Source code for statsmodels.stats.robust_compare

# -*- coding: utf-8 -*-
"""Anova k-sample comparison without and with trimming

Created on Sun Jun 09 23:51:34 2013

Author: Josef Perktold

import numbers
import numpy as np

# the trimboth and trim_mean are taken from scipy.stats.stats
# and enhanced by axis

[docs]def trimboth(a, proportiontocut, axis=0): """ Slices off a proportion of items from both ends of an array. Slices off the passed proportion of items from both ends of the passed array (i.e., with `proportiontocut` = 0.1, slices leftmost 10% **and** rightmost 10% of scores). You must pre-sort the array if you want 'proper' trimming. Slices off less if proportion results in a non-integer slice index (i.e., conservatively slices off `proportiontocut`). Parameters ---------- a : array_like Data to trim. proportiontocut : float or int Proportion of total data set to trim of each end. axis : int or None Axis along which the observations are trimmed. The default is to trim along axis=0. If axis is None then the array will be flattened before trimming. Returns ------- out : ndarray Trimmed version of array `a`. Examples -------- >>> from scipy import stats >>> a = np.arange(20) >>> b = stats.trimboth(a, 0.1) >>> b.shape (16,) """ a = np.asarray(a) if axis is None: a = a.ravel() axis = 0 nobs = a.shape[axis] lowercut = int(proportiontocut * nobs) uppercut = nobs - lowercut if (lowercut >= uppercut): raise ValueError("Proportion too big.") sl = [slice(None)] * a.ndim sl[axis] = slice(lowercut, uppercut) return a[tuple(sl)]
[docs]def trim_mean(a, proportiontocut, axis=0): """ Return mean of array after trimming observations from both lower and upper tails. If `proportiontocut` = 0.1, slices off 'leftmost' and 'rightmost' 10% of scores. Slices off LESS if proportion results in a non-integer slice index (i.e., conservatively slices off `proportiontocut` ). Parameters ---------- a : array_like Input array proportiontocut : float Fraction to cut off of both tails of the observations axis : int or None Axis along which the trimmed means are computed. The default is axis=0. If axis is None then the trimmed mean will be computed for the flattened array. Returns ------- trim_mean : ndarray Mean of trimmed array. """ newa = trimboth(np.sort(a, axis), proportiontocut, axis=axis) return np.mean(newa, axis=axis)
[docs]class TrimmedMean(object): """ class for trimmed and winsorized one sample statistics axis is None, i.e. ravelling, is not supported """ def __init__(self, data, fraction, is_sorted=False, axis=0): = np.asarray(data) # TODO: add pandas handling, maybe not if this stays internal self.axis = axis self.fraction = fraction self.nobs = nobs =[axis] self.lowercut = lowercut = int(fraction * nobs) self.uppercut = uppercut = nobs - lowercut if (lowercut >= uppercut): raise ValueError("Proportion too big.") self.nobs_reduced = nobs - 2 * lowercut = [slice(None)] *[axis] = slice(self.lowercut, self.uppercut) # numpy requires now tuple for indexing, not list = tuple( if not is_sorted: self.data_sorted = np.sort(, axis=axis) else: self.data_sorted = # this only works for axis=0 self.lowerbound = np.take(self.data_sorted, lowercut, axis=axis) self.upperbound = np.take(self.data_sorted, uppercut - 1, axis=axis) # self.lowerbound = self.data_sorted[lowercut] # self.upperbound = self.data_sorted[uppercut - 1] @property def data_trimmed(self): # returns a view return self.data_sorted[] @property # cache def data_winsorized(self): """winsorized data """ lb = np.expand_dims(self.lowerbound, self.axis) ub = np.expand_dims(self.upperbound, self.axis) return np.clip(self.data_sorted, lb, ub) @property def mean_trimmed(self): """mean of trimmed data """ return np.mean(self.data_sorted[tuple(], self.axis) @property def mean_winsorized(self): """mean of winsorized data """ return np.mean(self.data_winsorized, self.axis) @property def var_winsorized(self): """variance of winsorized data """ # hardcoded ddof = 1 return np.var(self.data_winsorized, ddof=1, axis=self.axis) @property def std_mean_trimmed(self): """standard error of trimmed mean """ se = np.sqrt(self.var_winsorized / self.nobs_reduced) # trimming creates correlation across trimmed observations # trimming is based on order statistics of the data # wilcox 2012, p.61 se *= np.sqrt(self.nobs / self.nobs_reduced) return se @property def std_mean_winsorized(self): """standard error of winsorized mean """ # the following matches Wilcox, WRS2 std_ = np.sqrt(self.var_winsorized / self.nobs) std_ *= (self.nobs - 1) / (self.nobs_reduced - 1) # old version # tm = self # formula from an old SAS manual page, simplified # std_ = np.sqrt(tm.var_winsorized / (tm.nobs_reduced - 1) * # (tm.nobs - 1.) / tm.nobs) return std_
[docs] def ttest_mean(self, value=0, transform='trimmed', alternative='two-sided'): """ One sample ttest for trimmed or Winsorized mean Parameters ---------- value : float Value of the mean under the Null hypothesis transform : {'trimmed', 'winsorized'} Specified whether the mean test is based on trimmed or winsorized data. alternative : {'two-sided', 'larger', 'smaller'} Notes ----- p-value is based on the approximate t-distribution of the test statistic. The approximation is valid if the underlying distribution is symmetric. """ import statsmodels.stats.weightstats as smws df = self.nobs_reduced - 1 if transform == 'trimmed': mean_ = self.mean_trimmed std_ = self.std_mean_trimmed elif transform == 'winsorized': mean_ = self.mean_winsorized std_ = self.std_mean_winsorized else: raise ValueError("transform can only be 'trimmed' or 'winsorized'") res = smws._tstat_generic(mean_, 0, std_, df, alternative=alternative, diff=value) return res + (df,)
[docs] def reset_fraction(self, frac): """create a TrimmedMean instance with a new trimming fraction This reuses the sorted array from the current instance. """ tm = TrimmedMean(self.data_sorted, frac, is_sorted=True, axis=self.axis) = # TODO: this will not work if there is processing of meta-information # in __init__, # for example storing a pandas DataFrame or Series index return tm
[docs]def scale_transform(data, center='median', transform='abs', trim_frac=0.2, axis=0): """Transform data for variance comparison for Levene type tests Parameters ---------- data : array_like Observations for the data. center : "median", "mean", "trimmed" or float Statistic used for centering observations. If a float, then this value is used to center. Default is median. transform : 'abs', 'square', 'identity' or a callable The transform for the centered data. trim_frac : float in [0, 0.5) Fraction of observations that are trimmed on each side of the sorted observations. This is only used if center is `trimmed`. axis : int Axis along which the data are transformed when centering. Returns ------- res : ndarray transformed data in the same shape as the original data. """ x = np.asarray(data) # x is shorthand from earlier code if transform == 'abs': tfunc = np.abs elif transform == 'square': tfunc = lambda x: x * x # noqa elif transform == 'identity': tfunc = lambda x: x # noqa elif callable(transform): tfunc = transform else: raise ValueError('transform should be abs, square or exp') if center == 'median': res = tfunc(x - np.expand_dims(np.median(x, axis=axis), axis)) elif center == 'mean': res = tfunc(x - np.expand_dims(np.mean(x, axis=axis), axis)) elif center == 'trimmed': center = trim_mean(x, trim_frac, axis=axis) res = tfunc(x - np.expand_dims(center, axis)) elif isinstance(center, numbers.Number): res = tfunc(x - center) else: raise ValueError('center should be median, mean or trimmed') return res