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Source code for statsmodels.graphics.gofplots

import numpy as np
from scipy import stats
from statsmodels.regression.linear_model import OLS
from statsmodels.tools.tools import add_constant

from . import utils


__all__ = ['qqplot']


[docs]def qqplot(data, dist=stats.norm, distargs=(), a=0, loc=0, scale=1, fit=False, line=False, ax=None): """ qqplot of the quantiles of x versus the quantiles/ppf of a distribution. Can take arguments specifying the parameters for dist or fit them automatically. (See fit under kwargs.) Parameters ---------- data : array-like 1d data array dist : A scipy.stats or statsmodels distribution Compare x against dist. The default is scipy.stats.distributions.norm (a standard normal). distargs : tuple A tuple of arguments passed to dist to specify it fully so dist.ppf may be called. loc : float Location parameter for dist a : float Offset for the plotting position of an expected order statistic, for example. The plotting positions are given by (i - a)/(nobs - 2*a + 1) for i in range(0,nobs+1) scale : float Scale parameter for dist fit : boolean If fit is false, loc, scale, and distargs are passed to the distribution. If fit is True then the parameters for dist are fit automatically using dist.fit. The quantiles are formed from the standardized data, after subtracting the fitted loc and dividing by the fitted scale. line : str {'45', 's', 'r', q'} or None Options for the reference line to which the data is compared.: - '45' - 45-degree line - 's' - standardized line, the expected order statistics are scaled by the standard deviation of the given sample and have the mean added to them - 'r' - A regression line is fit - 'q' - A line is fit through the quartiles. - None - by default no reference line is added to the plot. - If True a reference line is drawn on the graph. The default is to fit a line via OLS regression. ax : Matplotlib AxesSubplot instance, optional If given, this subplot is used to plot in instead of a new figure being created. Returns ------- fig : Matplotlib figure instance If `ax` is None, the created figure. Otherwise the figure to which `ax` is connected. Examples -------- >>> import statsmodels.api as sm >>> from matplotlib import pyplot as plt >>> data = sm.datasets.longley.load() >>> data.exog = sm.add_constant(data.exog) >>> mod_fit = sm.OLS(data.endog, data.exog).fit() >>> res = mod_fit.resid >>> fig = sm.qqplot(res) >>> plt.show() qqplot against quantiles of t-distribution with 4 degrees of freedom: >>> import scipy.stats as stats >>> fig = sm.qqplot(res, stats.t, distargs=(4,)) >>> plt.show() qqplot against same as above, but with mean 3 and std 10: >>> fig = sm.qqplot(res, stats.t, distargs=(4,), loc=3, scale=10) >>> plt.show() Automatically determine parameters for t distribution including the loc and scale: >>> fig = sm.qqplot(res, stats.t, fit=True, line='45') >>> plt.show() The following plot displays some options, follow the link to see the code. .. plot:: plots/graphics_gofplots_qqplot.py Notes ----- Depends on matplotlib. If `fit` is True then the parameters are fit using the distribution's fit() method. """ fig, ax = utils.create_mpl_ax(ax) if not hasattr(dist, 'ppf'): raise ValueError("distribution must have a ppf method") nobs = data.shape[0] if fit: fit_params = dist.fit(data) loc = fit_params[-2] scale = fit_params[-1] if len(fit_params)>2: dist = dist(*fit_params[:-2], **dict(loc = 0, scale = 1)) else: dist = dist(loc=0, scale=1) elif distargs or loc != 0 or scale != 1: dist = dist(*distargs, **dict(loc=loc, scale=scale)) try: theoretical_quantiles = dist.ppf(plotting_pos(nobs, a)) except: raise ValueError('distribution requires more parameters') sample_quantiles = np.array(data, copy=True) sample_quantiles.sort() if fit: sample_quantiles -= loc sample_quantiles /= scale ax.set_xmargin(0.02) ax.plot(theoretical_quantiles, sample_quantiles, 'bo') if line: if line not in ['r','q','45','s']: msg = "%s option for line not understood" % line raise ValueError(msg) qqline(ax, line, theoretical_quantiles, sample_quantiles, dist) ax.set_xlabel("Theoretical Quantiles") ax.set_ylabel("Sample Quantiles") return fig
[docs]def qqline(ax, line, x=None, y=None, dist=None, fmt='r-'): """ Plot a reference line for a qqplot. Parameters ---------- ax : matplotlib axes instance The axes on which to plot the line line : str {'45','r','s','q'} Options for the reference line to which the data is compared.: - '45' - 45-degree line - 's' - standardized line, the expected order statistics are scaled by the standard deviation of the given sample and have the mean added to them - 'r' - A regression line is fit - 'q' - A line is fit through the quartiles. - None - By default no reference line is added to the plot. x : array X data for plot. Not needed if line is '45'. y : array Y data for plot. Not needed if line is '45'. dist : scipy.stats.distribution A scipy.stats distribution, needed if line is 'q'. Notes ----- There is no return value. The line is plotted on the given `ax`. """ if line == '45': end_pts = zip(ax.get_xlim(), ax.get_ylim()) end_pts[0] = max(end_pts[0]) end_pts[1] = min(end_pts[1]) ax.plot(end_pts, end_pts, fmt) return # does this have any side effects? if x is None and y is None: raise ValueError("If line is not 45, x and y cannot be None.") elif line == 'r': # could use ax.lines[0].get_xdata(), get_ydata(), # but don't know axes are 'clean' y = OLS(y, add_constant(x)).fit().fittedvalues ax.plot(x,y,fmt) elif line == 's': m,b = y.std(), y.mean() ref_line = x*m + b ax.plot(x, ref_line, fmt) elif line == 'q': q25 = stats.scoreatpercentile(y, 25) q75 = stats.scoreatpercentile(y, 75) theoretical_quartiles = dist.ppf([.25,.75]) m = (q75 - q25) / np.diff(theoretical_quartiles) b = q25 - m*theoretical_quartiles[0] ax.plot(x, m*x + b, fmt) #about 10x faster than plotting_position in sandbox and mstats
def plotting_pos(nobs, a): """ Generates sequence of plotting positions Parameters ---------- nobs : int Number of probability points to plot a : float Offset for the plotting position of an expected order statistic, for example. Returns ------- plotting_positions : array The plotting positions Notes ----- The plotting positions are given by (i - a)/(nobs - 2*a + 1) for i in range(0,nobs+1) See also -------- scipy.stats.mstats.plotting_positions """ return (np.arange(1.,nobs+1) - a)/(nobs- 2*a + 1)