_generic(self.mean, self.std_mean, alpha, alternative) | two-sided confidence interval for weighted mean of data
Confidence interval is based on normal distribution.
If the data is 2d, then these are separate confidence intervals
for each column.
Parameters
----------
alpha : float
significance level for the confidence interval, coverage is
``1-alpha``
alternative : str
This specifies the alternative hypothesis for the test that
corresponds to the confidence interval.
The alternative hypothesis, H1, has to be one of the following
'two-sided': H1: mean not equal to value (default)
'larger' : H1: mean larger than value
'smaller' : H1: mean smaller than value
Returns
-------
lower, upper : floats or ndarrays
lower and upper bound of confidence interval
Notes
-----
In a previous version, statsmodels 0.4, alpha was the confidence
level, e.g. 0.95 | zconfint_mean | python | statsmodels/statsmodels | statsmodels/stats/weightstats.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/stats/weightstats.py | BSD-3-Clause |
def ttest_mean(self, value=0, alternative="two-sided"):
"""ttest of Null hypothesis that mean is equal to value.
The alternative hypothesis H1 is defined by the following
- 'two-sided': H1: mean not equal to value
- 'larger' : H1: mean larger than value
- 'smaller' : H1: mean smaller than value
Parameters
----------
value : float or array
the hypothesized value for the mean
alternative : str
The alternative hypothesis, H1, has to be one of the following:
- 'two-sided': H1: mean not equal to value (default)
- 'larger' : H1: mean larger than value
- 'smaller' : H1: mean smaller than value
Returns
-------
tstat : float
test statistic
pvalue : float
pvalue of the t-test
df : int or float
"""
# TODO: check direction with R, smaller=less, larger=greater
tstat = (self.mean - value) / self.std_mean
dof = self.sum_weights - 1
# TODO: use outsourced
if alternative == "two-sided":
pvalue = stats.t.sf(np.abs(tstat), dof) * 2
elif alternative == "larger":
pvalue = stats.t.sf(tstat, dof)
elif alternative == "smaller":
pvalue = stats.t.cdf(tstat, dof)
else:
raise ValueError("alternative not recognized")
return tstat, pvalue, dof | ttest of Null hypothesis that mean is equal to value.
The alternative hypothesis H1 is defined by the following
- 'two-sided': H1: mean not equal to value
- 'larger' : H1: mean larger than value
- 'smaller' : H1: mean smaller than value
Parameters
----------
value : float or array
the hypothesized value for the mean
alternative : str
The alternative hypothesis, H1, has to be one of the following:
- 'two-sided': H1: mean not equal to value (default)
- 'larger' : H1: mean larger than value
- 'smaller' : H1: mean smaller than value
Returns
-------
tstat : float
test statistic
pvalue : float
pvalue of the t-test
df : int or float | ttest_mean | python | statsmodels/statsmodels | statsmodels/stats/weightstats.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/stats/weightstats.py | BSD-3-Clause |
def ttost_mean(self, low, upp):
"""test of (non-)equivalence of one sample
TOST: two one-sided t tests
null hypothesis: m < low or m > upp
alternative hypothesis: low < m < upp
where m is the expected value of the sample (mean of the population).
If the pvalue is smaller than a threshold, say 0.05, then we reject the
hypothesis that the expected value of the sample (mean of the
population) is outside of the interval given by thresholds low and upp.
Parameters
----------
low, upp : float
equivalence interval low < mean < upp
Returns
-------
pvalue : float
pvalue of the non-equivalence test
t1, pv1, df1 : tuple
test statistic, pvalue and degrees of freedom for lower threshold
test
t2, pv2, df2 : tuple
test statistic, pvalue and degrees of freedom for upper threshold
test
"""
t1, pv1, df1 = self.ttest_mean(low, alternative="larger")
t2, pv2, df2 = self.ttest_mean(upp, alternative="smaller")
return np.maximum(pv1, pv2), (t1, pv1, df1), (t2, pv2, df2) | test of (non-)equivalence of one sample
TOST: two one-sided t tests
null hypothesis: m < low or m > upp
alternative hypothesis: low < m < upp
where m is the expected value of the sample (mean of the population).
If the pvalue is smaller than a threshold, say 0.05, then we reject the
hypothesis that the expected value of the sample (mean of the
population) is outside of the interval given by thresholds low and upp.
Parameters
----------
low, upp : float
equivalence interval low < mean < upp
Returns
-------
pvalue : float
pvalue of the non-equivalence test
t1, pv1, df1 : tuple
test statistic, pvalue and degrees of freedom for lower threshold
test
t2, pv2, df2 : tuple
test statistic, pvalue and degrees of freedom for upper threshold
test | ttost_mean | python | statsmodels/statsmodels | statsmodels/stats/weightstats.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/stats/weightstats.py | BSD-3-Clause |
def ztest_mean(self, value=0, alternative="two-sided"):
"""z-test of Null hypothesis that mean is equal to value.
The alternative hypothesis H1 is defined by the following
'two-sided': H1: mean not equal to value
'larger' : H1: mean larger than value
'smaller' : H1: mean smaller than value
Parameters
----------
value : float or array
the hypothesized value for the mean
alternative : str
The alternative hypothesis, H1, has to be one of the following
'two-sided': H1: mean not equal to value (default)
'larger' : H1: mean larger than value
'smaller' : H1: mean smaller than value
Returns
-------
tstat : float
test statistic
pvalue : float
pvalue of the z-test
Notes
-----
This uses the same degrees of freedom correction as the t-test in the
calculation of the standard error of the mean, i.e it uses
`(sum_weights - 1)` instead of `sum_weights` in the denominator.
See Examples below for the difference.
Examples
--------
z-test on a proportion, with 20 observations, 15 of those are our event
>>> import statsmodels.api as sm
>>> x1 = [0, 1]
>>> w1 = [5, 15]
>>> d1 = sm.stats.DescrStatsW(x1, w1)
>>> d1.ztest_mean(0.5)
(2.5166114784235836, 0.011848940928347452)
This differs from the proportions_ztest because of the degrees of
freedom correction:
>>> sm.stats.proportions_ztest(15, 20.0, value=0.5)
(2.5819888974716112, 0.009823274507519247).
We can replicate the results from ``proportions_ztest`` if we increase
the weights to have artificially one more observation:
>>> sm.stats.DescrStatsW(x1, np.array(w1)*21./20).ztest_mean(0.5)
(2.5819888974716116, 0.0098232745075192366)
"""
tstat = (self.mean - value) / self.std_mean
# TODO: use outsourced
if alternative == "two-sided":
pvalue = stats.norm.sf(np.abs(tstat)) * 2
elif alternative == "larger":
pvalue = stats.norm.sf(tstat)
elif alternative == "smaller":
pvalue = stats.norm.cdf(tstat)
return tstat, pvalue | z-test of Null hypothesis that mean is equal to value.
The alternative hypothesis H1 is defined by the following
'two-sided': H1: mean not equal to value
'larger' : H1: mean larger than value
'smaller' : H1: mean smaller than value
Parameters
----------
value : float or array
the hypothesized value for the mean
alternative : str
The alternative hypothesis, H1, has to be one of the following
'two-sided': H1: mean not equal to value (default)
'larger' : H1: mean larger than value
'smaller' : H1: mean smaller than value
Returns
-------
tstat : float
test statistic
pvalue : float
pvalue of the z-test
Notes
-----
This uses the same degrees of freedom correction as the t-test in the
calculation of the standard error of the mean, i.e it uses
`(sum_weights - 1)` instead of `sum_weights` in the denominator.
See Examples below for the difference.
Examples
--------
z-test on a proportion, with 20 observations, 15 of those are our event
>>> import statsmodels.api as sm
>>> x1 = [0, 1]
>>> w1 = [5, 15]
>>> d1 = sm.stats.DescrStatsW(x1, w1)
>>> d1.ztest_mean(0.5)
(2.5166114784235836, 0.011848940928347452)
This differs from the proportions_ztest because of the degrees of
freedom correction:
>>> sm.stats.proportions_ztest(15, 20.0, value=0.5)
(2.5819888974716112, 0.009823274507519247).
We can replicate the results from ``proportions_ztest`` if we increase
the weights to have artificially one more observation:
>>> sm.stats.DescrStatsW(x1, np.array(w1)*21./20).ztest_mean(0.5)
(2.5819888974716116, 0.0098232745075192366) | ztest_mean | python | statsmodels/statsmodels | statsmodels/stats/weightstats.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/stats/weightstats.py | BSD-3-Clause |
def ztost_mean(self, low, upp):
"""test of (non-)equivalence of one sample, based on z-test
TOST: two one-sided z-tests
null hypothesis: m < low or m > upp
alternative hypothesis: low < m < upp
where m is the expected value of the sample (mean of the population).
If the pvalue is smaller than a threshold, say 0.05, then we reject the
hypothesis that the expected value of the sample (mean of the
population) is outside of the interval given by thresholds low and upp.
Parameters
----------
low, upp : float
equivalence interval low < mean < upp
Returns
-------
pvalue : float
pvalue of the non-equivalence test
t1, pv1 : tuple
test statistic and p-value for lower threshold test
t2, pv2 : tuple
test statistic and p-value for upper threshold test
"""
t1, pv1 = self.ztest_mean(low, alternative="larger")
t2, pv2 = self.ztest_mean(upp, alternative="smaller")
return np.maximum(pv1, pv2), (t1, pv1), (t2, pv2) | test of (non-)equivalence of one sample, based on z-test
TOST: two one-sided z-tests
null hypothesis: m < low or m > upp
alternative hypothesis: low < m < upp
where m is the expected value of the sample (mean of the population).
If the pvalue is smaller than a threshold, say 0.05, then we reject the
hypothesis that the expected value of the sample (mean of the
population) is outside of the interval given by thresholds low and upp.
Parameters
----------
low, upp : float
equivalence interval low < mean < upp
Returns
-------
pvalue : float
pvalue of the non-equivalence test
t1, pv1 : tuple
test statistic and p-value for lower threshold test
t2, pv2 : tuple
test statistic and p-value for upper threshold test | ztost_mean | python | statsmodels/statsmodels | statsmodels/stats/weightstats.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/stats/weightstats.py | BSD-3-Clause |
def get_compare(self, other, weights=None):
"""return an instance of CompareMeans with self and other
Parameters
----------
other : array_like or instance of DescrStatsW
If array_like then this creates an instance of DescrStatsW with
the given weights.
weights : None or array
weights are only used if other is not an instance of DescrStatsW
Returns
-------
cm : instance of CompareMeans
the instance has self attached as d1 and other as d2.
See Also
--------
CompareMeans
"""
if not isinstance(other, self.__class__):
d2 = DescrStatsW(other, weights)
else:
d2 = other
return CompareMeans(self, d2) | return an instance of CompareMeans with self and other
Parameters
----------
other : array_like or instance of DescrStatsW
If array_like then this creates an instance of DescrStatsW with
the given weights.
weights : None or array
weights are only used if other is not an instance of DescrStatsW
Returns
-------
cm : instance of CompareMeans
the instance has self attached as d1 and other as d2.
See Also
--------
CompareMeans | get_compare | python | statsmodels/statsmodels | statsmodels/stats/weightstats.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/stats/weightstats.py | BSD-3-Clause |
def asrepeats(self):
"""get array that has repeats given by floor(weights)
observations with weight=0 are dropped
"""
w_int = np.floor(self.weights).astype(int)
return np.repeat(self.data, w_int, axis=0) | get array that has repeats given by floor(weights)
observations with weight=0 are dropped | asrepeats | python | statsmodels/statsmodels | statsmodels/stats/weightstats.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/stats/weightstats.py | BSD-3-Clause |
def _tstat_generic(value1, value2, std_diff, dof, alternative, diff=0):
"""generic ttest based on summary statistic
The test statistic is :
tstat = (value1 - value2 - diff) / std_diff
and is assumed to be t-distributed with ``dof`` degrees of freedom.
Parameters
----------
value1 : float or ndarray
Value, for example mean, of the first sample.
value2 : float or ndarray
Value, for example mean, of the second sample.
std_diff : float or ndarray
Standard error of the difference value1 - value2
dof : int or float
Degrees of freedom
alternative : str
The alternative hypothesis, H1, has to be one of the following
* 'two-sided' : H1: ``value1 - value2 - diff`` not equal to 0.
* 'larger' : H1: ``value1 - value2 - diff > 0``
* 'smaller' : H1: ``value1 - value2 - diff < 0``
diff : float
value of difference ``value1 - value2`` under the null hypothesis
Returns
-------
tstat : float or ndarray
Test statistic.
pvalue : float or ndarray
P-value of the hypothesis test assuming that the test statistic is
t-distributed with ``df`` degrees of freedom.
"""
tstat = (value1 - value2 - diff) / std_diff
if alternative in ["two-sided", "2-sided", "2s"]:
pvalue = stats.t.sf(np.abs(tstat), dof) * 2
elif alternative in ["larger", "l"]:
pvalue = stats.t.sf(tstat, dof)
elif alternative in ["smaller", "s"]:
pvalue = stats.t.cdf(tstat, dof)
else:
raise ValueError("invalid alternative")
return tstat, pvalue | generic ttest based on summary statistic
The test statistic is :
tstat = (value1 - value2 - diff) / std_diff
and is assumed to be t-distributed with ``dof`` degrees of freedom.
Parameters
----------
value1 : float or ndarray
Value, for example mean, of the first sample.
value2 : float or ndarray
Value, for example mean, of the second sample.
std_diff : float or ndarray
Standard error of the difference value1 - value2
dof : int or float
Degrees of freedom
alternative : str
The alternative hypothesis, H1, has to be one of the following
* 'two-sided' : H1: ``value1 - value2 - diff`` not equal to 0.
* 'larger' : H1: ``value1 - value2 - diff > 0``
* 'smaller' : H1: ``value1 - value2 - diff < 0``
diff : float
value of difference ``value1 - value2`` under the null hypothesis
Returns
-------
tstat : float or ndarray
Test statistic.
pvalue : float or ndarray
P-value of the hypothesis test assuming that the test statistic is
t-distributed with ``df`` degrees of freedom. | _tstat_generic | python | statsmodels/statsmodels | statsmodels/stats/weightstats.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/stats/weightstats.py | BSD-3-Clause |
def _tconfint_generic(mean, std_mean, dof, alpha, alternative):
"""generic t-confint based on summary statistic
Parameters
----------
mean : float or ndarray
Value, for example mean, of the first sample.
std_mean : float or ndarray
Standard error of the difference value1 - value2
dof : int or float
Degrees of freedom
alpha : float
Significance level for the confidence interval, coverage is
``1-alpha``.
alternative : str
The alternative hypothesis, H1, has to be one of the following
* 'two-sided' : H1: ``value1 - value2 - diff`` not equal to 0.
* 'larger' : H1: ``value1 - value2 - diff > 0``
* 'smaller' : H1: ``value1 - value2 - diff < 0``
Returns
-------
lower : float or ndarray
Lower confidence limit. This is -inf for the one-sided alternative
"smaller".
upper : float or ndarray
Upper confidence limit. This is inf for the one-sided alternative
"larger".
"""
if alternative in ["two-sided", "2-sided", "2s"]:
tcrit = stats.t.ppf(1 - alpha / 2.0, dof)
lower = mean - tcrit * std_mean
upper = mean + tcrit * std_mean
elif alternative in ["larger", "l"]:
tcrit = stats.t.ppf(alpha, dof)
lower = mean + tcrit * std_mean
upper = np.inf
elif alternative in ["smaller", "s"]:
tcrit = stats.t.ppf(1 - alpha, dof)
lower = -np.inf
upper = mean + tcrit * std_mean
else:
raise ValueError("invalid alternative")
return lower, upper | generic t-confint based on summary statistic
Parameters
----------
mean : float or ndarray
Value, for example mean, of the first sample.
std_mean : float or ndarray
Standard error of the difference value1 - value2
dof : int or float
Degrees of freedom
alpha : float
Significance level for the confidence interval, coverage is
``1-alpha``.
alternative : str
The alternative hypothesis, H1, has to be one of the following
* 'two-sided' : H1: ``value1 - value2 - diff`` not equal to 0.
* 'larger' : H1: ``value1 - value2 - diff > 0``
* 'smaller' : H1: ``value1 - value2 - diff < 0``
Returns
-------
lower : float or ndarray
Lower confidence limit. This is -inf for the one-sided alternative
"smaller".
upper : float or ndarray
Upper confidence limit. This is inf for the one-sided alternative
"larger". | _tconfint_generic | python | statsmodels/statsmodels | statsmodels/stats/weightstats.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/stats/weightstats.py | BSD-3-Clause |
def _zstat_generic(value1, value2, std_diff, alternative, diff=0):
"""generic (normal) z-test based on summary statistic
The test statistic is :
tstat = (value1 - value2 - diff) / std_diff
and is assumed to be normally distributed.
Parameters
----------
value1 : float or ndarray
Value, for example mean, of the first sample.
value2 : float or ndarray
Value, for example mean, of the second sample.
std_diff : float or ndarray
Standard error of the difference value1 - value2
alternative : str
The alternative hypothesis, H1, has to be one of the following
* 'two-sided' : H1: ``value1 - value2 - diff`` not equal to 0.
* 'larger' : H1: ``value1 - value2 - diff > 0``
* 'smaller' : H1: ``value1 - value2 - diff < 0``
diff : float
value of difference ``value1 - value2`` under the null hypothesis
Returns
-------
tstat : float or ndarray
Test statistic.
pvalue : float or ndarray
P-value of the hypothesis test assuming that the test statistic is
t-distributed with ``df`` degrees of freedom.
"""
zstat = (value1 - value2 - diff) / std_diff
if alternative in ["two-sided", "2-sided", "2s"]:
pvalue = stats.norm.sf(np.abs(zstat)) * 2
elif alternative in ["larger", "l"]:
pvalue = stats.norm.sf(zstat)
elif alternative in ["smaller", "s"]:
pvalue = stats.norm.cdf(zstat)
else:
raise ValueError("invalid alternative")
return zstat, pvalue | generic (normal) z-test based on summary statistic
The test statistic is :
tstat = (value1 - value2 - diff) / std_diff
and is assumed to be normally distributed.
Parameters
----------
value1 : float or ndarray
Value, for example mean, of the first sample.
value2 : float or ndarray
Value, for example mean, of the second sample.
std_diff : float or ndarray
Standard error of the difference value1 - value2
alternative : str
The alternative hypothesis, H1, has to be one of the following
* 'two-sided' : H1: ``value1 - value2 - diff`` not equal to 0.
* 'larger' : H1: ``value1 - value2 - diff > 0``
* 'smaller' : H1: ``value1 - value2 - diff < 0``
diff : float
value of difference ``value1 - value2`` under the null hypothesis
Returns
-------
tstat : float or ndarray
Test statistic.
pvalue : float or ndarray
P-value of the hypothesis test assuming that the test statistic is
t-distributed with ``df`` degrees of freedom. | _zstat_generic | python | statsmodels/statsmodels | statsmodels/stats/weightstats.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/stats/weightstats.py | BSD-3-Clause |
def _zstat_generic2(value, std, alternative):
"""generic (normal) z-test based on summary statistic
The test statistic is :
zstat = value / std
and is assumed to be normally distributed with standard deviation ``std``.
Parameters
----------
value : float or ndarray
Value of a sample statistic, for example mean.
value2 : float or ndarray
Value, for example mean, of the second sample.
std : float or ndarray
Standard error of the sample statistic value.
alternative : str
The alternative hypothesis, H1, has to be one of the following
* 'two-sided' : H1: ``value1 - value2 - diff`` not equal to 0.
* 'larger' : H1: ``value1 - value2 - diff > 0``
* 'smaller' : H1: ``value1 - value2 - diff < 0``
Returns
-------
zstat : float or ndarray
Test statistic.
pvalue : float or ndarray
P-value of the hypothesis test assuming that the test statistic is
normally distributed.
"""
zstat = value / std
if alternative in ["two-sided", "2-sided", "2s"]:
pvalue = stats.norm.sf(np.abs(zstat)) * 2
elif alternative in ["larger", "l"]:
pvalue = stats.norm.sf(zstat)
elif alternative in ["smaller", "s"]:
pvalue = stats.norm.cdf(zstat)
else:
raise ValueError("invalid alternative")
return zstat, pvalue | generic (normal) z-test based on summary statistic
The test statistic is :
zstat = value / std
and is assumed to be normally distributed with standard deviation ``std``.
Parameters
----------
value : float or ndarray
Value of a sample statistic, for example mean.
value2 : float or ndarray
Value, for example mean, of the second sample.
std : float or ndarray
Standard error of the sample statistic value.
alternative : str
The alternative hypothesis, H1, has to be one of the following
* 'two-sided' : H1: ``value1 - value2 - diff`` not equal to 0.
* 'larger' : H1: ``value1 - value2 - diff > 0``
* 'smaller' : H1: ``value1 - value2 - diff < 0``
Returns
-------
zstat : float or ndarray
Test statistic.
pvalue : float or ndarray
P-value of the hypothesis test assuming that the test statistic is
normally distributed. | _zstat_generic2 | python | statsmodels/statsmodels | statsmodels/stats/weightstats.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/stats/weightstats.py | BSD-3-Clause |
def _zconfint_generic(mean, std_mean, alpha, alternative):
"""generic normal-confint based on summary statistic
Parameters
----------
mean : float or ndarray
Value, for example mean, of the first sample.
std_mean : float or ndarray
Standard error of the difference value1 - value2
alpha : float
Significance level for the confidence interval, coverage is
``1-alpha``
alternative : str
The alternative hypothesis, H1, has to be one of the following
* 'two-sided' : H1: ``value1 - value2 - diff`` not equal to 0.
* 'larger' : H1: ``value1 - value2 - diff > 0``
* 'smaller' : H1: ``value1 - value2 - diff < 0``
Returns
-------
lower : float or ndarray
Lower confidence limit. This is -inf for the one-sided alternative
"smaller".
upper : float or ndarray
Upper confidence limit. This is inf for the one-sided alternative
"larger".
"""
if alternative in ["two-sided", "2-sided", "2s"]:
zcrit = stats.norm.ppf(1 - alpha / 2.0)
lower = mean - zcrit * std_mean
upper = mean + zcrit * std_mean
elif alternative in ["larger", "l"]:
zcrit = stats.norm.ppf(alpha)
lower = mean + zcrit * std_mean
upper = np.inf
elif alternative in ["smaller", "s"]:
zcrit = stats.norm.ppf(1 - alpha)
lower = -np.inf
upper = mean + zcrit * std_mean
else:
raise ValueError("invalid alternative")
return lower, upper | generic normal-confint based on summary statistic
Parameters
----------
mean : float or ndarray
Value, for example mean, of the first sample.
std_mean : float or ndarray
Standard error of the difference value1 - value2
alpha : float
Significance level for the confidence interval, coverage is
``1-alpha``
alternative : str
The alternative hypothesis, H1, has to be one of the following
* 'two-sided' : H1: ``value1 - value2 - diff`` not equal to 0.
* 'larger' : H1: ``value1 - value2 - diff > 0``
* 'smaller' : H1: ``value1 - value2 - diff < 0``
Returns
-------
lower : float or ndarray
Lower confidence limit. This is -inf for the one-sided alternative
"smaller".
upper : float or ndarray
Upper confidence limit. This is inf for the one-sided alternative
"larger". | _zconfint_generic | python | statsmodels/statsmodels | statsmodels/stats/weightstats.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/stats/weightstats.py | BSD-3-Clause |
def __init__(self, d1, d2):
"""assume d1, d2 hold the relevant attributes
"""
self.d1 = d1
self.d2 = d2 | assume d1, d2 hold the relevant attributes | __init__ | python | statsmodels/statsmodels | statsmodels/stats/weightstats.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/stats/weightstats.py | BSD-3-Clause |
def from_data(
cls, data1, data2, weights1=None, weights2=None, ddof1=0, ddof2=0
):
"""construct a CompareMeans object from data
Parameters
----------
data1, data2 : array_like, 1-D or 2-D
compared datasets
weights1, weights2 : None or 1-D ndarray
weights for each observation of data1 and data2 respectively,
with same length as zero axis of corresponding dataset.
ddof1, ddof2 : int
default ddof1=0, ddof2=0, degrees of freedom for data1,
data2 respectively.
Returns
-------
A CompareMeans instance.
"""
return cls(
DescrStatsW(data1, weights=weights1, ddof=ddof1),
DescrStatsW(data2, weights=weights2, ddof=ddof2),
) | construct a CompareMeans object from data
Parameters
----------
data1, data2 : array_like, 1-D or 2-D
compared datasets
weights1, weights2 : None or 1-D ndarray
weights for each observation of data1 and data2 respectively,
with same length as zero axis of corresponding dataset.
ddof1, ddof2 : int
default ddof1=0, ddof2=0, degrees of freedom for data1,
data2 respectively.
Returns
-------
A CompareMeans instance. | from_data | python | statsmodels/statsmodels | statsmodels/stats/weightstats.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/stats/weightstats.py | BSD-3-Clause |
def summary(self, use_t=True, alpha=0.05, usevar="pooled", value=0):
"""summarize the results of the hypothesis test
Parameters
----------
use_t : bool, optional
if use_t is True, then t test results are returned
if use_t is False, then z test results are returned
alpha : float
significance level for the confidence interval, coverage is
``1-alpha``
usevar : str, 'pooled' or 'unequal'
If ``pooled``, then the standard deviation of the samples is
assumed to be the same. If ``unequal``, then the variance of
Welch ttest will be used, and the degrees of freedom are those
of Satterthwaite if ``use_t`` is True.
value : float
difference between the means under the Null hypothesis.
Returns
-------
smry : SimpleTable
"""
d1 = self.d1
d2 = self.d2
if use_t:
tstat, pvalue, _ = self.ttest_ind(usevar=usevar, value=value)
lower, upper = self.tconfint_diff(alpha=alpha, usevar=usevar)
else:
tstat, pvalue = self.ztest_ind(usevar=usevar, value=value)
lower, upper = self.zconfint_diff(alpha=alpha, usevar=usevar)
if usevar == "pooled":
std_err = self.std_meandiff_pooledvar
else:
std_err = self.std_meandiff_separatevar
std_err = np.atleast_1d(std_err)
tstat = np.atleast_1d(tstat)
pvalue = np.atleast_1d(pvalue)
lower = np.atleast_1d(lower)
upper = np.atleast_1d(upper)
conf_int = np.column_stack((lower, upper))
params = np.atleast_1d(d1.mean - d2.mean - value)
title = "Test for equality of means"
yname = "y" # not used in params_frame
xname = ["subset #%d" % (ii + 1) for ii in range(tstat.shape[0])]
from statsmodels.iolib.summary import summary_params
return summary_params(
(None, params, std_err, tstat, pvalue, conf_int),
alpha=alpha,
use_t=use_t,
yname=yname,
xname=xname,
title=title,
) | summarize the results of the hypothesis test
Parameters
----------
use_t : bool, optional
if use_t is True, then t test results are returned
if use_t is False, then z test results are returned
alpha : float
significance level for the confidence interval, coverage is
``1-alpha``
usevar : str, 'pooled' or 'unequal'
If ``pooled``, then the standard deviation of the samples is
assumed to be the same. If ``unequal``, then the variance of
Welch ttest will be used, and the degrees of freedom are those
of Satterthwaite if ``use_t`` is True.
value : float
difference between the means under the Null hypothesis.
Returns
-------
smry : SimpleTable | summary | python | statsmodels/statsmodels | statsmodels/stats/weightstats.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/stats/weightstats.py | BSD-3-Clause |
def std_meandiff_pooledvar(self):
"""variance assuming equal variance in both data sets
"""
# this uses ``_var`` to use ddof=0 for formula
d1 = self.d1
d2 = self.d2
# could make var_pooled into attribute
var_pooled = (
(d1.sumsquares + d2.sumsquares)
/
# (d1.nobs - d1.ddof + d2.nobs - d2.ddof))
(d1.nobs - 1 + d2.nobs - 1)
)
return np.sqrt(var_pooled * (1.0 / d1.nobs + 1.0 / d2.nobs)) | variance assuming equal variance in both data sets | std_meandiff_pooledvar | python | statsmodels/statsmodels | statsmodels/stats/weightstats.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/stats/weightstats.py | BSD-3-Clause |
def dof_satt(self):
"""degrees of freedom of Satterthwaite for unequal variance
"""
d1 = self.d1
d2 = self.d2
# this follows blindly the SPSS manual
# except I use ``_var`` which has ddof=0
sem1 = d1._var / (d1.nobs - 1)
sem2 = d2._var / (d2.nobs - 1)
semsum = sem1 + sem2
z1 = (sem1 / semsum) ** 2 / (d1.nobs - 1)
z2 = (sem2 / semsum) ** 2 / (d2.nobs - 1)
dof = 1.0 / (z1 + z2)
return dof | degrees of freedom of Satterthwaite for unequal variance | dof_satt | python | statsmodels/statsmodels | statsmodels/stats/weightstats.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/stats/weightstats.py | BSD-3-Clause |
def ttest_ind(self, alternative="two-sided", usevar="pooled", value=0):
"""ttest for the null hypothesis of identical means
this should also be the same as onewaygls, except for ddof differences
Parameters
----------
x1 : array_like, 1-D or 2-D
first of the two independent samples, see notes for 2-D case
x2 : array_like, 1-D or 2-D
second of the two independent samples, see notes for 2-D case
alternative : str
The alternative hypothesis, H1, has to be one of the following
'two-sided': H1: difference in means not equal to value (default)
'larger' : H1: difference in means larger than value
'smaller' : H1: difference in means smaller than value
usevar : str, 'pooled' or 'unequal'
If ``pooled``, then the standard deviation of the samples is assumed to be
the same. If ``unequal``, then Welch ttest with Satterthwait degrees
of freedom is used
value : float
difference between the means under the Null hypothesis.
Returns
-------
tstat : float
test statistic
pvalue : float
pvalue of the t-test
df : int or float
degrees of freedom used in the t-test
Notes
-----
The result is independent of the user specified ddof.
"""
d1 = self.d1
d2 = self.d2
if usevar == "pooled":
stdm = self.std_meandiff_pooledvar
dof = d1.nobs - 1 + d2.nobs - 1
elif usevar == "unequal":
stdm = self.std_meandiff_separatevar
dof = self.dof_satt()
else:
raise ValueError('usevar can only be "pooled" or "unequal"')
tstat, pval = _tstat_generic(
d1.mean, d2.mean, stdm, dof, alternative, diff=value
)
return tstat, pval, dof | ttest for the null hypothesis of identical means
this should also be the same as onewaygls, except for ddof differences
Parameters
----------
x1 : array_like, 1-D or 2-D
first of the two independent samples, see notes for 2-D case
x2 : array_like, 1-D or 2-D
second of the two independent samples, see notes for 2-D case
alternative : str
The alternative hypothesis, H1, has to be one of the following
'two-sided': H1: difference in means not equal to value (default)
'larger' : H1: difference in means larger than value
'smaller' : H1: difference in means smaller than value
usevar : str, 'pooled' or 'unequal'
If ``pooled``, then the standard deviation of the samples is assumed to be
the same. If ``unequal``, then Welch ttest with Satterthwait degrees
of freedom is used
value : float
difference between the means under the Null hypothesis.
Returns
-------
tstat : float
test statistic
pvalue : float
pvalue of the t-test
df : int or float
degrees of freedom used in the t-test
Notes
-----
The result is independent of the user specified ddof. | ttest_ind | python | statsmodels/statsmodels | statsmodels/stats/weightstats.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/stats/weightstats.py | BSD-3-Clause |
def ztest_ind(self, alternative="two-sided", usevar="pooled", value=0):
"""z-test for the null hypothesis of identical means
Parameters
----------
x1 : array_like, 1-D or 2-D
first of the two independent samples, see notes for 2-D case
x2 : array_like, 1-D or 2-D
second of the two independent samples, see notes for 2-D case
alternative : str
The alternative hypothesis, H1, has to be one of the following
'two-sided': H1: difference in means not equal to value (default)
'larger' : H1: difference in means larger than value
'smaller' : H1: difference in means smaller than value
usevar : str, 'pooled' or 'unequal'
If ``pooled``, then the standard deviation of the samples is assumed to be
the same. If ``unequal``, then the standard deviations of the samples may
be different.
value : float
difference between the means under the Null hypothesis.
Returns
-------
tstat : float
test statistic
pvalue : float
pvalue of the z-test
"""
d1 = self.d1
d2 = self.d2
if usevar == "pooled":
stdm = self.std_meandiff_pooledvar
elif usevar == "unequal":
stdm = self.std_meandiff_separatevar
else:
raise ValueError('usevar can only be "pooled" or "unequal"')
tstat, pval = _zstat_generic(
d1.mean, d2.mean, stdm, alternative, diff=value
)
return tstat, pval | z-test for the null hypothesis of identical means
Parameters
----------
x1 : array_like, 1-D or 2-D
first of the two independent samples, see notes for 2-D case
x2 : array_like, 1-D or 2-D
second of the two independent samples, see notes for 2-D case
alternative : str
The alternative hypothesis, H1, has to be one of the following
'two-sided': H1: difference in means not equal to value (default)
'larger' : H1: difference in means larger than value
'smaller' : H1: difference in means smaller than value
usevar : str, 'pooled' or 'unequal'
If ``pooled``, then the standard deviation of the samples is assumed to be
the same. If ``unequal``, then the standard deviations of the samples may
be different.
value : float
difference between the means under the Null hypothesis.
Returns
-------
tstat : float
test statistic
pvalue : float
pvalue of the z-test | ztest_ind | python | statsmodels/statsmodels | statsmodels/stats/weightstats.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/stats/weightstats.py | BSD-3-Clause |
def tconfint_diff(
self, alpha=0.05, alternative="two-sided", usevar="pooled"
):
"""confidence interval for the difference in means
Parameters
----------
alpha : float
significance level for the confidence interval, coverage is
``1-alpha``
alternative : str
This specifies the alternative hypothesis for the test that
corresponds to the confidence interval.
The alternative hypothesis, H1, has to be one of the following :
'two-sided': H1: difference in means not equal to value (default)
'larger' : H1: difference in means larger than value
'smaller' : H1: difference in means smaller than value
usevar : str, 'pooled' or 'unequal'
If ``pooled``, then the standard deviation of the samples is assumed to be
the same. If ``unequal``, then Welch ttest with Satterthwait degrees
of freedom is used
Returns
-------
lower, upper : floats
lower and upper limits of the confidence interval
Notes
-----
The result is independent of the user specified ddof.
"""
d1 = self.d1
d2 = self.d2
diff = d1.mean - d2.mean
if usevar == "pooled":
std_diff = self.std_meandiff_pooledvar
dof = d1.nobs - 1 + d2.nobs - 1
elif usevar == "unequal":
std_diff = self.std_meandiff_separatevar
dof = self.dof_satt()
else:
raise ValueError('usevar can only be "pooled" or "unequal"')
res = _tconfint_generic(
diff, std_diff, dof, alpha=alpha, alternative=alternative
)
return res | confidence interval for the difference in means
Parameters
----------
alpha : float
significance level for the confidence interval, coverage is
``1-alpha``
alternative : str
This specifies the alternative hypothesis for the test that
corresponds to the confidence interval.
The alternative hypothesis, H1, has to be one of the following :
'two-sided': H1: difference in means not equal to value (default)
'larger' : H1: difference in means larger than value
'smaller' : H1: difference in means smaller than value
usevar : str, 'pooled' or 'unequal'
If ``pooled``, then the standard deviation of the samples is assumed to be
the same. If ``unequal``, then Welch ttest with Satterthwait degrees
of freedom is used
Returns
-------
lower, upper : floats
lower and upper limits of the confidence interval
Notes
-----
The result is independent of the user specified ddof. | tconfint_diff | python | statsmodels/statsmodels | statsmodels/stats/weightstats.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/stats/weightstats.py | BSD-3-Clause |
def zconfint_diff(
self, alpha=0.05, alternative="two-sided", usevar="pooled"
):
"""confidence interval for the difference in means
Parameters
----------
alpha : float
significance level for the confidence interval, coverage is
``1-alpha``
alternative : str
This specifies the alternative hypothesis for the test that
corresponds to the confidence interval.
The alternative hypothesis, H1, has to be one of the following :
'two-sided': H1: difference in means not equal to value (default)
'larger' : H1: difference in means larger than value
'smaller' : H1: difference in means smaller than value
usevar : str, 'pooled' or 'unequal'
If ``pooled``, then the standard deviation of the samples is assumed to be
the same. If ``unequal``, then Welch ttest with Satterthwait degrees
of freedom is used
Returns
-------
lower, upper : floats
lower and upper limits of the confidence interval
Notes
-----
The result is independent of the user specified ddof.
"""
d1 = self.d1
d2 = self.d2
diff = d1.mean - d2.mean
if usevar == "pooled":
std_diff = self.std_meandiff_pooledvar
elif usevar == "unequal":
std_diff = self.std_meandiff_separatevar
else:
raise ValueError('usevar can only be "pooled" or "unequal"')
res = _zconfint_generic(
diff, std_diff, alpha=alpha, alternative=alternative
)
return res | confidence interval for the difference in means
Parameters
----------
alpha : float
significance level for the confidence interval, coverage is
``1-alpha``
alternative : str
This specifies the alternative hypothesis for the test that
corresponds to the confidence interval.
The alternative hypothesis, H1, has to be one of the following :
'two-sided': H1: difference in means not equal to value (default)
'larger' : H1: difference in means larger than value
'smaller' : H1: difference in means smaller than value
usevar : str, 'pooled' or 'unequal'
If ``pooled``, then the standard deviation of the samples is assumed to be
the same. If ``unequal``, then Welch ttest with Satterthwait degrees
of freedom is used
Returns
-------
lower, upper : floats
lower and upper limits of the confidence interval
Notes
-----
The result is independent of the user specified ddof. | zconfint_diff | python | statsmodels/statsmodels | statsmodels/stats/weightstats.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/stats/weightstats.py | BSD-3-Clause |
def ttost_ind(self, low, upp, usevar="pooled"):
"""
test of equivalence for two independent samples, base on t-test
Parameters
----------
low, upp : float
equivalence interval low < m1 - m2 < upp
usevar : str, 'pooled' or 'unequal'
If ``pooled``, then the standard deviation of the samples is assumed to be
the same. If ``unequal``, then Welch ttest with Satterthwait degrees
of freedom is used
Returns
-------
pvalue : float
pvalue of the non-equivalence test
t1, pv1 : tuple of floats
test statistic and pvalue for lower threshold test
t2, pv2 : tuple of floats
test statistic and pvalue for upper threshold test
"""
tt1 = self.ttest_ind(alternative="larger", usevar=usevar, value=low)
tt2 = self.ttest_ind(alternative="smaller", usevar=usevar, value=upp)
# TODO: remove tuple return, use same as for function tost_ind
return np.maximum(tt1[1], tt2[1]), (tt1, tt2) | test of equivalence for two independent samples, base on t-test
Parameters
----------
low, upp : float
equivalence interval low < m1 - m2 < upp
usevar : str, 'pooled' or 'unequal'
If ``pooled``, then the standard deviation of the samples is assumed to be
the same. If ``unequal``, then Welch ttest with Satterthwait degrees
of freedom is used
Returns
-------
pvalue : float
pvalue of the non-equivalence test
t1, pv1 : tuple of floats
test statistic and pvalue for lower threshold test
t2, pv2 : tuple of floats
test statistic and pvalue for upper threshold test | ttost_ind | python | statsmodels/statsmodels | statsmodels/stats/weightstats.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/stats/weightstats.py | BSD-3-Clause |
def ztost_ind(self, low, upp, usevar="pooled"):
"""
test of equivalence for two independent samples, based on z-test
Parameters
----------
low, upp : float
equivalence interval low < m1 - m2 < upp
usevar : str, 'pooled' or 'unequal'
If ``pooled``, then the standard deviation of the samples is assumed to be
the same. If ``unequal``, then Welch ttest with Satterthwait degrees
of freedom is used
Returns
-------
pvalue : float
pvalue of the non-equivalence test
t1, pv1 : tuple of floats
test statistic and pvalue for lower threshold test
t2, pv2 : tuple of floats
test statistic and pvalue for upper threshold test
"""
tt1 = self.ztest_ind(alternative="larger", usevar=usevar, value=low)
tt2 = self.ztest_ind(alternative="smaller", usevar=usevar, value=upp)
# TODO: remove tuple return, use same as for function tost_ind
return np.maximum(tt1[1], tt2[1]), tt1, tt2 | test of equivalence for two independent samples, based on z-test
Parameters
----------
low, upp : float
equivalence interval low < m1 - m2 < upp
usevar : str, 'pooled' or 'unequal'
If ``pooled``, then the standard deviation of the samples is assumed to be
the same. If ``unequal``, then Welch ttest with Satterthwait degrees
of freedom is used
Returns
-------
pvalue : float
pvalue of the non-equivalence test
t1, pv1 : tuple of floats
test statistic and pvalue for lower threshold test
t2, pv2 : tuple of floats
test statistic and pvalue for upper threshold test | ztost_ind | python | statsmodels/statsmodels | statsmodels/stats/weightstats.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/stats/weightstats.py | BSD-3-Clause |
def ttest_ind(
x1,
x2,
alternative="two-sided",
usevar="pooled",
weights=(None, None),
value=0,
):
"""ttest independent sample
Convenience function that uses the classes and throws away the intermediate
results,
compared to scipy stats: drops axis option, adds alternative, usevar, and
weights option.
Parameters
----------
x1 : array_like, 1-D or 2-D
first of the two independent samples, see notes for 2-D case
x2 : array_like, 1-D or 2-D
second of the two independent samples, see notes for 2-D case
alternative : str
The alternative hypothesis, H1, has to be one of the following
* 'two-sided' (default): H1: difference in means not equal to value
* 'larger' : H1: difference in means larger than value
* 'smaller' : H1: difference in means smaller than value
usevar : str, 'pooled' or 'unequal'
If ``pooled``, then the standard deviation of the samples is assumed to be
the same. If ``unequal``, then Welch ttest with Satterthwait degrees
of freedom is used
weights : tuple of None or ndarrays
Case weights for the two samples. For details on weights see
``DescrStatsW``
value : float
difference between the means under the Null hypothesis.
Returns
-------
tstat : float
test statistic
pvalue : float
pvalue of the t-test
df : int or float
degrees of freedom used in the t-test
"""
cm = CompareMeans(
DescrStatsW(x1, weights=weights[0], ddof=0),
DescrStatsW(x2, weights=weights[1], ddof=0),
)
tstat, pval, dof = cm.ttest_ind(
alternative=alternative, usevar=usevar, value=value
)
return tstat, pval, dof | ttest independent sample
Convenience function that uses the classes and throws away the intermediate
results,
compared to scipy stats: drops axis option, adds alternative, usevar, and
weights option.
Parameters
----------
x1 : array_like, 1-D or 2-D
first of the two independent samples, see notes for 2-D case
x2 : array_like, 1-D or 2-D
second of the two independent samples, see notes for 2-D case
alternative : str
The alternative hypothesis, H1, has to be one of the following
* 'two-sided' (default): H1: difference in means not equal to value
* 'larger' : H1: difference in means larger than value
* 'smaller' : H1: difference in means smaller than value
usevar : str, 'pooled' or 'unequal'
If ``pooled``, then the standard deviation of the samples is assumed to be
the same. If ``unequal``, then Welch ttest with Satterthwait degrees
of freedom is used
weights : tuple of None or ndarrays
Case weights for the two samples. For details on weights see
``DescrStatsW``
value : float
difference between the means under the Null hypothesis.
Returns
-------
tstat : float
test statistic
pvalue : float
pvalue of the t-test
df : int or float
degrees of freedom used in the t-test | ttest_ind | python | statsmodels/statsmodels | statsmodels/stats/weightstats.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/stats/weightstats.py | BSD-3-Clause |
def ttost_ind(
x1, x2, low, upp, usevar="pooled", weights=(None, None), transform=None
):
"""test of (non-)equivalence for two independent samples
TOST: two one-sided t tests
null hypothesis: m1 - m2 < low or m1 - m2 > upp
alternative hypothesis: low < m1 - m2 < upp
where m1, m2 are the means, expected values of the two samples.
If the pvalue is smaller than a threshold, say 0.05, then we reject the
hypothesis that the difference between the two samples is larger than the
the thresholds given by low and upp.
Parameters
----------
x1 : array_like, 1-D or 2-D
first of the two independent samples, see notes for 2-D case
x2 : array_like, 1-D or 2-D
second of the two independent samples, see notes for 2-D case
low, upp : float
equivalence interval low < m1 - m2 < upp
usevar : str, 'pooled' or 'unequal'
If ``pooled``, then the standard deviation of the samples is assumed to be
the same. If ``unequal``, then Welch ttest with Satterthwait degrees
of freedom is used
weights : tuple of None or ndarrays
Case weights for the two samples. For details on weights see
``DescrStatsW``
transform : None or function
If None (default), then the data is not transformed. Given a function,
sample data and thresholds are transformed. If transform is log, then
the equivalence interval is in ratio: low < m1 / m2 < upp
Returns
-------
pvalue : float
pvalue of the non-equivalence test
t1, pv1 : tuple of floats
test statistic and pvalue for lower threshold test
t2, pv2 : tuple of floats
test statistic and pvalue for upper threshold test
Notes
-----
The test rejects if the 2*alpha confidence interval for the difference
is contained in the ``(low, upp)`` interval.
This test works also for multi-endpoint comparisons: If d1 and d2
have the same number of columns, then each column of the data in d1 is
compared with the corresponding column in d2. This is the same as
comparing each of the corresponding columns separately. Currently no
multi-comparison correction is used. The raw p-values reported here can
be correction with the functions in ``multitest``.
"""
if transform:
if transform is np.log:
# avoid hstack in special case
x1 = transform(x1)
x2 = transform(x2)
else:
# for transforms like rankdata that will need both datasets
# concatenate works for stacking 1d and 2d arrays
xx = transform(np.concatenate((x1, x2), 0))
x1 = xx[: len(x1)]
x2 = xx[len(x1) :]
low = transform(low)
upp = transform(upp)
cm = CompareMeans(
DescrStatsW(x1, weights=weights[0], ddof=0),
DescrStatsW(x2, weights=weights[1], ddof=0),
)
pval, res = cm.ttost_ind(low, upp, usevar=usevar)
return pval, res[0], res[1] | test of (non-)equivalence for two independent samples
TOST: two one-sided t tests
null hypothesis: m1 - m2 < low or m1 - m2 > upp
alternative hypothesis: low < m1 - m2 < upp
where m1, m2 are the means, expected values of the two samples.
If the pvalue is smaller than a threshold, say 0.05, then we reject the
hypothesis that the difference between the two samples is larger than the
the thresholds given by low and upp.
Parameters
----------
x1 : array_like, 1-D or 2-D
first of the two independent samples, see notes for 2-D case
x2 : array_like, 1-D or 2-D
second of the two independent samples, see notes for 2-D case
low, upp : float
equivalence interval low < m1 - m2 < upp
usevar : str, 'pooled' or 'unequal'
If ``pooled``, then the standard deviation of the samples is assumed to be
the same. If ``unequal``, then Welch ttest with Satterthwait degrees
of freedom is used
weights : tuple of None or ndarrays
Case weights for the two samples. For details on weights see
``DescrStatsW``
transform : None or function
If None (default), then the data is not transformed. Given a function,
sample data and thresholds are transformed. If transform is log, then
the equivalence interval is in ratio: low < m1 / m2 < upp
Returns
-------
pvalue : float
pvalue of the non-equivalence test
t1, pv1 : tuple of floats
test statistic and pvalue for lower threshold test
t2, pv2 : tuple of floats
test statistic and pvalue for upper threshold test
Notes
-----
The test rejects if the 2*alpha confidence interval for the difference
is contained in the ``(low, upp)`` interval.
This test works also for multi-endpoint comparisons: If d1 and d2
have the same number of columns, then each column of the data in d1 is
compared with the corresponding column in d2. This is the same as
comparing each of the corresponding columns separately. Currently no
multi-comparison correction is used. The raw p-values reported here can
be correction with the functions in ``multitest``. | ttost_ind | python | statsmodels/statsmodels | statsmodels/stats/weightstats.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/stats/weightstats.py | BSD-3-Clause |
def ttost_paired(x1, x2, low, upp, transform=None, weights=None):
"""test of (non-)equivalence for two dependent, paired sample
TOST: two one-sided t tests
null hypothesis: md < low or md > upp
alternative hypothesis: low < md < upp
where md is the mean, expected value of the difference x1 - x2
If the pvalue is smaller than a threshold,say 0.05, then we reject the
hypothesis that the difference between the two samples is larger than the
the thresholds given by low and upp.
Parameters
----------
x1 : array_like
first of the two independent samples
x2 : array_like
second of the two independent samples
low, upp : float
equivalence interval low < mean of difference < upp
weights : None or ndarray
case weights for the two samples. For details on weights see
``DescrStatsW``
transform : None or function
If None (default), then the data is not transformed. Given a function
sample data and thresholds are transformed. If transform is log the
the equivalence interval is in ratio: low < x1 / x2 < upp
Returns
-------
pvalue : float
pvalue of the non-equivalence test
t1, pv1, df1 : tuple
test statistic, pvalue and degrees of freedom for lower threshold test
t2, pv2, df2 : tuple
test statistic, pvalue and degrees of freedom for upper threshold test
"""
if transform:
if transform is np.log:
# avoid hstack in special case
x1 = transform(x1)
x2 = transform(x2)
else:
# for transforms like rankdata that will need both datasets
# concatenate works for stacking 1d and 2d arrays
xx = transform(np.concatenate((x1, x2), 0))
x1 = xx[: len(x1)]
x2 = xx[len(x1) :]
low = transform(low)
upp = transform(upp)
dd = DescrStatsW(x1 - x2, weights=weights, ddof=0)
t1, pv1, df1 = dd.ttest_mean(low, alternative="larger")
t2, pv2, df2 = dd.ttest_mean(upp, alternative="smaller")
return np.maximum(pv1, pv2), (t1, pv1, df1), (t2, pv2, df2) | test of (non-)equivalence for two dependent, paired sample
TOST: two one-sided t tests
null hypothesis: md < low or md > upp
alternative hypothesis: low < md < upp
where md is the mean, expected value of the difference x1 - x2
If the pvalue is smaller than a threshold,say 0.05, then we reject the
hypothesis that the difference between the two samples is larger than the
the thresholds given by low and upp.
Parameters
----------
x1 : array_like
first of the two independent samples
x2 : array_like
second of the two independent samples
low, upp : float
equivalence interval low < mean of difference < upp
weights : None or ndarray
case weights for the two samples. For details on weights see
``DescrStatsW``
transform : None or function
If None (default), then the data is not transformed. Given a function
sample data and thresholds are transformed. If transform is log the
the equivalence interval is in ratio: low < x1 / x2 < upp
Returns
-------
pvalue : float
pvalue of the non-equivalence test
t1, pv1, df1 : tuple
test statistic, pvalue and degrees of freedom for lower threshold test
t2, pv2, df2 : tuple
test statistic, pvalue and degrees of freedom for upper threshold test | ttost_paired | python | statsmodels/statsmodels | statsmodels/stats/weightstats.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/stats/weightstats.py | BSD-3-Clause |
def ztest(
x1, x2=None, value=0, alternative="two-sided", usevar="pooled", ddof=1.0
):
"""test for mean based on normal distribution, one or two samples
In the case of two samples, the samples are assumed to be independent.
Parameters
----------
x1 : array_like, 1-D or 2-D
first of the two independent samples
x2 : array_like, 1-D or 2-D
second of the two independent samples
value : float
In the one sample case, value is the mean of x1 under the Null
hypothesis.
In the two sample case, value is the difference between mean of x1 and
mean of x2 under the Null hypothesis. The test statistic is
`x1_mean - x2_mean - value`.
alternative : str
The alternative hypothesis, H1, has to be one of the following
'two-sided': H1: difference in means not equal to value (default)
'larger' : H1: difference in means larger than value
'smaller' : H1: difference in means smaller than value
usevar : str, 'pooled' or 'unequal'
If ``pooled``, then the standard deviation of the samples is assumed to be
the same. If ``unequal``, then the standard deviation of the sample is
assumed to be different.
ddof : int
Degrees of freedom use in the calculation of the variance of the mean
estimate. In the case of comparing means this is one, however it can
be adjusted for testing other statistics (proportion, correlation)
Returns
-------
tstat : float
test statistic
pvalue : float
pvalue of the z-test
Notes
-----
usevar can be pooled or unequal in two sample case
"""
# TODO: this should delegate to CompareMeans like ttest_ind
# However that does not implement ddof
# usevar can be pooled or unequal
if usevar not in {"pooled", "unequal"}:
raise NotImplementedError('usevar can only be "pooled" or "unequal"')
x1 = np.asarray(x1)
nobs1 = x1.shape[0]
x1_mean = x1.mean(0)
x1_var = x1.var(0)
if x2 is not None:
x2 = np.asarray(x2)
nobs2 = x2.shape[0]
x2_mean = x2.mean(0)
x2_var = x2.var(0)
if usevar == "pooled":
var = nobs1 * x1_var + nobs2 * x2_var
var /= nobs1 + nobs2 - 2 * ddof
var *= 1.0 / nobs1 + 1.0 / nobs2
elif usevar == "unequal":
var = x1_var / (nobs1 - ddof) + x2_var / (nobs2 - ddof)
else:
var = x1_var / (nobs1 - ddof)
x2_mean = 0
std_diff = np.sqrt(var)
# stat = x1_mean - x2_mean - value
return _zstat_generic(x1_mean, x2_mean, std_diff, alternative, diff=value) | test for mean based on normal distribution, one or two samples
In the case of two samples, the samples are assumed to be independent.
Parameters
----------
x1 : array_like, 1-D or 2-D
first of the two independent samples
x2 : array_like, 1-D or 2-D
second of the two independent samples
value : float
In the one sample case, value is the mean of x1 under the Null
hypothesis.
In the two sample case, value is the difference between mean of x1 and
mean of x2 under the Null hypothesis. The test statistic is
`x1_mean - x2_mean - value`.
alternative : str
The alternative hypothesis, H1, has to be one of the following
'two-sided': H1: difference in means not equal to value (default)
'larger' : H1: difference in means larger than value
'smaller' : H1: difference in means smaller than value
usevar : str, 'pooled' or 'unequal'
If ``pooled``, then the standard deviation of the samples is assumed to be
the same. If ``unequal``, then the standard deviation of the sample is
assumed to be different.
ddof : int
Degrees of freedom use in the calculation of the variance of the mean
estimate. In the case of comparing means this is one, however it can
be adjusted for testing other statistics (proportion, correlation)
Returns
-------
tstat : float
test statistic
pvalue : float
pvalue of the z-test
Notes
-----
usevar can be pooled or unequal in two sample case | ztest | python | statsmodels/statsmodels | statsmodels/stats/weightstats.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/stats/weightstats.py | BSD-3-Clause |
def zconfint(
x1,
x2=None,
value=0,
alpha=0.05,
alternative="two-sided",
usevar="pooled",
ddof=1.0,
):
"""confidence interval based on normal distribution z-test
Parameters
----------
x1 : array_like, 1-D or 2-D
first of the two independent samples, see notes for 2-D case
x2 : array_like, 1-D or 2-D
second of the two independent samples, see notes for 2-D case
value : float
In the one sample case, value is the mean of x1 under the Null
hypothesis.
In the two sample case, value is the difference between mean of x1 and
mean of x2 under the Null hypothesis. The test statistic is
`x1_mean - x2_mean - value`.
usevar : str, 'pooled'
Currently, only 'pooled' is implemented.
If ``pooled``, then the standard deviation of the samples is assumed to be
the same. see CompareMeans.ztest_ind for different options.
ddof : int
Degrees of freedom use in the calculation of the variance of the mean
estimate. In the case of comparing means this is one, however it can
be adjusted for testing other statistics (proportion, correlation)
Notes
-----
checked only for 1 sample case
usevar not implemented, is always pooled in two sample case
``value`` shifts the confidence interval so it is centered at
`x1_mean - x2_mean - value`
See Also
--------
ztest
CompareMeans
"""
# usevar is not used, always pooled
# mostly duplicate code from ztest
if usevar != "pooled":
raise NotImplementedError('only usevar="pooled" is implemented')
x1 = np.asarray(x1)
nobs1 = x1.shape[0]
x1_mean = x1.mean(0)
x1_var = x1.var(0)
if x2 is not None:
x2 = np.asarray(x2)
nobs2 = x2.shape[0]
x2_mean = x2.mean(0)
x2_var = x2.var(0)
var_pooled = nobs1 * x1_var + nobs2 * x2_var
var_pooled /= nobs1 + nobs2 - 2 * ddof
var_pooled *= 1.0 / nobs1 + 1.0 / nobs2
else:
var_pooled = x1_var / (nobs1 - ddof)
x2_mean = 0
std_diff = np.sqrt(var_pooled)
ci = _zconfint_generic(
x1_mean - x2_mean - value, std_diff, alpha, alternative
)
return ci | confidence interval based on normal distribution z-test
Parameters
----------
x1 : array_like, 1-D or 2-D
first of the two independent samples, see notes for 2-D case
x2 : array_like, 1-D or 2-D
second of the two independent samples, see notes for 2-D case
value : float
In the one sample case, value is the mean of x1 under the Null
hypothesis.
In the two sample case, value is the difference between mean of x1 and
mean of x2 under the Null hypothesis. The test statistic is
`x1_mean - x2_mean - value`.
usevar : str, 'pooled'
Currently, only 'pooled' is implemented.
If ``pooled``, then the standard deviation of the samples is assumed to be
the same. see CompareMeans.ztest_ind for different options.
ddof : int
Degrees of freedom use in the calculation of the variance of the mean
estimate. In the case of comparing means this is one, however it can
be adjusted for testing other statistics (proportion, correlation)
Notes
-----
checked only for 1 sample case
usevar not implemented, is always pooled in two sample case
``value`` shifts the confidence interval so it is centered at
`x1_mean - x2_mean - value`
See Also
--------
ztest
CompareMeans | zconfint | python | statsmodels/statsmodels | statsmodels/stats/weightstats.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/stats/weightstats.py | BSD-3-Clause |
def ztost(x1, low, upp, x2=None, usevar="pooled", ddof=1.0):
"""Equivalence test based on normal distribution
Parameters
----------
x1 : array_like
one sample or first sample for 2 independent samples
low, upp : float
equivalence interval low < m1 - m2 < upp
x1 : array_like or None
second sample for 2 independent samples test. If None, then a
one-sample test is performed.
usevar : str, 'pooled'
If `pooled`, then the standard deviation of the samples is assumed to be
the same. Only `pooled` is currently implemented.
Returns
-------
pvalue : float
pvalue of the non-equivalence test
t1, pv1 : tuple of floats
test statistic and pvalue for lower threshold test
t2, pv2 : tuple of floats
test statistic and pvalue for upper threshold test
Notes
-----
checked only for 1 sample case
"""
tt1 = ztest(
x1, x2, alternative="larger", usevar=usevar, value=low, ddof=ddof
)
tt2 = ztest(
x1, x2, alternative="smaller", usevar=usevar, value=upp, ddof=ddof
)
return (
np.maximum(tt1[1], tt2[1]),
tt1,
tt2,
) | Equivalence test based on normal distribution
Parameters
----------
x1 : array_like
one sample or first sample for 2 independent samples
low, upp : float
equivalence interval low < m1 - m2 < upp
x1 : array_like or None
second sample for 2 independent samples test. If None, then a
one-sample test is performed.
usevar : str, 'pooled'
If `pooled`, then the standard deviation of the samples is assumed to be
the same. Only `pooled` is currently implemented.
Returns
-------
pvalue : float
pvalue of the non-equivalence test
t1, pv1 : tuple of floats
test statistic and pvalue for lower threshold test
t2, pv2 : tuple of floats
test statistic and pvalue for upper threshold test
Notes
-----
checked only for 1 sample case | ztost | python | statsmodels/statsmodels | statsmodels/stats/weightstats.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/stats/weightstats.py | BSD-3-Clause |
def outlier_test(model_results, method='bonf', alpha=.05, labels=None,
order=False, cutoff=None):
"""
Outlier Tests for RegressionResults instances.
Parameters
----------
model_results : RegressionResults
Linear model results
method : str
- `bonferroni` : one-step correction
- `sidak` : one-step correction
- `holm-sidak` :
- `holm` :
- `simes-hochberg` :
- `hommel` :
- `fdr_bh` : Benjamini/Hochberg
- `fdr_by` : Benjamini/Yekutieli
See `statsmodels.stats.multitest.multipletests` for details.
alpha : float
familywise error rate
labels : None or array_like
If `labels` is not None, then it will be used as index to the
returned pandas DataFrame. See also Returns below
order : bool
Whether or not to order the results by the absolute value of the
studentized residuals. If labels are provided they will also be sorted.
cutoff : None or float in [0, 1]
If cutoff is not None, then the return only includes observations with
multiple testing corrected p-values strictly below the cutoff. The
returned array or dataframe can be empty if there are no outlier
candidates at the specified cutoff.
Returns
-------
table : ndarray or DataFrame
Returns either an ndarray or a DataFrame if labels is not None.
Will attempt to get labels from model_results if available. The
columns are the Studentized residuals, the unadjusted p-value,
and the corrected p-value according to method.
Notes
-----
The unadjusted p-value is stats.t.sf(abs(resid), df) where
df = df_resid - 1.
"""
from scipy import stats # lazy import
if labels is None:
labels = getattr(model_results.model.data, 'row_labels', None)
infl = getattr(model_results, 'get_influence', None)
if infl is None:
results = maybe_unwrap_results(model_results)
raise AttributeError("model_results object %s does not have a "
"get_influence "
"method." % results.__class__.__name__)
resid = infl().resid_studentized_external
if order:
idx = np.abs(resid).argsort()[::-1]
resid = resid[idx]
if labels is not None:
labels = np.asarray(labels)[idx]
df = model_results.df_resid - 1
unadj_p = stats.t.sf(np.abs(resid), df) * 2
adj_p = multipletests(unadj_p, alpha=alpha, method=method)
data = np.c_[resid, unadj_p, adj_p[1]]
if cutoff is not None:
mask = data[:, -1] < cutoff
data = data[mask]
else:
mask = slice(None)
if labels is not None:
from pandas import DataFrame
return DataFrame(data,
columns=['student_resid', 'unadj_p', method + "(p)"],
index=np.asarray(labels)[mask])
return data | Outlier Tests for RegressionResults instances.
Parameters
----------
model_results : RegressionResults
Linear model results
method : str
- `bonferroni` : one-step correction
- `sidak` : one-step correction
- `holm-sidak` :
- `holm` :
- `simes-hochberg` :
- `hommel` :
- `fdr_bh` : Benjamini/Hochberg
- `fdr_by` : Benjamini/Yekutieli
See `statsmodels.stats.multitest.multipletests` for details.
alpha : float
familywise error rate
labels : None or array_like
If `labels` is not None, then it will be used as index to the
returned pandas DataFrame. See also Returns below
order : bool
Whether or not to order the results by the absolute value of the
studentized residuals. If labels are provided they will also be sorted.
cutoff : None or float in [0, 1]
If cutoff is not None, then the return only includes observations with
multiple testing corrected p-values strictly below the cutoff. The
returned array or dataframe can be empty if there are no outlier
candidates at the specified cutoff.
Returns
-------
table : ndarray or DataFrame
Returns either an ndarray or a DataFrame if labels is not None.
Will attempt to get labels from model_results if available. The
columns are the Studentized residuals, the unadjusted p-value,
and the corrected p-value according to method.
Notes
-----
The unadjusted p-value is stats.t.sf(abs(resid), df) where
df = df_resid - 1. | outlier_test | python | statsmodels/statsmodels | statsmodels/stats/outliers_influence.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/stats/outliers_influence.py | BSD-3-Clause |
def reset_ramsey(res, degree=5):
"""Ramsey's RESET specification test for linear models
This is a general specification test, for additional non-linear effects
in a model.
Parameters
----------
degree : int
Maximum power to include in the RESET test. Powers 0 and 1 are
excluded, so that degree tests powers 2, ..., degree of the fitted
values.
Notes
-----
The test fits an auxiliary OLS regression where the design matrix, exog,
is augmented by powers 2 to degree of the fitted values. Then it performs
an F-test whether these additional terms are significant.
If the p-value of the f-test is below a threshold, e.g. 0.1, then this
indicates that there might be additional non-linear effects in the model
and that the linear model is mis-specified.
References
----------
https://en.wikipedia.org/wiki/Ramsey_RESET_test
"""
order = degree + 1
k_vars = res.model.exog.shape[1]
# vander without constant and x, and drop constant
norm_values = np.asarray(res.fittedvalues)
norm_values = norm_values / np.sqrt((norm_values ** 2).mean())
y_fitted_vander = np.vander(norm_values, order)[:, :-2]
exog = np.column_stack((res.model.exog, y_fitted_vander))
exog /= np.sqrt((exog ** 2).mean(0))
endog = res.model.endog / (res.model.endog ** 2).mean()
res_aux = OLS(endog, exog).fit()
# r_matrix = np.eye(degree, exog.shape[1], k_vars)
r_matrix = np.eye(degree - 1, exog.shape[1], k_vars)
# df1 = degree - 1
# df2 = exog.shape[0] - degree - res.df_model (without constant)
return res_aux.f_test(r_matrix) # , r_matrix, res_aux | Ramsey's RESET specification test for linear models
This is a general specification test, for additional non-linear effects
in a model.
Parameters
----------
degree : int
Maximum power to include in the RESET test. Powers 0 and 1 are
excluded, so that degree tests powers 2, ..., degree of the fitted
values.
Notes
-----
The test fits an auxiliary OLS regression where the design matrix, exog,
is augmented by powers 2 to degree of the fitted values. Then it performs
an F-test whether these additional terms are significant.
If the p-value of the f-test is below a threshold, e.g. 0.1, then this
indicates that there might be additional non-linear effects in the model
and that the linear model is mis-specified.
References
----------
https://en.wikipedia.org/wiki/Ramsey_RESET_test | reset_ramsey | python | statsmodels/statsmodels | statsmodels/stats/outliers_influence.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/stats/outliers_influence.py | BSD-3-Clause |
def variance_inflation_factor(exog, exog_idx):
"""
Variance inflation factor, VIF, for one exogenous variable
The variance inflation factor is a measure for the increase of the
variance of the parameter estimates if an additional variable, given by
exog_idx is added to the linear regression. It is a measure for
multicollinearity of the design matrix, exog.
One recommendation is that if VIF is greater than 5, then the explanatory
variable given by exog_idx is highly collinear with the other explanatory
variables, and the parameter estimates will have large standard errors
because of this.
Parameters
----------
exog : {ndarray, DataFrame}
design matrix with all explanatory variables, as for example used in
regression
exog_idx : int
index of the exogenous variable in the columns of exog
Returns
-------
float
variance inflation factor
Notes
-----
This function does not save the auxiliary regression.
See Also
--------
xxx : class for regression diagnostics TODO: does not exist yet
References
----------
https://en.wikipedia.org/wiki/Variance_inflation_factor
"""
k_vars = exog.shape[1]
exog = np.asarray(exog)
x_i = exog[:, exog_idx]
mask = np.arange(k_vars) != exog_idx
x_noti = exog[:, mask]
r_squared_i = OLS(x_i, x_noti).fit().rsquared
vif = 1. / (1. - r_squared_i)
return vif | Variance inflation factor, VIF, for one exogenous variable
The variance inflation factor is a measure for the increase of the
variance of the parameter estimates if an additional variable, given by
exog_idx is added to the linear regression. It is a measure for
multicollinearity of the design matrix, exog.
One recommendation is that if VIF is greater than 5, then the explanatory
variable given by exog_idx is highly collinear with the other explanatory
variables, and the parameter estimates will have large standard errors
because of this.
Parameters
----------
exog : {ndarray, DataFrame}
design matrix with all explanatory variables, as for example used in
regression
exog_idx : int
index of the exogenous variable in the columns of exog
Returns
-------
float
variance inflation factor
Notes
-----
This function does not save the auxiliary regression.
See Also
--------
xxx : class for regression diagnostics TODO: does not exist yet
References
----------
https://en.wikipedia.org/wiki/Variance_inflation_factor | variance_inflation_factor | python | statsmodels/statsmodels | statsmodels/stats/outliers_influence.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/stats/outliers_influence.py | BSD-3-Clause |
def plot_index(self, y_var='cooks', threshold=None, title=None, ax=None,
idx=None, **kwds):
"""index plot for influence attributes
Parameters
----------
y_var : str
Name of attribute or shortcut for predefined attributes that will
be plotted on the y-axis.
threshold : None or float
Threshold for adding annotation with observation labels.
Observations for which the absolute value of the y_var is larger
than the threshold will be annotated. Set to a negative number to
label all observations or to a large number to have no annotation.
title : str
If provided, the title will replace the default "Index Plot" title.
ax : matplolib axis instance
The plot will be added to the `ax` if provided, otherwise a new
figure is created.
idx : {None, int}
Some attributes require an additional index to select the y-var.
In dfbetas this refers to the column indes.
kwds : optional keywords
Keywords will be used in the call to matplotlib scatter function.
"""
criterion = y_var # alias
if threshold is None:
# TODO: criterion specific defaults
threshold = 'all'
if criterion == 'dfbeta':
y = self.dfbetas[:, idx]
ylabel = 'DFBETA for ' + self.results.model.exog_names[idx]
elif criterion.startswith('cook'):
y = self.cooks_distance[0]
ylabel = "Cook's distance"
elif criterion.startswith('hat') or criterion.startswith('lever'):
y = self.hat_matrix_diag
ylabel = "Leverage (diagonal of hat matrix)"
elif criterion.startswith('cook'):
y = self.cooks_distance[0]
ylabel = "Cook's distance"
elif criterion.startswith('resid_stu'):
y = self.resid_studentized
ylabel = "Internally Studentized Residuals"
else:
# assume we have the name of an attribute
y = getattr(self, y_var)
if idx is not None:
y = y[idx]
ylabel = y_var
fig = self._plot_index(y, ylabel, threshold=threshold, title=title,
ax=ax, **kwds)
return fig | index plot for influence attributes
Parameters
----------
y_var : str
Name of attribute or shortcut for predefined attributes that will
be plotted on the y-axis.
threshold : None or float
Threshold for adding annotation with observation labels.
Observations for which the absolute value of the y_var is larger
than the threshold will be annotated. Set to a negative number to
label all observations or to a large number to have no annotation.
title : str
If provided, the title will replace the default "Index Plot" title.
ax : matplolib axis instance
The plot will be added to the `ax` if provided, otherwise a new
figure is created.
idx : {None, int}
Some attributes require an additional index to select the y-var.
In dfbetas this refers to the column indes.
kwds : optional keywords
Keywords will be used in the call to matplotlib scatter function. | plot_index | python | statsmodels/statsmodels | statsmodels/stats/outliers_influence.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/stats/outliers_influence.py | BSD-3-Clause |
def hat_matrix_diag(self):
"""Diagonal of the generalized leverage
This is the analogue of the hat matrix diagonal for general MLE.
"""
if hasattr(self, '_hat_matrix_diag'):
return self._hat_matrix_diag
try:
dsdy = self.results.model._deriv_score_obs_dendog(
self.results.params)
except NotImplementedError:
dsdy = None
if dsdy is None:
warnings.warn("hat matrix is not available, missing derivatives",
UserWarning)
return None
dmu_dp = self.results.model._deriv_mean_dparams(self.results.params)
# dmu_dp = 1 /
# self.results.model.family.link.deriv(self.results.fittedvalues)
h = (dmu_dp * np.linalg.solve(-self.hessian, dsdy.T).T).sum(1)
return h | Diagonal of the generalized leverage
This is the analogue of the hat matrix diagonal for general MLE. | hat_matrix_diag | python | statsmodels/statsmodels | statsmodels/stats/outliers_influence.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/stats/outliers_influence.py | BSD-3-Clause |
def hat_matrix_exog_diag(self):
"""Diagonal of the hat_matrix using only exog as in OLS
"""
get_exogs = getattr(self.results.model, "_get_exogs", None)
if get_exogs is not None:
exog = np.column_stack(get_exogs())
else:
exog = self.exog
return (exog * np.linalg.pinv(exog).T).sum(1) | Diagonal of the hat_matrix using only exog as in OLS | hat_matrix_exog_diag | python | statsmodels/statsmodels | statsmodels/stats/outliers_influence.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/stats/outliers_influence.py | BSD-3-Clause |
def d_params(self):
"""Approximate change in parameter estimates when dropping observation.
This uses one-step approximation of the parameter change to deleting
one observation.
"""
so_noti = self.score_obs.sum(0) - self.score_obs
beta_i = np.linalg.solve(self.hessian, so_noti.T).T
if self.hat_matrix_diag is not None:
beta_i /= (1 - self.hat_matrix_diag)[:, None]
return beta_i | Approximate change in parameter estimates when dropping observation.
This uses one-step approximation of the parameter change to deleting
one observation. | d_params | python | statsmodels/statsmodels | statsmodels/stats/outliers_influence.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/stats/outliers_influence.py | BSD-3-Clause |
def dfbetas(self):
"""Scaled change in parameter estimates.
The one-step change of parameters in d_params is rescaled by dividing
by the standard error of the parameter estimate given by results.bse.
"""
beta_i = self.d_params / self.results.bse
return beta_i | Scaled change in parameter estimates.
The one-step change of parameters in d_params is rescaled by dividing
by the standard error of the parameter estimate given by results.bse. | dfbetas | python | statsmodels/statsmodels | statsmodels/stats/outliers_influence.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/stats/outliers_influence.py | BSD-3-Clause |
def params_one(self):
"""Parameter estimate based on one-step approximation.
This the one step parameter estimate computed as
``params`` from the full sample minus ``d_params``.
"""
return self.results.params - self.d_params | Parameter estimate based on one-step approximation.
This the one step parameter estimate computed as
``params`` from the full sample minus ``d_params``. | params_one | python | statsmodels/statsmodels | statsmodels/stats/outliers_influence.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/stats/outliers_influence.py | BSD-3-Clause |
def cooks_distance(self):
"""Cook's distance and p-values.
Based on one step approximation d_params and on results.cov_params
Cook's distance divides by the number of explanatory variables.
p-values are based on the F-distribution which are only approximate
outside of linear Gaussian models.
Warning: The definition of p-values might change if we switch to using
chi-square distribution instead of F-distribution, or if we make it
dependent on the fit keyword use_t.
"""
cooks_d2 = (self.d_params * np.linalg.solve(self.cov_params,
self.d_params.T).T).sum(1)
cooks_d2 /= self.k_params
from scipy import stats
# alpha = 0.1
# print stats.f.isf(1-alpha, n_params, res.df_modelwc)
# TODO use chi2 # use_f option
pvals = stats.f.sf(cooks_d2, self.k_params, self.results.df_resid)
return cooks_d2, pvals | Cook's distance and p-values.
Based on one step approximation d_params and on results.cov_params
Cook's distance divides by the number of explanatory variables.
p-values are based on the F-distribution which are only approximate
outside of linear Gaussian models.
Warning: The definition of p-values might change if we switch to using
chi-square distribution instead of F-distribution, or if we make it
dependent on the fit keyword use_t. | cooks_distance | python | statsmodels/statsmodels | statsmodels/stats/outliers_influence.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/stats/outliers_influence.py | BSD-3-Clause |
def resid_studentized(self):
"""studentized default residuals.
This uses the residual in `resid` attribute, which is by default
resid_pearson and studentizes is using the generalized leverage.
self.resid / np.sqrt(1 - self.hat_matrix_diag)
Studentized residuals are not available if hat_matrix_diag is None.
"""
return self.resid / np.sqrt(1 - self.hat_matrix_diag) | studentized default residuals.
This uses the residual in `resid` attribute, which is by default
resid_pearson and studentizes is using the generalized leverage.
self.resid / np.sqrt(1 - self.hat_matrix_diag)
Studentized residuals are not available if hat_matrix_diag is None. | resid_studentized | python | statsmodels/statsmodels | statsmodels/stats/outliers_influence.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/stats/outliers_influence.py | BSD-3-Clause |
def resid_score_factor(self):
"""Score residual divided by sqrt of hessian factor.
experimental, agrees with GLMInfluence for Binomial and Gaussian.
This corresponds to considering the linear predictors as parameters
of the model.
Note: Nhis might have nan values if second derivative, hessian_factor,
is positive, i.e. loglikelihood is not globally concave w.r.t. linear
predictor. (This occured in an example for GeneralizedPoisson)
"""
from statsmodels.genmod.generalized_linear_model import GLM
sf = self.results.model.score_factor(self.results.params)
hf = self.results.model.hessian_factor(self.results.params)
if isinstance(sf, tuple):
sf = sf[0]
if isinstance(hf, tuple):
hf = hf[0]
if not isinstance(self.results.model, GLM):
# hessian_factor in GLM has wrong sign, is already positive
hf = -hf
return sf / np.sqrt(hf) / np.sqrt(1 - self.hat_matrix_diag) | Score residual divided by sqrt of hessian factor.
experimental, agrees with GLMInfluence for Binomial and Gaussian.
This corresponds to considering the linear predictors as parameters
of the model.
Note: Nhis might have nan values if second derivative, hessian_factor,
is positive, i.e. loglikelihood is not globally concave w.r.t. linear
predictor. (This occured in an example for GeneralizedPoisson) | resid_score_factor | python | statsmodels/statsmodels | statsmodels/stats/outliers_influence.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/stats/outliers_influence.py | BSD-3-Clause |
def resid_score(self, joint=True, index=None, studentize=False):
"""Score observations scaled by inverse hessian.
Score residual in resid_score are defined in analogy to a score test
statistic for each observation.
Parameters
----------
joint : bool
If joint is true, then a quadratic form similar to score_test is
returned for each observation.
If joint is false, then standardized score_obs are returned. The
returned array is two-dimensional
index : ndarray (optional)
Optional index to select a subset of score_obs columns.
By default, all columns of score_obs will be used.
studentize : bool
If studentize is true, the the scaled residuals are also
studentized using the generalized leverage.
Returns
-------
array : 1-D or 2-D residuals
Notes
-----
Status: experimental
Because of the one srep approacimation of d_params, score residuals
are identical to cooks_distance, except for
- cooks_distance is normalized by the number of parameters
- cooks_distance uses cov_params, resid_score is based on Hessian.
This will make them differ in the case of robust cov_params.
"""
# currently no caching
score_obs = self.results.model.score_obs(self.results.params)
hess = self.results.model.hessian(self.results.params)
if index is not None:
score_obs = score_obs[:, index]
hess = hess[index[:, None], index]
if joint:
resid = (score_obs.T * np.linalg.solve(-hess, score_obs.T)).sum(0)
else:
resid = score_obs / np.sqrt(np.diag(-hess))
if studentize:
if joint:
resid /= np.sqrt(1 - self.hat_matrix_diag)
else:
# 2-dim resid
resid /= np.sqrt(1 - self.hat_matrix_diag[:, None])
return resid | Score observations scaled by inverse hessian.
Score residual in resid_score are defined in analogy to a score test
statistic for each observation.
Parameters
----------
joint : bool
If joint is true, then a quadratic form similar to score_test is
returned for each observation.
If joint is false, then standardized score_obs are returned. The
returned array is two-dimensional
index : ndarray (optional)
Optional index to select a subset of score_obs columns.
By default, all columns of score_obs will be used.
studentize : bool
If studentize is true, the the scaled residuals are also
studentized using the generalized leverage.
Returns
-------
array : 1-D or 2-D residuals
Notes
-----
Status: experimental
Because of the one srep approacimation of d_params, score residuals
are identical to cooks_distance, except for
- cooks_distance is normalized by the number of parameters
- cooks_distance uses cov_params, resid_score is based on Hessian.
This will make them differ in the case of robust cov_params. | resid_score | python | statsmodels/statsmodels | statsmodels/stats/outliers_influence.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/stats/outliers_influence.py | BSD-3-Clause |
def d_fittedvalues(self):
"""Change in expected response, fittedvalues.
Local change of expected mean given the change in the parameters as
computed in d_params.
Notes
-----
This uses the one-step approximation of the parameter change to
deleting one observation ``d_params``.
"""
# results.params might be a pandas.Series
params = np.asarray(self.results.params)
deriv = self.results.model._deriv_mean_dparams(params)
return (deriv * self.d_params).sum(1) | Change in expected response, fittedvalues.
Local change of expected mean given the change in the parameters as
computed in d_params.
Notes
-----
This uses the one-step approximation of the parameter change to
deleting one observation ``d_params``. | d_fittedvalues | python | statsmodels/statsmodels | statsmodels/stats/outliers_influence.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/stats/outliers_influence.py | BSD-3-Clause |
def d_fittedvalues_scaled(self):
"""
Change in fittedvalues scaled by standard errors.
This uses one-step approximation of the parameter change to deleting
one observation ``d_params``, and divides by the standard errors
for the predicted mean provided by results.get_prediction.
"""
# Note: this and the previous methods are for the response
# and not for a weighted response, i.e. not the self.exog, self.endog
# this will be relevant for WLS comparing fitted endog versus wendog
return self.d_fittedvalues / self._get_prediction.se | Change in fittedvalues scaled by standard errors.
This uses one-step approximation of the parameter change to deleting
one observation ``d_params``, and divides by the standard errors
for the predicted mean provided by results.get_prediction. | d_fittedvalues_scaled | python | statsmodels/statsmodels | statsmodels/stats/outliers_influence.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/stats/outliers_influence.py | BSD-3-Clause |
def summary_frame(self):
"""
Creates a DataFrame with influence results.
Returns
-------
frame : pandas DataFrame
A DataFrame with selected results for each observation.
The index will be the same as provided to the model.
Notes
-----
The resultant DataFrame contains six variables in addition to the
``dfbetas``. These are:
* cooks_d : Cook's Distance defined in ``cooks_distance``
* standard_resid : Standardized residuals defined in
`resid_studentizedl`
* hat_diag : The diagonal of the projection, or hat, matrix defined in
`hat_matrix_diag`. Not included if None.
* dffits_internal : DFFITS statistics using internally Studentized
residuals defined in `d_fittedvalues_scaled`
"""
from pandas import DataFrame
# row and column labels
data = self.results.model.data
row_labels = data.row_labels
beta_labels = ['dfb_' + i for i in data.xnames]
# grab the results
if self.hat_matrix_diag is not None:
summary_data = DataFrame(dict(
cooks_d=self.cooks_distance[0],
standard_resid=self.resid_studentized,
hat_diag=self.hat_matrix_diag,
dffits_internal=self.d_fittedvalues_scaled),
index=row_labels)
else:
summary_data = DataFrame(dict(
cooks_d=self.cooks_distance[0],
# standard_resid=self.resid_studentized,
# hat_diag=self.hat_matrix_diag,
dffits_internal=self.d_fittedvalues_scaled),
index=row_labels)
# NOTE: if we do not give columns, order of above will be arbitrary
dfbeta = DataFrame(self.dfbetas, columns=beta_labels,
index=row_labels)
return dfbeta.join(summary_data) | Creates a DataFrame with influence results.
Returns
-------
frame : pandas DataFrame
A DataFrame with selected results for each observation.
The index will be the same as provided to the model.
Notes
-----
The resultant DataFrame contains six variables in addition to the
``dfbetas``. These are:
* cooks_d : Cook's Distance defined in ``cooks_distance``
* standard_resid : Standardized residuals defined in
`resid_studentizedl`
* hat_diag : The diagonal of the projection, or hat, matrix defined in
`hat_matrix_diag`. Not included if None.
* dffits_internal : DFFITS statistics using internally Studentized
residuals defined in `d_fittedvalues_scaled` | summary_frame | python | statsmodels/statsmodels | statsmodels/stats/outliers_influence.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/stats/outliers_influence.py | BSD-3-Clause |
def hat_matrix_diag(self):
"""Diagonal of the hat_matrix for OLS
Notes
-----
temporarily calculated here, this should go to model class
"""
return (self.exog * self.results.model.pinv_wexog.T).sum(1) | Diagonal of the hat_matrix for OLS
Notes
-----
temporarily calculated here, this should go to model class | hat_matrix_diag | python | statsmodels/statsmodels | statsmodels/stats/outliers_influence.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/stats/outliers_influence.py | BSD-3-Clause |
def resid_press(self):
"""PRESS residuals
"""
hii = self.hat_matrix_diag
return self.resid / (1 - hii) | PRESS residuals | resid_press | python | statsmodels/statsmodels | statsmodels/stats/outliers_influence.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/stats/outliers_influence.py | BSD-3-Clause |
def influence(self):
"""Influence measure
matches the influence measure that gretl reports
u * h / (1 - h)
where u are the residuals and h is the diagonal of the hat_matrix
"""
hii = self.hat_matrix_diag
return self.resid * hii / (1 - hii) | Influence measure
matches the influence measure that gretl reports
u * h / (1 - h)
where u are the residuals and h is the diagonal of the hat_matrix | influence | python | statsmodels/statsmodels | statsmodels/stats/outliers_influence.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/stats/outliers_influence.py | BSD-3-Clause |
def hat_diag_factor(self):
"""Factor of diagonal of hat_matrix used in influence
this might be useful for internal reuse
h / (1 - h)
"""
hii = self.hat_matrix_diag
return hii / (1 - hii) | Factor of diagonal of hat_matrix used in influence
this might be useful for internal reuse
h / (1 - h) | hat_diag_factor | python | statsmodels/statsmodels | statsmodels/stats/outliers_influence.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/stats/outliers_influence.py | BSD-3-Clause |
def ess_press(self):
"""Error sum of squares of PRESS residuals
"""
return np.dot(self.resid_press, self.resid_press) | Error sum of squares of PRESS residuals | ess_press | python | statsmodels/statsmodels | statsmodels/stats/outliers_influence.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/stats/outliers_influence.py | BSD-3-Clause |
def resid_studentized(self):
"""Studentized residuals using variance from OLS
alias for resid_studentized_internal for compatibility with
MLEInfluence this uses sigma from original estimate and does
not require leave one out loop
"""
return self.resid_studentized_internal | Studentized residuals using variance from OLS
alias for resid_studentized_internal for compatibility with
MLEInfluence this uses sigma from original estimate and does
not require leave one out loop | resid_studentized | python | statsmodels/statsmodels | statsmodels/stats/outliers_influence.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/stats/outliers_influence.py | BSD-3-Clause |
def resid_studentized_internal(self):
"""Studentized residuals using variance from OLS
this uses sigma from original estimate
does not require leave one out loop
"""
return self.get_resid_studentized_external(sigma=None) | Studentized residuals using variance from OLS
this uses sigma from original estimate
does not require leave one out loop | resid_studentized_internal | python | statsmodels/statsmodels | statsmodels/stats/outliers_influence.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/stats/outliers_influence.py | BSD-3-Clause |
def resid_studentized_external(self):
"""Studentized residuals using LOOO variance
this uses sigma from leave-one-out estimates
requires leave one out loop for observations
"""
sigma_looo = np.sqrt(self.sigma2_not_obsi)
return self.get_resid_studentized_external(sigma=sigma_looo) | Studentized residuals using LOOO variance
this uses sigma from leave-one-out estimates
requires leave one out loop for observations | resid_studentized_external | python | statsmodels/statsmodels | statsmodels/stats/outliers_influence.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/stats/outliers_influence.py | BSD-3-Clause |
def get_resid_studentized_external(self, sigma=None):
"""calculate studentized residuals
Parameters
----------
sigma : None or float
estimate of the standard deviation of the residuals. If None, then
the estimate from the regression results is used.
Returns
-------
stzd_resid : ndarray
studentized residuals
Notes
-----
studentized residuals are defined as ::
resid / sigma / np.sqrt(1 - hii)
where resid are the residuals from the regression, sigma is an
estimate of the standard deviation of the residuals, and hii is the
diagonal of the hat_matrix.
"""
hii = self.hat_matrix_diag
if sigma is None:
sigma2_est = self.scale
# can be replace by different estimators of sigma
sigma = np.sqrt(sigma2_est)
return self.resid / sigma / np.sqrt(1 - hii) | calculate studentized residuals
Parameters
----------
sigma : None or float
estimate of the standard deviation of the residuals. If None, then
the estimate from the regression results is used.
Returns
-------
stzd_resid : ndarray
studentized residuals
Notes
-----
studentized residuals are defined as ::
resid / sigma / np.sqrt(1 - hii)
where resid are the residuals from the regression, sigma is an
estimate of the standard deviation of the residuals, and hii is the
diagonal of the hat_matrix. | get_resid_studentized_external | python | statsmodels/statsmodels | statsmodels/stats/outliers_influence.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/stats/outliers_influence.py | BSD-3-Clause |
def cooks_distance(self):
"""
Cooks distance
Uses original results, no nobs loop
References
----------
.. [*] Eubank, R. L. (1999). Nonparametric regression and spline
smoothing. CRC press.
.. [*] Cook's distance. (n.d.). In Wikipedia. July 2019, from
https://en.wikipedia.org/wiki/Cook%27s_distance
"""
hii = self.hat_matrix_diag
# Eubank p.93, 94
cooks_d2 = self.resid_studentized ** 2 / self.k_vars
cooks_d2 *= hii / (1 - hii)
from scipy import stats
# alpha = 0.1
# print stats.f.isf(1-alpha, n_params, res.df_modelwc)
pvals = stats.f.sf(cooks_d2, self.k_vars, self.results.df_resid)
return cooks_d2, pvals | Cooks distance
Uses original results, no nobs loop
References
----------
.. [*] Eubank, R. L. (1999). Nonparametric regression and spline
smoothing. CRC press.
.. [*] Cook's distance. (n.d.). In Wikipedia. July 2019, from
https://en.wikipedia.org/wiki/Cook%27s_distance | cooks_distance | python | statsmodels/statsmodels | statsmodels/stats/outliers_influence.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/stats/outliers_influence.py | BSD-3-Clause |
def dffits_internal(self):
"""dffits measure for influence of an observation
based on resid_studentized_internal
uses original results, no nobs loop
"""
# TODO: do I want to use different sigma estimate in
# resid_studentized_external
# -> move definition of sigma_error to the __init__
hii = self.hat_matrix_diag
dffits_ = self.resid_studentized_internal * np.sqrt(hii / (1 - hii))
dffits_threshold = 2 * np.sqrt(self.k_vars * 1. / self.nobs)
return dffits_, dffits_threshold | dffits measure for influence of an observation
based on resid_studentized_internal
uses original results, no nobs loop | dffits_internal | python | statsmodels/statsmodels | statsmodels/stats/outliers_influence.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/stats/outliers_influence.py | BSD-3-Clause |
def dffits(self):
"""
dffits measure for influence of an observation
based on resid_studentized_external,
uses results from leave-one-observation-out loop
It is recommended that observations with dffits large than a
threshold of 2 sqrt{k / n} where k is the number of parameters, should
be investigated.
Returns
-------
dffits : float
dffits_threshold : float
References
----------
`Wikipedia <https://en.wikipedia.org/wiki/DFFITS>`_
"""
# TODO: do I want to use different sigma estimate in
# resid_studentized_external
# -> move definition of sigma_error to the __init__
hii = self.hat_matrix_diag
dffits_ = self.resid_studentized_external * np.sqrt(hii / (1 - hii))
dffits_threshold = 2 * np.sqrt(self.k_vars * 1. / self.nobs)
return dffits_, dffits_threshold | dffits measure for influence of an observation
based on resid_studentized_external,
uses results from leave-one-observation-out loop
It is recommended that observations with dffits large than a
threshold of 2 sqrt{k / n} where k is the number of parameters, should
be investigated.
Returns
-------
dffits : float
dffits_threshold : float
References
----------
`Wikipedia <https://en.wikipedia.org/wiki/DFFITS>`_ | dffits | python | statsmodels/statsmodels | statsmodels/stats/outliers_influence.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/stats/outliers_influence.py | BSD-3-Clause |
def dfbetas(self):
"""dfbetas
uses results from leave-one-observation-out loop
"""
dfbetas = self.results.params - self.params_not_obsi # [None,:]
dfbetas /= np.sqrt(self.sigma2_not_obsi[:, None])
dfbetas /= np.sqrt(np.diag(self.results.normalized_cov_params))
return dfbetas | dfbetas
uses results from leave-one-observation-out loop | dfbetas | python | statsmodels/statsmodels | statsmodels/stats/outliers_influence.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/stats/outliers_influence.py | BSD-3-Clause |
def dfbeta(self):
"""dfbetas
uses results from leave-one-observation-out loop
"""
dfbeta = self.results.params - self.params_not_obsi
return dfbeta | dfbetas
uses results from leave-one-observation-out loop | dfbeta | python | statsmodels/statsmodels | statsmodels/stats/outliers_influence.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/stats/outliers_influence.py | BSD-3-Clause |
def sigma2_not_obsi(self):
"""error variance for all LOOO regressions
This is 'mse_resid' from each auxiliary regression.
uses results from leave-one-observation-out loop
"""
return np.asarray(self._res_looo['mse_resid']) | error variance for all LOOO regressions
This is 'mse_resid' from each auxiliary regression.
uses results from leave-one-observation-out loop | sigma2_not_obsi | python | statsmodels/statsmodels | statsmodels/stats/outliers_influence.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/stats/outliers_influence.py | BSD-3-Clause |
def params_not_obsi(self):
"""parameter estimates for all LOOO regressions
uses results from leave-one-observation-out loop
"""
return np.asarray(self._res_looo['params']) | parameter estimates for all LOOO regressions
uses results from leave-one-observation-out loop | params_not_obsi | python | statsmodels/statsmodels | statsmodels/stats/outliers_influence.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/stats/outliers_influence.py | BSD-3-Clause |
def det_cov_params_not_obsi(self):
"""determinant of cov_params of all LOOO regressions
uses results from leave-one-observation-out loop
"""
return np.asarray(self._res_looo['det_cov_params']) | determinant of cov_params of all LOOO regressions
uses results from leave-one-observation-out loop | det_cov_params_not_obsi | python | statsmodels/statsmodels | statsmodels/stats/outliers_influence.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/stats/outliers_influence.py | BSD-3-Clause |
def cov_ratio(self):
"""covariance ratio between LOOO and original
This uses determinant of the estimate of the parameter covariance
from leave-one-out estimates.
requires leave one out loop for observations
"""
# do not use inplace division / because then we change original
cov_ratio = (self.det_cov_params_not_obsi
/ np.linalg.det(self.results.cov_params()))
return cov_ratio | covariance ratio between LOOO and original
This uses determinant of the estimate of the parameter covariance
from leave-one-out estimates.
requires leave one out loop for observations | cov_ratio | python | statsmodels/statsmodels | statsmodels/stats/outliers_influence.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/stats/outliers_influence.py | BSD-3-Clause |
def resid_var(self):
"""estimate of variance of the residuals
::
sigma2 = sigma2_OLS * (1 - hii)
where hii is the diagonal of the hat matrix
"""
# TODO:check if correct outside of ols
return self.scale * (1 - self.hat_matrix_diag) | estimate of variance of the residuals
::
sigma2 = sigma2_OLS * (1 - hii)
where hii is the diagonal of the hat matrix | resid_var | python | statsmodels/statsmodels | statsmodels/stats/outliers_influence.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/stats/outliers_influence.py | BSD-3-Clause |
def resid_std(self):
"""estimate of standard deviation of the residuals
See Also
--------
resid_var
"""
return np.sqrt(self.resid_var) | estimate of standard deviation of the residuals
See Also
--------
resid_var | resid_std | python | statsmodels/statsmodels | statsmodels/stats/outliers_influence.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/stats/outliers_influence.py | BSD-3-Clause |
def _ols_xnoti(self, drop_idx, endog_idx='endog', store=True):
"""regression results from LOVO auxiliary regression with cache
The result instances are stored, which could use a large amount of
memory if the datasets are large. There are too many combinations to
store them all, except for small problems.
Parameters
----------
drop_idx : int
index of exog that is dropped from the regression
endog_idx : 'endog' or int
If 'endog', then the endogenous variable of the result instance
is regressed on the exogenous variables, excluding the one at
drop_idx. If endog_idx is an integer, then the exog with that
index is regressed with OLS on all other exogenous variables.
(The latter is the auxiliary regression for the variance inflation
factor.)
this needs more thought, memory versus speed
not yet used in any other parts, not sufficiently tested
"""
# reverse the structure, access store, if fail calculate ?
# this creates keys in store even if store = false ! bug
if endog_idx == 'endog':
stored = self.aux_regression_endog
if hasattr(stored, drop_idx):
return stored[drop_idx]
x_i = self.results.model.endog
else:
# nested dictionary
try:
self.aux_regression_exog[endog_idx][drop_idx]
except KeyError:
pass
stored = self.aux_regression_exog[endog_idx]
stored = {}
x_i = self.exog[:, endog_idx]
k_vars = self.exog.shape[1]
mask = np.arange(k_vars) != drop_idx
x_noti = self.exog[:, mask]
res = OLS(x_i, x_noti).fit()
if store:
stored[drop_idx] = res
return res | regression results from LOVO auxiliary regression with cache
The result instances are stored, which could use a large amount of
memory if the datasets are large. There are too many combinations to
store them all, except for small problems.
Parameters
----------
drop_idx : int
index of exog that is dropped from the regression
endog_idx : 'endog' or int
If 'endog', then the endogenous variable of the result instance
is regressed on the exogenous variables, excluding the one at
drop_idx. If endog_idx is an integer, then the exog with that
index is regressed with OLS on all other exogenous variables.
(The latter is the auxiliary regression for the variance inflation
factor.)
this needs more thought, memory versus speed
not yet used in any other parts, not sufficiently tested | _ols_xnoti | python | statsmodels/statsmodels | statsmodels/stats/outliers_influence.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/stats/outliers_influence.py | BSD-3-Clause |
def _get_drop_vari(self, attributes):
"""
regress endog on exog without one of the variables
This uses a k_vars loop, only attributes of the OLS instance are
stored.
Parameters
----------
attributes : list[str]
These are the names of the attributes of the auxiliary OLS results
instance that are stored and returned.
not yet used
"""
from statsmodels.sandbox.tools.cross_val import LeaveOneOut
endog = self.results.model.endog
exog = self.exog
cv_iter = LeaveOneOut(self.k_vars)
res_loo = defaultdict(list)
for inidx, outidx in cv_iter:
for att in attributes:
res_i = self.model_class(endog, exog[:, inidx]).fit()
res_loo[att].append(getattr(res_i, att))
return res_loo | regress endog on exog without one of the variables
This uses a k_vars loop, only attributes of the OLS instance are
stored.
Parameters
----------
attributes : list[str]
These are the names of the attributes of the auxiliary OLS results
instance that are stored and returned.
not yet used | _get_drop_vari | python | statsmodels/statsmodels | statsmodels/stats/outliers_influence.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/stats/outliers_influence.py | BSD-3-Clause |
def _res_looo(self):
"""collect required results from the LOOO loop
all results will be attached.
currently only 'params', 'mse_resid', 'det_cov_params' are stored
regresses endog on exog dropping one observation at a time
this uses a nobs loop, only attributes of the OLS instance are stored.
"""
from statsmodels.sandbox.tools.cross_val import LeaveOneOut
def get_det_cov_params(res):
return np.linalg.det(res.cov_params())
endog = self.results.model.endog
exog = self.results.model.exog
params = np.zeros(exog.shape, dtype=float)
mse_resid = np.zeros(endog.shape, dtype=float)
det_cov_params = np.zeros(endog.shape, dtype=float)
cv_iter = LeaveOneOut(self.nobs)
for inidx, outidx in cv_iter:
res_i = self.model_class(endog[inidx], exog[inidx]).fit()
params[outidx] = res_i.params
mse_resid[outidx] = res_i.mse_resid
det_cov_params[outidx] = get_det_cov_params(res_i)
return dict(params=params, mse_resid=mse_resid,
det_cov_params=det_cov_params) | collect required results from the LOOO loop
all results will be attached.
currently only 'params', 'mse_resid', 'det_cov_params' are stored
regresses endog on exog dropping one observation at a time
this uses a nobs loop, only attributes of the OLS instance are stored. | _res_looo | python | statsmodels/statsmodels | statsmodels/stats/outliers_influence.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/stats/outliers_influence.py | BSD-3-Clause |
def summary_frame(self):
"""
Creates a DataFrame with all available influence results.
Returns
-------
frame : DataFrame
A DataFrame with all results.
Notes
-----
The resultant DataFrame contains six variables in addition to the
DFBETAS. These are:
* cooks_d : Cook's Distance defined in `Influence.cooks_distance`
* standard_resid : Standardized residuals defined in
`Influence.resid_studentized_internal`
* hat_diag : The diagonal of the projection, or hat, matrix defined in
`Influence.hat_matrix_diag`
* dffits_internal : DFFITS statistics using internally Studentized
residuals defined in `Influence.dffits_internal`
* dffits : DFFITS statistics using externally Studentized residuals
defined in `Influence.dffits`
* student_resid : Externally Studentized residuals defined in
`Influence.resid_studentized_external`
"""
from pandas import DataFrame
# row and column labels
data = self.results.model.data
row_labels = data.row_labels
beta_labels = ['dfb_' + i for i in data.xnames]
# grab the results
summary_data = DataFrame(dict(
cooks_d=self.cooks_distance[0],
standard_resid=self.resid_studentized_internal,
hat_diag=self.hat_matrix_diag,
dffits_internal=self.dffits_internal[0],
student_resid=self.resid_studentized_external,
dffits=self.dffits[0],
),
index=row_labels)
# NOTE: if we do not give columns, order of above will be arbitrary
dfbeta = DataFrame(self.dfbetas, columns=beta_labels,
index=row_labels)
return dfbeta.join(summary_data) | Creates a DataFrame with all available influence results.
Returns
-------
frame : DataFrame
A DataFrame with all results.
Notes
-----
The resultant DataFrame contains six variables in addition to the
DFBETAS. These are:
* cooks_d : Cook's Distance defined in `Influence.cooks_distance`
* standard_resid : Standardized residuals defined in
`Influence.resid_studentized_internal`
* hat_diag : The diagonal of the projection, or hat, matrix defined in
`Influence.hat_matrix_diag`
* dffits_internal : DFFITS statistics using internally Studentized
residuals defined in `Influence.dffits_internal`
* dffits : DFFITS statistics using externally Studentized residuals
defined in `Influence.dffits`
* student_resid : Externally Studentized residuals defined in
`Influence.resid_studentized_external` | summary_frame | python | statsmodels/statsmodels | statsmodels/stats/outliers_influence.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/stats/outliers_influence.py | BSD-3-Clause |
def summary_table(self, float_fmt="%6.3f"):
"""create a summary table with all influence and outlier measures
This does currently not distinguish between statistics that can be
calculated from the original regression results and for which a
leave-one-observation-out loop is needed
Returns
-------
res : SimpleTable
SimpleTable instance with the results, can be printed
Notes
-----
This also attaches table_data to the instance.
"""
# print self.dfbetas
# table_raw = [ np.arange(self.nobs),
# self.endog,
# self.fittedvalues,
# self.cooks_distance(),
# self.resid_studentized_internal,
# self.hat_matrix_diag,
# self.dffits_internal,
# self.resid_studentized_external,
# self.dffits,
# self.dfbetas
# ]
table_raw = [('obs', np.arange(self.nobs)),
('endog', self.endog),
('fitted\nvalue', self.results.fittedvalues),
("Cook's\nd", self.cooks_distance[0]),
("student.\nresidual", self.resid_studentized_internal),
('hat diag', self.hat_matrix_diag),
('dffits \ninternal', self.dffits_internal[0]),
("ext.stud.\nresidual", self.resid_studentized_external),
('dffits', self.dffits[0])
]
colnames, data = lzip(*table_raw) # unzip
data = np.column_stack(data)
self.table_data = data
from copy import deepcopy
from statsmodels.iolib.table import SimpleTable, default_html_fmt
from statsmodels.iolib.tableformatting import fmt_base
fmt = deepcopy(fmt_base)
fmt_html = deepcopy(default_html_fmt)
fmt['data_fmts'] = ["%4d"] + [float_fmt] * (data.shape[1] - 1)
# fmt_html['data_fmts'] = fmt['data_fmts']
return SimpleTable(data, headers=colnames, txt_fmt=fmt,
html_fmt=fmt_html) | create a summary table with all influence and outlier measures
This does currently not distinguish between statistics that can be
calculated from the original regression results and for which a
leave-one-observation-out loop is needed
Returns
-------
res : SimpleTable
SimpleTable instance with the results, can be printed
Notes
-----
This also attaches table_data to the instance. | summary_table | python | statsmodels/statsmodels | statsmodels/stats/outliers_influence.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/stats/outliers_influence.py | BSD-3-Clause |
def summary_table(res, alpha=0.05):
"""
Generate summary table of outlier and influence similar to SAS
Parameters
----------
alpha : float
significance level for confidence interval
Returns
-------
st : SimpleTable
table with results that can be printed
data : ndarray
calculated measures and statistics for the table
ss2 : list[str]
column_names for table (Note: rows of table are observations)
"""
from scipy import stats
from statsmodels.sandbox.regression.predstd import wls_prediction_std
infl = OLSInfluence(res)
# standard error for predicted mean
# Note: using hat_matrix only works for fitted values
predict_mean_se = np.sqrt(infl.hat_matrix_diag * res.mse_resid)
tppf = stats.t.isf(alpha / 2., res.df_resid)
predict_mean_ci = np.column_stack([
res.fittedvalues - tppf * predict_mean_se,
res.fittedvalues + tppf * predict_mean_se])
# standard error for predicted observation
tmp = wls_prediction_std(res, alpha=alpha)
predict_se, predict_ci_low, predict_ci_upp = tmp
predict_ci = np.column_stack((predict_ci_low, predict_ci_upp))
# standard deviation of residual
resid_se = np.sqrt(res.mse_resid * (1 - infl.hat_matrix_diag))
table_sm = np.column_stack([
np.arange(res.nobs) + 1,
res.model.endog,
res.fittedvalues,
predict_mean_se,
predict_mean_ci[:, 0],
predict_mean_ci[:, 1],
predict_ci[:, 0],
predict_ci[:, 1],
res.resid,
resid_se,
infl.resid_studentized_internal,
infl.cooks_distance[0]
])
# colnames, data = lzip(*table_raw) #unzip
data = table_sm
ss2 = ['Obs', 'Dep Var\nPopulation', 'Predicted\nValue',
'Std Error\nMean Predict', 'Mean ci\n95% low', 'Mean ci\n95% upp',
'Predict ci\n95% low', 'Predict ci\n95% upp', 'Residual',
'Std Error\nResidual', 'Student\nResidual', "Cook's\nD"]
colnames = ss2
# self.table_data = data
# data = np.column_stack(data)
from copy import deepcopy
from statsmodels.iolib.table import SimpleTable, default_html_fmt
from statsmodels.iolib.tableformatting import fmt_base
fmt = deepcopy(fmt_base)
fmt_html = deepcopy(default_html_fmt)
fmt['data_fmts'] = ["%4d"] + ["%6.3f"] * (data.shape[1] - 1)
# fmt_html['data_fmts'] = fmt['data_fmts']
st = SimpleTable(data, headers=colnames, txt_fmt=fmt,
html_fmt=fmt_html)
return st, data, ss2 | Generate summary table of outlier and influence similar to SAS
Parameters
----------
alpha : float
significance level for confidence interval
Returns
-------
st : SimpleTable
table with results that can be printed
data : ndarray
calculated measures and statistics for the table
ss2 : list[str]
column_names for table (Note: rows of table are observations) | summary_table | python | statsmodels/statsmodels | statsmodels/stats/outliers_influence.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/stats/outliers_influence.py | BSD-3-Clause |
def hat_matrix_diag(self):
"""
Diagonal of the hat_matrix for GLM
Notes
-----
This returns the diagonal of the hat matrix that was provided as
argument to GLMInfluence or computes it using the results method
`get_hat_matrix`.
"""
if hasattr(self, '_hat_matrix_diag'):
return self._hat_matrix_diag
else:
return self.results.get_hat_matrix() | Diagonal of the hat_matrix for GLM
Notes
-----
This returns the diagonal of the hat matrix that was provided as
argument to GLMInfluence or computes it using the results method
`get_hat_matrix`. | hat_matrix_diag | python | statsmodels/statsmodels | statsmodels/stats/outliers_influence.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/stats/outliers_influence.py | BSD-3-Clause |
def d_params(self):
"""Change in parameter estimates
Notes
-----
This uses one-step approximation of the parameter change to deleting
one observation.
"""
beta_i = np.linalg.pinv(self.exog) * self.resid_studentized
beta_i /= np.sqrt(1 - self.hat_matrix_diag)
return beta_i.T | Change in parameter estimates
Notes
-----
This uses one-step approximation of the parameter change to deleting
one observation. | d_params | python | statsmodels/statsmodels | statsmodels/stats/outliers_influence.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/stats/outliers_influence.py | BSD-3-Clause |
def resid_studentized(self):
"""
Internally studentized pearson residuals
Notes
-----
residuals / sqrt( scale * (1 - hii))
where residuals are those provided to GLMInfluence which are
pearson residuals by default, and
hii is the diagonal of the hat matrix.
"""
# redundant with scaled resid_pearson, keep for docstring for now
return super().resid_studentized | Internally studentized pearson residuals
Notes
-----
residuals / sqrt( scale * (1 - hii))
where residuals are those provided to GLMInfluence which are
pearson residuals by default, and
hii is the diagonal of the hat matrix. | resid_studentized | python | statsmodels/statsmodels | statsmodels/stats/outliers_influence.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/stats/outliers_influence.py | BSD-3-Clause |
def cooks_distance(self):
"""Cook's distance
Notes
-----
Based on one step approximation using resid_studentized and
hat_matrix_diag for the computation.
Cook's distance divides by the number of explanatory variables.
Computed using formulas for GLM and does not use results.cov_params.
It includes p-values based on the F-distribution which are only
approximate outside of linear Gaussian models.
"""
hii = self.hat_matrix_diag
# Eubank p.93, 94
cooks_d2 = self.resid_studentized ** 2 / self.k_vars
cooks_d2 *= hii / (1 - hii)
from scipy import stats
# alpha = 0.1
# print stats.f.isf(1-alpha, n_params, res.df_modelwc)
pvals = stats.f.sf(cooks_d2, self.k_vars, self.results.df_resid)
return cooks_d2, pvals | Cook's distance
Notes
-----
Based on one step approximation using resid_studentized and
hat_matrix_diag for the computation.
Cook's distance divides by the number of explanatory variables.
Computed using formulas for GLM and does not use results.cov_params.
It includes p-values based on the F-distribution which are only
approximate outside of linear Gaussian models. | cooks_distance | python | statsmodels/statsmodels | statsmodels/stats/outliers_influence.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/stats/outliers_influence.py | BSD-3-Clause |
def d_linpred(self):
"""
Change in linear prediction
This uses one-step approximation of the parameter change to deleting
one observation ``d_params``.
"""
# TODO: This will need adjustment for extra params in Poisson
# use original model exog not transformed influence exog
exog = self.results.model.exog
return (exog * self.d_params).sum(1) | Change in linear prediction
This uses one-step approximation of the parameter change to deleting
one observation ``d_params``. | d_linpred | python | statsmodels/statsmodels | statsmodels/stats/outliers_influence.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/stats/outliers_influence.py | BSD-3-Clause |
def d_linpred_scaled(self):
"""
Change in linpred scaled by standard errors
This uses one-step approximation of the parameter change to deleting
one observation ``d_params``, and divides by the standard errors
for linpred provided by results.get_prediction.
"""
# Note: this and the previous methods are for the response
# and not for a weighted response, i.e. not the self.exog, self.endog
# this will be relevant for WLS comparing fitted endog versus wendog
return self.d_linpred / self._get_prediction.linpred.se | Change in linpred scaled by standard errors
This uses one-step approximation of the parameter change to deleting
one observation ``d_params``, and divides by the standard errors
for linpred provided by results.get_prediction. | d_linpred_scaled | python | statsmodels/statsmodels | statsmodels/stats/outliers_influence.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/stats/outliers_influence.py | BSD-3-Clause |
def _fittedvalues_one(self):
"""experimental code
"""
warnings.warn('this ignores offset and exposure', UserWarning)
# TODO: we need to handle offset, exposure and weights
# use original model exog not transformed influence exog
exog = self.results.model.exog
fitted = np.array([self.results.model.predict(pi, exog[i])
for i, pi in enumerate(self.params_one)])
return fitted.squeeze() | experimental code | _fittedvalues_one | python | statsmodels/statsmodels | statsmodels/stats/outliers_influence.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/stats/outliers_influence.py | BSD-3-Clause |
def _diff_fittedvalues_one(self):
"""experimental code
"""
# in discrete we cannot reuse results.fittedvalues
return self.results.predict() - self._fittedvalues_one | experimental code | _diff_fittedvalues_one | python | statsmodels/statsmodels | statsmodels/stats/outliers_influence.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/stats/outliers_influence.py | BSD-3-Clause |
def _res_looo(self):
"""collect required results from the LOOO loop
all results will be attached.
currently only 'params', 'mse_resid', 'det_cov_params' are stored
Reestimates the model with endog and exog dropping one observation
at a time
This uses a nobs loop, only attributes of the results instance are
stored.
Warning: This will need refactoring and API changes to be able to
add options.
"""
from statsmodels.sandbox.tools.cross_val import LeaveOneOut
def get_det_cov_params(res):
return np.linalg.det(res.cov_params())
endog = self.results.model.endog
exog = self.results.model.exog
init_kwds = self.results.model._get_init_kwds()
# We need to drop obs also from extra arrays
freq_weights = init_kwds.pop('freq_weights')
var_weights = init_kwds.pop('var_weights')
offset = offset_ = init_kwds.pop('offset')
exposure = exposure_ = init_kwds.pop('exposure')
n_trials = init_kwds.pop('n_trials', None)
# family Binomial creates `n` i.e. `n_trials`
# we need to reset it
# TODO: figure out how to do this properly
if hasattr(init_kwds['family'], 'initialize'):
# assume we have Binomial
is_binomial = True
else:
is_binomial = False
params = np.zeros(exog.shape, dtype=float)
scale = np.zeros(endog.shape, dtype=float)
det_cov_params = np.zeros(endog.shape, dtype=float)
cv_iter = LeaveOneOut(self.nobs)
for inidx, outidx in cv_iter:
if offset is not None:
offset_ = offset[inidx]
if exposure is not None:
exposure_ = exposure[inidx]
if n_trials is not None:
init_kwds['n_trials'] = n_trials[inidx]
mod_i = self.model_class(endog[inidx], exog[inidx],
offset=offset_,
exposure=exposure_,
freq_weights=freq_weights[inidx],
var_weights=var_weights[inidx],
**init_kwds)
if is_binomial:
mod_i.family.n = init_kwds['n_trials']
res_i = mod_i.fit(start_params=self.results.params,
method='newton')
params[outidx] = res_i.params.copy()
scale[outidx] = res_i.scale
det_cov_params[outidx] = get_det_cov_params(res_i)
return dict(params=params, scale=scale, mse_resid=scale,
# alias for now
det_cov_params=det_cov_params) | collect required results from the LOOO loop
all results will be attached.
currently only 'params', 'mse_resid', 'det_cov_params' are stored
Reestimates the model with endog and exog dropping one observation
at a time
This uses a nobs loop, only attributes of the results instance are
stored.
Warning: This will need refactoring and API changes to be able to
add options. | _res_looo | python | statsmodels/statsmodels | statsmodels/stats/outliers_influence.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/stats/outliers_influence.py | BSD-3-Clause |
def _simulate_params(self, result):
"""
Simulate model parameters from fitted sampling distribution.
"""
mn = result.params
cov = result.cov_params()
return np.random.multivariate_normal(mn, cov) | Simulate model parameters from fitted sampling distribution. | _simulate_params | python | statsmodels/statsmodels | statsmodels/stats/mediation.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/stats/mediation.py | BSD-3-Clause |
def _get_mediator_exog(self, exposure):
"""
Return the mediator exog matrix with exposure set to the given
value. Set values of moderated variables as needed.
"""
mediator_exog = self._mediator_exog
if not hasattr(self.mediator_model, 'formula'):
mediator_exog[:, self._exp_pos_mediator] = exposure
for ix in self.moderators:
v = self.moderators[ix]
mediator_exog[:, ix[1]] = v
else:
# Need to regenerate the model exog
df = self.mediator_model.data.frame.copy()
df[self.exposure] = exposure
for vname in self.moderators:
v = self.moderators[vname]
df.loc[:, vname] = v
klass = self.mediator_model.__class__
init_kwargs = self.mediator_model._get_init_kwds()
model = klass.from_formula(data=df, **init_kwargs)
mediator_exog = model.exog
return mediator_exog | Return the mediator exog matrix with exposure set to the given
value. Set values of moderated variables as needed. | _get_mediator_exog | python | statsmodels/statsmodels | statsmodels/stats/mediation.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/stats/mediation.py | BSD-3-Clause |
def _get_outcome_exog(self, exposure, mediator):
"""
Retun the exog design matrix with mediator and exposure set to
the given values. Set values of moderated variables as
needed.
"""
outcome_exog = self._outcome_exog
if not hasattr(self.outcome_model, 'formula'):
outcome_exog[:, self._med_pos_outcome] = mediator
outcome_exog[:, self._exp_pos_outcome] = exposure
for ix in self.moderators:
v = self.moderators[ix]
outcome_exog[:, ix[0]] = v
else:
# Need to regenerate the model exog
df = self.outcome_model.data.frame.copy()
df[self.exposure] = exposure
df[self.mediator] = mediator
for vname in self.moderators:
v = self.moderators[vname]
df[vname] = v
klass = self.outcome_model.__class__
init_kwargs = self.outcome_model._get_init_kwds()
model = klass.from_formula(data=df, **init_kwargs)
outcome_exog = model.exog
return outcome_exog | Retun the exog design matrix with mediator and exposure set to
the given values. Set values of moderated variables as
needed. | _get_outcome_exog | python | statsmodels/statsmodels | statsmodels/stats/mediation.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/stats/mediation.py | BSD-3-Clause |
def fit(self, method="parametric", n_rep=1000):
"""
Fit a regression model to assess mediation.
Parameters
----------
method : str
Either 'parametric' or 'bootstrap'.
n_rep : int
The number of simulation replications.
Returns a MediationResults object.
"""
if method.startswith("para"):
# Initial fit to unperturbed data.
outcome_result = self._fit_model(self.outcome_model, self._outcome_fit_kwargs)
mediator_result = self._fit_model(self.mediator_model, self._mediator_fit_kwargs)
elif not method.startswith("boot"):
raise ValueError(
"method must be either 'parametric' or 'bootstrap'"
)
indirect_effects = [[], []]
direct_effects = [[], []]
for iter in range(n_rep):
if method == "parametric":
# Realization of outcome model parameters from sampling distribution
outcome_params = self._simulate_params(outcome_result)
# Realization of mediation model parameters from sampling distribution
mediation_params = self._simulate_params(mediator_result)
else:
outcome_result = self._fit_model(self.outcome_model,
self._outcome_fit_kwargs, boot=True)
outcome_params = outcome_result.params
mediator_result = self._fit_model(self.mediator_model,
self._mediator_fit_kwargs, boot=True)
mediation_params = mediator_result.params
# predicted outcomes[tm][te] is the outcome when the
# mediator is set to tm and the outcome/exposure is set to
# te.
predicted_outcomes = [[None, None], [None, None]]
for tm in 0, 1:
mex = self._get_mediator_exog(tm)
kwargs = {"exog": mex}
if hasattr(mediator_result, "scale"):
kwargs["scale"] = mediator_result.scale
gen = self.mediator_model.get_distribution(mediation_params,
**kwargs)
potential_mediator = gen.rvs(mex.shape[0])
for te in 0, 1:
oex = self._get_outcome_exog(te, potential_mediator)
po = self.outcome_model.predict(outcome_params, oex,
**self._outcome_predict_kwargs)
predicted_outcomes[tm][te] = po
for t in 0, 1:
indirect_effects[t].append(predicted_outcomes[1][t] - predicted_outcomes[0][t])
direct_effects[t].append(predicted_outcomes[t][1] - predicted_outcomes[t][0])
for t in 0, 1:
indirect_effects[t] = np.asarray(indirect_effects[t]).T
direct_effects[t] = np.asarray(direct_effects[t]).T
self.indirect_effects = indirect_effects
self.direct_effects = direct_effects
rslt = MediationResults(self.indirect_effects, self.direct_effects)
rslt.method = method
return rslt | Fit a regression model to assess mediation.
Parameters
----------
method : str
Either 'parametric' or 'bootstrap'.
n_rep : int
The number of simulation replications.
Returns a MediationResults object. | fit | python | statsmodels/statsmodels | statsmodels/stats/mediation.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/stats/mediation.py | BSD-3-Clause |
def summary(self, alpha=0.05):
"""
Provide a summary of a mediation analysis.
"""
columns = ["Estimate", "Lower CI bound", "Upper CI bound", "P-value"]
index = ["ACME (control)", "ACME (treated)",
"ADE (control)", "ADE (treated)",
"Total effect",
"Prop. mediated (control)",
"Prop. mediated (treated)",
"ACME (average)", "ADE (average)",
"Prop. mediated (average)"]
smry = pd.DataFrame(columns=columns, index=index)
for i, vec in enumerate([self.ACME_ctrl, self.ACME_tx,
self.ADE_ctrl, self.ADE_tx,
self.total_effect, self.prop_med_ctrl,
self.prop_med_tx, self.ACME_avg,
self.ADE_avg, self.prop_med_avg]):
if ((vec is self.prop_med_ctrl) or (vec is self.prop_med_tx) or
(vec is self.prop_med_avg)):
smry.iloc[i, 0] = np.median(vec)
else:
smry.iloc[i, 0] = vec.mean()
smry.iloc[i, 1] = np.percentile(vec, 100 * alpha / 2)
smry.iloc[i, 2] = np.percentile(vec, 100 * (1 - alpha / 2))
smry.iloc[i, 3] = _pvalue(vec)
smry = smry.apply(pd.to_numeric, errors='coerce')
return smry | Provide a summary of a mediation analysis. | summary | python | statsmodels/statsmodels | statsmodels/stats/mediation.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/stats/mediation.py | BSD-3-Clause |
def test_single_factor_repeated_measures_anova():
"""
Testing single factor repeated measures anova
Results reproduces R `ezANOVA` function from library ez
"""
df = AnovaRM(data.iloc[:16, :], 'DV', 'id', within=['B']).fit()
a = [[1, 7, 22.4, 0.002125452]]
assert_array_almost_equal(df.anova_table.iloc[:, [1, 2, 0, 3]].values,
a, decimal=5) | Testing single factor repeated measures anova
Results reproduces R `ezANOVA` function from library ez | test_single_factor_repeated_measures_anova | python | statsmodels/statsmodels | statsmodels/stats/tests/test_anova_rm.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/stats/tests/test_anova_rm.py | BSD-3-Clause |
def test_two_factors_repeated_measures_anova():
"""
Testing two factors repeated measures anova
Results reproduces R `ezANOVA` function from library ez
"""
df = AnovaRM(data.iloc[:48, :], 'DV', 'id', within=['A', 'B']).fit()
a = [[1, 7, 40.14159, 3.905263e-04],
[2, 14, 29.21739, 1.007549e-05],
[2, 14, 17.10545, 1.741322e-04]]
assert_array_almost_equal(df.anova_table.iloc[:, [1, 2, 0, 3]].values,
a, decimal=5) | Testing two factors repeated measures anova
Results reproduces R `ezANOVA` function from library ez | test_two_factors_repeated_measures_anova | python | statsmodels/statsmodels | statsmodels/stats/tests/test_anova_rm.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/stats/tests/test_anova_rm.py | BSD-3-Clause |
def test_three_factors_repeated_measures_anova():
"""
Testing three factors repeated measures anova
Results reproduces R `ezANOVA` function from library ez
"""
df = AnovaRM(data, 'DV', 'id', within=['A', 'B', 'D']).fit()
a = [[1, 7, 8.7650709, 0.021087505],
[2, 14, 8.4985785, 0.003833921],
[1, 7, 20.5076546, 0.002704428],
[2, 14, 0.8457797, 0.450021759],
[1, 7, 21.7593382, 0.002301792],
[2, 14, 6.2416695, 0.011536846],
[2, 14, 5.4253359, 0.018010647]]
assert_array_almost_equal(df.anova_table.iloc[:, [1, 2, 0, 3]].values,
a, decimal=5) | Testing three factors repeated measures anova
Results reproduces R `ezANOVA` function from library ez | test_three_factors_repeated_measures_anova | python | statsmodels/statsmodels | statsmodels/stats/tests/test_anova_rm.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/stats/tests/test_anova_rm.py | BSD-3-Clause |
def test_repeated_measures_invalid_factor_name():
"""
Test with a factor name of 'C', which conflicts with patsy.
"""
assert_raises(ValueError, AnovaRM, data.iloc[:16, :], 'DV', 'id',
within=['C']) | Test with a factor name of 'C', which conflicts with patsy. | test_repeated_measures_invalid_factor_name | python | statsmodels/statsmodels | statsmodels/stats/tests/test_anova_rm.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/stats/tests/test_anova_rm.py | BSD-3-Clause |
def _expand_table(table):
'''expand a 2 by 2 contingency table to observations
'''
return np.repeat([[1, 1], [1, 0], [0, 1], [0, 0]], table.ravel(), axis=0) | expand a 2 by 2 contingency table to observations | _expand_table | python | statsmodels/statsmodels | statsmodels/stats/tests/test_nonparametric.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/stats/tests/test_nonparametric.py | BSD-3-Clause |
def test_compute_rank_placements(test_cases):
"""
Test the `_compute_rank_placements` helper for
computing ranks and placements based on two
input samples. Data validation logic is assumed
to be handled by the caller and is not necessary
to test here.
"""
x1, x2, expected_holder = test_cases
res = _compute_rank_placements(x1, x2)
assert_allclose(res.n_1, expected_holder.n_1)
assert_allclose(res.n_2, expected_holder.n_2)
assert_allclose(
res.overall_ranks_pooled, expected_holder.overall_ranks_pooled
)
assert_allclose(
res.overall_ranks_1, expected_holder.overall_ranks_1
)
assert_allclose(
res.overall_ranks_2, expected_holder.overall_ranks_2
)
assert_allclose(
res.within_group_ranks_1, expected_holder.within_group_ranks_1
)
assert_allclose(
res.within_group_ranks_2, expected_holder.within_group_ranks_2
)
assert_allclose(res.placements_1, expected_holder.placements_1)
assert_allclose(res.placements_2, expected_holder.placements_2) | Test the `_compute_rank_placements` helper for
computing ranks and placements based on two
input samples. Data validation logic is assumed
to be handled by the caller and is not necessary
to test here. | test_compute_rank_placements | python | statsmodels/statsmodels | statsmodels/stats/tests/test_nonparametric.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/stats/tests/test_nonparametric.py | BSD-3-Clause |
def reference_implementation_results():
"""
Results from R's rankFD::WMWSSP function.
"""
parent_dir = Path(__file__).resolve().parent
results = pd.read_csv(
parent_dir / "results/results_samplesize_rank_compare_onetail.csv"
)
return results | Results from R's rankFD::WMWSSP function. | reference_implementation_results | python | statsmodels/statsmodels | statsmodels/stats/tests/test_nonparametric.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/stats/tests/test_nonparametric.py | BSD-3-Clause |
def test_samplesize_rank_compare_onetail(reference_implementation_results):
"""
Test the `samplesize_rank_compare_onetail` function against the reference
implementation from R's rankFD package. Examples are taken from the
reference paper directly. The reference implementation results are
generated using the `generate_results_samplesize_rank_compare_onetail.R`
script.
"""
for _, r_result in reference_implementation_results.iterrows():
synthetic_sample = np.array(
r_result["synthetic_sample"].split(","), dtype=np.float64
)
reference_sample = np.array(
r_result["reference_sample"].split(","), dtype=np.float64
)
# Convert `prop_reference` to `nobs_ratio`
nobs_ratio = r_result["prop_reference"] / (1 - r_result["prop_reference"])
py_result = samplesize_rank_compare_onetail(
synthetic_sample=synthetic_sample,
reference_sample=reference_sample,
alpha=r_result["alpha"],
power=r_result["power"],
nobs_ratio=nobs_ratio,
alternative=r_result["alternative"],
)
# Integers can be compared directly
assert_allclose(
py_result.nobs_total,
r_result["nobs_total"],
rtol=1e-9,
atol=0,
)
assert_allclose(
py_result.nobs_ref,
r_result["nobs_ref"],
rtol=1e-9,
)
assert_allclose(
py_result.nobs_treat,
r_result["nobs_treat"],
rtol=1e-9,
)
assert_allclose(
py_result.relative_effect,
r_result["relative_effect"],
rtol=1e-9,
atol=0,
) | Test the `samplesize_rank_compare_onetail` function against the reference
implementation from R's rankFD package. Examples are taken from the
reference paper directly. The reference implementation results are
generated using the `generate_results_samplesize_rank_compare_onetail.R`
script. | test_samplesize_rank_compare_onetail | python | statsmodels/statsmodels | statsmodels/stats/tests/test_nonparametric.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/stats/tests/test_nonparametric.py | BSD-3-Clause |
def test_samplesize_rank_compare_onetail_invalid(
synthetic_sample,
reference_sample,
alpha,
power,
nobs_ratio,
alternative,
expected_exception,
exception_msg,
):
"""
Test the samplesize_rank_compare_onetail function with various invalid inputs.
"""
with pytest.raises(expected_exception, match=exception_msg):
samplesize_rank_compare_onetail(
synthetic_sample=synthetic_sample,
reference_sample=reference_sample,
alpha=alpha,
power=power,
nobs_ratio=nobs_ratio,
alternative=alternative,
) | Test the samplesize_rank_compare_onetail function with various invalid inputs. | test_samplesize_rank_compare_onetail_invalid | python | statsmodels/statsmodels | statsmodels/stats/tests/test_nonparametric.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/stats/tests/test_nonparametric.py | BSD-3-Clause |
def norm_f(x, y):
'''Frobenious norm (squared sum) of difference between two arrays
'''
d = ((x - y)**2).sum()
return np.sqrt(d) | Frobenious norm (squared sum) of difference between two arrays | norm_f | python | statsmodels/statsmodels | statsmodels/stats/tests/test_corrpsd.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/stats/tests/test_corrpsd.py | BSD-3-Clause |
def setup_class(cls):
"""
Values were obtained via the R `energy` package.
R code:
------
> dcov.test(x, y, R=200)
dCov independence test (permutation test)
data: index 1, replicates 200
nV^2 = 45829, p-value = 0.004975
sample estimates:
dCov
47.86925
> DCOR(x, y)
$dCov
[1] 47.86925
$dCor
[1] 0.9999704
$dVarX
[1] 47.28702
$dVarY
[1] 48.46151
"""
np.random.seed(3)
cls.x = np.array(range(1, 101)).reshape((20, 5))
cls.y = cls.x + np.log(cls.x)
cls.dcor_exp = 0.9999704
cls.dcov_exp = 47.86925
cls.dvar_x_exp = 47.28702
cls.dvar_y_exp = 48.46151
cls.pval_emp_exp = 0.004975
cls.test_stat_emp_exp = 45829
# The values above are functions of the following values, and
# therefore when the above group of variables is computed correctly
# it means this group of variables was also correctly calculated.
cls.S_exp = 5686.03162
cls.test_stat_asym_exp = 2.8390102
cls.pval_asym_exp = 0.00452 | Values were obtained via the R `energy` package.
R code:
------
> dcov.test(x, y, R=200)
dCov independence test (permutation test)
data: index 1, replicates 200
nV^2 = 45829, p-value = 0.004975
sample estimates:
dCov
47.86925
> DCOR(x, y)
$dCov
[1] 47.86925
$dCor
[1] 0.9999704
$dVarX
[1] 47.28702
$dVarY
[1] 48.46151 | setup_class | python | statsmodels/statsmodels | statsmodels/stats/tests/test_dist_dependant_measures.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/stats/tests/test_dist_dependant_measures.py | BSD-3-Clause |
def test_results_on_the_iris_dataset(self):
"""
R code example from the `energy` package documentation for
`energy::distance_covariance.test`:
> x <- iris[1:50, 1:4]
> y <- iris[51:100, 1:4]
> set.seed(1)
> dcov.test(x, y, R=200)
dCov independence test (permutation test)
data: index 1, replicates 200
nV^2 = 0.5254, p-value = 0.9552
sample estimates:
dCov
0.1025087
"""
try:
iris = get_rdataset("iris").data.values[:, :4]
except IGNORED_EXCEPTIONS:
pytest.skip('Failed with HTTPError or URLError, these are random')
x = np.asarray(iris[:50], dtype=float)
y = np.asarray(iris[50:100], dtype=float)
stats = ddm.distance_statistics(x, y)
assert_almost_equal(stats.test_statistic, 0.5254, 4)
assert_almost_equal(stats.distance_correlation, 0.3060479, 4)
assert_almost_equal(stats.distance_covariance, 0.1025087, 4)
assert_almost_equal(stats.dvar_x, 0.2712927, 4)
assert_almost_equal(stats.dvar_y, 0.4135274, 4)
assert_almost_equal(stats.S, 0.667456, 4)
test_statistic, _, method = ddm.distance_covariance_test(x, y, B=199)
assert_almost_equal(test_statistic, 0.5254, 4)
assert method == "emp" | R code example from the `energy` package documentation for
`energy::distance_covariance.test`:
> x <- iris[1:50, 1:4]
> y <- iris[51:100, 1:4]
> set.seed(1)
> dcov.test(x, y, R=200)
dCov independence test (permutation test)
data: index 1, replicates 200
nV^2 = 0.5254, p-value = 0.9552
sample estimates:
dCov
0.1025087 | test_results_on_the_iris_dataset | python | statsmodels/statsmodels | statsmodels/stats/tests/test_dist_dependant_measures.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/stats/tests/test_dist_dependant_measures.py | BSD-3-Clause |
def test_results_on_the_quakes_dataset(self):
"""
R code:
------
> data("quakes")
> x = quakes[1:50, 1:3]
> y = quakes[51:100, 1:3]
> dcov.test(x, y, R=200)
dCov independence test (permutation test)
data: index 1, replicates 200
nV^2 = 45046, p-value = 0.4577
sample estimates:
dCov
30.01526
"""
try:
quakes = get_rdataset("quakes").data.values[:, :3]
except IGNORED_EXCEPTIONS:
pytest.skip('Failed with HTTPError or URLError, these are random')
x = np.asarray(quakes[:50], dtype=float)
y = np.asarray(quakes[50:100], dtype=float)
stats = ddm.distance_statistics(x, y)
assert_almost_equal(np.round(stats.test_statistic), 45046, 0)
assert_almost_equal(stats.distance_correlation, 0.1894193, 4)
assert_almost_equal(stats.distance_covariance, 30.01526, 4)
assert_almost_equal(stats.dvar_x, 170.1702, 4)
assert_almost_equal(stats.dvar_y, 147.5545, 4)
assert_almost_equal(stats.S, 52265, 0)
test_statistic, _, method = ddm.distance_covariance_test(x, y, B=199)
assert_almost_equal(np.round(test_statistic), 45046, 0)
assert method == "emp" | R code:
------
> data("quakes")
> x = quakes[1:50, 1:3]
> y = quakes[51:100, 1:3]
> dcov.test(x, y, R=200)
dCov independence test (permutation test)
data: index 1, replicates 200
nV^2 = 45046, p-value = 0.4577
sample estimates:
dCov
30.01526 | test_results_on_the_quakes_dataset | python | statsmodels/statsmodels | statsmodels/stats/tests/test_dist_dependant_measures.py | https://github.com/statsmodels/statsmodels/blob/master/statsmodels/stats/tests/test_dist_dependant_measures.py | BSD-3-Clause |
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