Source code for statsmodels.graphics.regressionplots

'''Partial Regression plot and residual plots to find misspecification


Author: Josef Perktold
License: BSD-3
Created: 2011-01-23

update
2011-06-05 : start to convert example to usable functions
2011-10-27 : docstrings

'''
from statsmodels.compat.python import lrange, string_types, lzip, range
import numpy as np
import pandas as pd
from patsy import dmatrix

from statsmodels.regression.linear_model import OLS, GLS, WLS
from statsmodels.genmod.generalized_linear_model import GLM
from statsmodels.genmod.generalized_estimating_equations import GEE
from statsmodels.sandbox.regression.predstd import wls_prediction_std
from statsmodels.graphics import utils
from statsmodels.nonparametric.smoothers_lowess import lowess
from statsmodels.tools.tools import maybe_unwrap_results
from statsmodels.base import model

from ._regressionplots_doc import (
    _plot_added_variable_doc,
    _plot_partial_residuals_doc,
    _plot_ceres_residuals_doc,
    _plot_influence_doc,
    _plot_leverage_resid2_doc)

__all__ = ['plot_fit', 'plot_regress_exog', 'plot_partregress', 'plot_ccpr',
           'plot_regress_exog', 'plot_partregress_grid', 'plot_ccpr_grid',
           'add_lowess', 'abline_plot', 'influence_plot',
           'plot_leverage_resid2', 'added_variable_resids',
           'partial_resids', 'ceres_resids', 'plot_added_variable',
           'plot_partial_residuals', 'plot_ceres_residuals']

#TODO: consider moving to influence module
def _high_leverage(results):
    #TODO: replace 1 with k_constant
    return 2. * (results.df_model + 1)/results.nobs


def add_lowess(ax, lines_idx=0, frac=.2, **lowess_kwargs):
    """
    Add Lowess line to a plot.

    Parameters
    ----------
    ax : matplotlib Axes instance
        The Axes to which to add the plot
    lines_idx : int
        This is the line on the existing plot to which you want to add
        a smoothed lowess line.
    frac : float
        The fraction of the points to use when doing the lowess fit.
    lowess_kwargs
        Additional keyword arguments are passes to lowess.

    Returns
    -------
    fig : matplotlib Figure instance
        The figure that holds the instance.
    """
    y0 = ax.get_lines()[lines_idx]._y
    x0 = ax.get_lines()[lines_idx]._x
    lres = lowess(y0, x0, frac=frac, **lowess_kwargs)
    ax.plot(lres[:, 0], lres[:, 1], 'r', lw=1.5)
    return ax.figure


[docs]def plot_fit(results, exog_idx, y_true=None, ax=None, **kwargs): """Plot fit against one regressor. This creates one graph with the scatterplot of observed values compared to fitted values. Parameters ---------- results : result instance result instance with resid, model.endog and model.exog as attributes x_var : int or str Name or index of regressor in exog matrix. y_true : array_like (optional) If this is not None, then the array is added to the plot ax : Matplotlib AxesSubplot instance, optional If given, this subplot is used to plot in instead of a new figure being created. kwargs The keyword arguments are passed to the plot command for the fitted values points. Returns ------- fig : Matplotlib figure instance If `ax` is None, the created figure. Otherwise the figure to which `ax` is connected. Examples -------- Load the Statewide Crime data set and perform linear regression with `poverty` and `hs_grad` as variables and `murder` as the response >>> import statsmodels.api as sm >>> import matplotlib.pyplot as plt >>> data = sm.datasets.statecrime.load_pandas().data >>> murder = data['murder'] >>> X = data[['poverty', 'hs_grad']] >>> X["constant"] = 1 >>> y = murder >>> model = sm.OLS(y, X) >>> results = model.fit() Create a plot just for the variable 'Poverty': >>> fig, ax = plt.subplots() >>> fig = sm.graphics.plot_fit(results, 0, ax=ax) >>> ax.set_ylabel("Murder Rate") >>> ax.set_xlabel("Poverty Level") >>> ax.set_title("Linear Regression") >>> plt.show() .. plot:: plots/graphics_plot_fit_ex.py """ fig, ax = utils.create_mpl_ax(ax) exog_name, exog_idx = utils.maybe_name_or_idx(exog_idx, results.model) results = maybe_unwrap_results(results) #maybe add option for wendog, wexog y = results.model.endog x1 = results.model.exog[:, exog_idx] x1_argsort = np.argsort(x1) y = y[x1_argsort] x1 = x1[x1_argsort] ax.plot(x1, y, 'bo', label=results.model.endog_names) if not y_true is None: ax.plot(x1, y_true[x1_argsort], 'b-', label='True values') title = 'Fitted values versus %s' % exog_name prstd, iv_l, iv_u = wls_prediction_std(results) ax.plot(x1, results.fittedvalues[x1_argsort], 'D', color='r', label='fitted', **kwargs) ax.vlines(x1, iv_l[x1_argsort], iv_u[x1_argsort], linewidth=1, color='k', alpha=.7) #ax.fill_between(x1, iv_l[x1_argsort], iv_u[x1_argsort], alpha=0.1, # color='k') ax.set_title(title) ax.set_xlabel(exog_name) ax.set_ylabel(results.model.endog_names) ax.legend(loc='best', numpoints=1) return fig
[docs]def plot_regress_exog(results, exog_idx, fig=None): """Plot regression results against one regressor. This plots four graphs in a 2 by 2 figure: 'endog versus exog', 'residuals versus exog', 'fitted versus exog' and 'fitted plus residual versus exog' Parameters ---------- results : result instance result instance with resid, model.endog and model.exog as attributes exog_idx : int index of regressor in exog matrix fig : Matplotlib figure instance, optional If given, this figure is simply returned. Otherwise a new figure is created. Returns ------- fig : matplotlib figure instance """ fig = utils.create_mpl_fig(fig) exog_name, exog_idx = utils.maybe_name_or_idx(exog_idx, results.model) results = maybe_unwrap_results(results) #maybe add option for wendog, wexog y_name = results.model.endog_names x1 = results.model.exog[:, exog_idx] prstd, iv_l, iv_u = wls_prediction_std(results) ax = fig.add_subplot(2, 2, 1) ax.plot(x1, results.model.endog, 'o', color='b', alpha=0.9, label=y_name) ax.plot(x1, results.fittedvalues, 'D', color='r', label='fitted', alpha=.5) ax.vlines(x1, iv_l, iv_u, linewidth=1, color='k', alpha=.7) ax.set_title('Y and Fitted vs. X', fontsize='large') ax.set_xlabel(exog_name) ax.set_ylabel(y_name) ax.legend(loc='best') ax = fig.add_subplot(2, 2, 2) ax.plot(x1, results.resid, 'o') ax.axhline(y=0, color='black') ax.set_title('Residuals versus %s' % exog_name, fontsize='large') ax.set_xlabel(exog_name) ax.set_ylabel("resid") ax = fig.add_subplot(2, 2, 3) exog_noti = np.ones(results.model.exog.shape[1], bool) exog_noti[exog_idx] = False exog_others = results.model.exog[:, exog_noti] from pandas import Series fig = plot_partregress(results.model.data.orig_endog, Series(x1, name=exog_name, index=results.model.data.row_labels), exog_others, obs_labels=False, ax=ax) ax.set_title('Partial regression plot', fontsize='large') #ax.set_ylabel("Fitted values") #ax.set_xlabel(exog_name) ax = fig.add_subplot(2, 2, 4) fig = plot_ccpr(results, exog_idx, ax=ax) ax.set_title('CCPR Plot', fontsize='large') #ax.set_xlabel(exog_name) #ax.set_ylabel("Fitted values + resids") fig.suptitle('Regression Plots for %s' % exog_name, fontsize="large") fig.tight_layout() fig.subplots_adjust(top=.90) return fig
def _partial_regression(endog, exog_i, exog_others): """Partial regression. regress endog on exog_i conditional on exog_others uses OLS Parameters ---------- endog : array_like exog : array_like exog_others : array_like Returns ------- res1c : OLS results instance (res1a, res1b) : tuple of OLS results instances results from regression of endog on exog_others and of exog_i on exog_others """ #FIXME: This function doesn't appear to be used. res1a = OLS(endog, exog_others).fit() res1b = OLS(exog_i, exog_others).fit() res1c = OLS(res1a.resid, res1b.resid).fit() return res1c, (res1a, res1b)
[docs]def plot_partregress(endog, exog_i, exog_others, data=None, title_kwargs={}, obs_labels=True, label_kwargs={}, ax=None, ret_coords=False, **kwargs): """Plot partial regression for a single regressor. Parameters ---------- endog : ndarray or string endogenous or response variable. If string is given, you can use a arbitrary translations as with a formula. exog_i : ndarray or string exogenous, explanatory variable. If string is given, you can use a arbitrary translations as with a formula. exog_others : ndarray or list of strings other exogenous, explanatory variables. If a list of strings is given, each item is a term in formula. You can use a arbitrary translations as with a formula. The effect of these variables will be removed by OLS regression. data : DataFrame, dict, or recarray Some kind of data structure with names if the other variables are given as strings. title_kwargs : dict Keyword arguments to pass on for the title. The key to control the fonts is fontdict. obs_labels : bool or array-like Whether or not to annotate the plot points with their observation labels. If obs_labels is a boolean, the point labels will try to do the right thing. First it will try to use the index of data, then fall back to the index of exog_i. Alternatively, you may give an array-like object corresponding to the obseveration numbers. labels_kwargs : dict Keyword arguments that control annotate for the observation labels. ax : Matplotlib AxesSubplot instance, optional If given, this subplot is used to plot in instead of a new figure being created. ret_coords : bool If True will return the coordinates of the points in the plot. You can use this to add your own annotations. kwargs The keyword arguments passed to plot for the points. Returns ------- fig : Matplotlib figure instance If `ax` is None, the created figure. Otherwise the figure to which `ax` is connected. coords : list, optional If ret_coords is True, return a tuple of arrays (x_coords, y_coords). Notes ----- The slope of the fitted line is the that of `exog_i` in the full multiple regression. The individual points can be used to assess the influence of points on the estimated coefficient. See Also -------- plot_partregress_grid : Plot partial regression for a set of regressors. """ #NOTE: there is no interaction between possible missing data and #obs_labels yet, so this will need to be tweaked a bit for this case fig, ax = utils.create_mpl_ax(ax) # strings, use patsy to transform to data if isinstance(endog, string_types): endog = dmatrix(endog + "-1", data) if isinstance(exog_others, string_types): RHS = dmatrix(exog_others, data) elif isinstance(exog_others, list): RHS = "+".join(exog_others) RHS = dmatrix(RHS, data) else: RHS = exog_others RHS_isemtpy = False if isinstance(RHS, np.ndarray) and RHS.size==0: RHS_isemtpy = True elif isinstance(RHS, pd.DataFrame) and RHS.empty: RHS_isemtpy = True if isinstance(exog_i, string_types): exog_i = dmatrix(exog_i + "-1", data) # all arrays or pandas-like if RHS_isemtpy: ax.plot(endog, exog_i, 'o', **kwargs) fitted_line = OLS(endog, exog_i).fit() x_axis_endog_name = 'x' if isinstance(exog_i, np.ndarray) else exog_i.name y_axis_endog_name = 'y' if isinstance(endog, np.ndarray) else endog.design_info.column_names[0] else: res_yaxis = OLS(endog, RHS).fit() res_xaxis = OLS(exog_i, RHS).fit() xaxis_resid = res_xaxis.resid yaxis_resid = res_yaxis.resid x_axis_endog_name = res_xaxis.model.endog_names y_axis_endog_name = res_yaxis.model.endog_names ax.plot(xaxis_resid, yaxis_resid, 'o', **kwargs) fitted_line = OLS(yaxis_resid, xaxis_resid).fit() fig = abline_plot(0, fitted_line.params[0], color='k', ax=ax) if x_axis_endog_name == 'y': # for no names regression will just get a y x_axis_endog_name = 'x' # this is misleading, so use x ax.set_xlabel("e(%s | X)" % x_axis_endog_name) ax.set_ylabel("e(%s | X)" % y_axis_endog_name) ax.set_title('Partial Regression Plot', **title_kwargs) #NOTE: if we want to get super fancy, we could annotate if a point is #clicked using this widget #http://stackoverflow.com/questions/4652439/ #is-there-a-matplotlib-equivalent-of-matlabs-datacursormode/ #4674445#4674445 if obs_labels is True: if data is not None: obs_labels = data.index elif hasattr(exog_i, "index"): obs_labels = exog_i.index else: obs_labels = res_xaxis.model.data.row_labels #NOTE: row_labels can be None. #Maybe we should fix this to never be the case. if obs_labels is None: obs_labels = lrange(len(exog_i)) if obs_labels is not False: # could be array-like if len(obs_labels) != len(exog_i): raise ValueError("obs_labels does not match length of exog_i") label_kwargs.update(dict(ha="center", va="bottom")) ax = utils.annotate_axes(lrange(len(obs_labels)), obs_labels, lzip(res_xaxis.resid, res_yaxis.resid), [(0, 5)] * len(obs_labels), "x-large", ax=ax, **label_kwargs) if ret_coords: return fig, (res_xaxis.resid, res_yaxis.resid) else: return fig
def plot_partregress_grid(results, exog_idx=None, grid=None, fig=None): """Plot partial regression for a set of regressors. Parameters ---------- results : results instance A regression model results instance exog_idx : None, list of ints, list of strings (column) indices of the exog used in the plot, default is all. grid : None or tuple of int (nrows, ncols) If grid is given, then it is used for the arrangement of the subplots. If grid is None, then ncol is one, if there are only 2 subplots, and the number of columns is two otherwise. fig : Matplotlib figure instance, optional If given, this figure is simply returned. Otherwise a new figure is created. Returns ------- fig : Matplotlib figure instance If `fig` is None, the created figure. Otherwise `fig` itself. Notes ----- A subplot is created for each explanatory variable given by exog_idx. The partial regression plot shows the relationship between the response and the given explanatory variable after removing the effect of all other explanatory variables in exog. See Also -------- plot_partregress : Plot partial regression for a single regressor. plot_ccpr References ---------- See http://www.itl.nist.gov/div898/software/dataplot/refman1/auxillar/partregr.htm """ import pandas fig = utils.create_mpl_fig(fig) exog_name, exog_idx = utils.maybe_name_or_idx(exog_idx, results.model) #maybe add option for using wendog, wexog instead y = pandas.Series(results.model.endog, name=results.model.endog_names) exog = results.model.exog k_vars = exog.shape[1] #this function doesn't make sense if k_vars=1 if not grid is None: nrows, ncols = grid else: if len(exog_idx) > 2: nrows = int(np.ceil(len(exog_idx)/2.)) ncols = 2 title_kwargs = {"fontdict" : {"fontsize" : 'small'}} else: nrows = len(exog_idx) ncols = 1 title_kwargs = {} # for indexing purposes other_names = np.array(results.model.exog_names) for i, idx in enumerate(exog_idx): others = lrange(k_vars) others.pop(idx) exog_others = pandas.DataFrame(exog[:, others], columns=other_names[others]) ax = fig.add_subplot(nrows, ncols, i+1) plot_partregress(y, pandas.Series(exog[:, idx], name=other_names[idx]), exog_others, ax=ax, title_kwargs=title_kwargs, obs_labels=False) ax.set_title("") fig.suptitle("Partial Regression Plot", fontsize="large") fig.tight_layout() fig.subplots_adjust(top=.95) return fig
[docs]def plot_ccpr(results, exog_idx, ax=None): """Plot CCPR against one regressor. Generates a CCPR (component and component-plus-residual) plot. Parameters ---------- results : result instance A regression results instance. exog_idx : int or string Exogenous, explanatory variable. If string is given, it should be the variable name that you want to use, and you can use arbitrary translations as with a formula. ax : Matplotlib AxesSubplot instance, optional If given, it 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. See Also -------- plot_ccpr_grid : Creates CCPR plot for multiple regressors in a plot grid. Notes ----- The CCPR plot provides a way to judge the effect of one regressor on the response variable by taking into account the effects of the other independent variables. The partial residuals plot is defined as Residuals + B_i*X_i versus X_i. The component adds the B_i*X_i versus X_i to show where the fitted line would lie. Care should be taken if X_i is highly correlated with any of the other independent variables. If this is the case, the variance evident in the plot will be an underestimate of the true variance. References ---------- http://www.itl.nist.gov/div898/software/dataplot/refman1/auxillar/ccpr.htm """ fig, ax = utils.create_mpl_ax(ax) exog_name, exog_idx = utils.maybe_name_or_idx(exog_idx, results.model) results = maybe_unwrap_results(results) x1 = results.model.exog[:, exog_idx] #namestr = ' for %s' % self.name if self.name else '' x1beta = x1*results.params[exog_idx] ax.plot(x1, x1beta + results.resid, 'o') from statsmodels.tools.tools import add_constant mod = OLS(x1beta, add_constant(x1)).fit() params = mod.params fig = abline_plot(*params, **dict(ax=ax)) #ax.plot(x1, x1beta, '-') ax.set_title('Component and component plus residual plot') ax.set_ylabel("Residual + %s*beta_%d" % (exog_name, exog_idx)) ax.set_xlabel("%s" % exog_name) return fig
def plot_ccpr_grid(results, exog_idx=None, grid=None, fig=None): """Generate CCPR plots against a set of regressors, plot in a grid. Generates a grid of CCPR (component and component-plus-residual) plots. Parameters ---------- results : result instance uses exog and params of the result instance exog_idx : None or list of int (column) indices of the exog used in the plot grid : None or tuple of int (nrows, ncols) If grid is given, then it is used for the arrangement of the subplots. If grid is None, then ncol is one, if there are only 2 subplots, and the number of columns is two otherwise. fig : Matplotlib figure instance, optional If given, this figure is simply returned. Otherwise a new figure is created. Returns ------- fig : Matplotlib figure instance If `ax` is None, the created figure. Otherwise the figure to which `ax` is connected. Notes ----- Partial residual plots are formed as:: Res + Betahat(i)*Xi versus Xi and CCPR adds:: Betahat(i)*Xi versus Xi See Also -------- plot_ccpr : Creates CCPR plot for a single regressor. References ---------- See http://www.itl.nist.gov/div898/software/dataplot/refman1/auxillar/ccpr.htm """ fig = utils.create_mpl_fig(fig) exog_name, exog_idx = utils.maybe_name_or_idx(exog_idx, results.model) if grid is not None: nrows, ncols = grid else: if len(exog_idx) > 2: nrows = int(np.ceil(len(exog_idx)/2.)) ncols = 2 else: nrows = len(exog_idx) ncols = 1 seen_constant = 0 for i, idx in enumerate(exog_idx): if results.model.exog[:, idx].var() == 0: seen_constant = 1 continue ax = fig.add_subplot(nrows, ncols, i+1-seen_constant) fig = plot_ccpr(results, exog_idx=idx, ax=ax) ax.set_title("") fig.suptitle("Component-Component Plus Residual Plot", fontsize="large") fig.tight_layout() fig.subplots_adjust(top=.95) return fig
[docs]def abline_plot(intercept=None, slope=None, horiz=None, vert=None, model_results=None, ax=None, **kwargs): """ Plots a line given an intercept and slope. intercept : float The intercept of the line slope : float The slope of the line horiz : float or array-like Data for horizontal lines on the y-axis vert : array-like Data for verterical lines on the x-axis model_results : statsmodels results instance Any object that has a two-value `params` attribute. Assumed that it is (intercept, slope) ax : axes, optional Matplotlib axes instance kwargs Options passed to matplotlib.pyplot.plt Returns ------- fig : Figure The figure given by `ax.figure` or a new instance. Examples -------- >>> import numpy as np >>> import statsmodels.api as sm >>> np.random.seed(12345) >>> X = sm.add_constant(np.random.normal(0, 20, size=30)) >>> y = np.dot(X, [25, 3.5]) + np.random.normal(0, 30, size=30) >>> mod = sm.OLS(y,X).fit() >>> fig = sm.graphics.abline_plot(model_results=mod) >>> ax = fig.axes[0] >>> ax.scatter(X[:,1], y) >>> ax.margins(.1) >>> import matplotlib.pyplot as plt >>> plt.show() """ if ax is not None: # get axis limits first thing, don't change these x = ax.get_xlim() else: x = None fig, ax = utils.create_mpl_ax(ax) if model_results: intercept, slope = model_results.params if x is None: x = [model_results.model.exog[:, 1].min(), model_results.model.exog[:, 1].max()] else: if not (intercept is not None and slope is not None): raise ValueError("specify slope and intercepty or model_results") if x is None: x = ax.get_xlim() data_y = [x[0]*slope+intercept, x[1]*slope+intercept] ax.set_xlim(x) #ax.set_ylim(y) from matplotlib.lines import Line2D class ABLine2D(Line2D): def __init__(self, *args, **kwargs): super(ABLine2D, self).__init__(*args, **kwargs) self.id_xlim_callback = None self.id_ylim_callback = None def remove(self): ax = self.axes if self.id_xlim_callback: ax.callbacks.disconnect(self.id_xlim_callback) if self.id_ylim_callback: ax.callbacks.disconnect(self.id_ylim_callback) super(ABLine2D, self).remove() def update_datalim(self, ax): ax.set_autoscale_on(False) children = ax.get_children() ablines = [child for child in children if child is self] abline = ablines[0] x = ax.get_xlim() y = [x[0] * slope + intercept, x[1] * slope + intercept] abline.set_data(x, y) ax.figure.canvas.draw() # TODO: how to intercept something like a margins call and adjust? line = ABLine2D(x, data_y, **kwargs) ax.add_line(line) line.id_xlim_callback = ax.callbacks.connect('xlim_changed', line.update_datalim) line.id_ylim_callback = ax.callbacks.connect('ylim_changed', line.update_datalim) if horiz: ax.hline(horiz) if vert: ax.vline(vert) return fig
def _influence_plot(results, influence, external=True, alpha=.05, criterion="cooks", size=48, plot_alpha=.75, ax=None, **kwargs): infl = influence fig, ax = utils.create_mpl_ax(ax) if criterion.lower().startswith('coo'): psize = infl.cooks_distance[0] elif criterion.lower().startswith('dff'): psize = np.abs(infl.dffits[0]) else: raise ValueError("Criterion %s not understood" % criterion) # scale the variables #TODO: what is the correct scaling and the assumption here? #we want plots to be comparable across different plots #so we would need to use the expected distribution of criterion probably old_range = np.ptp(psize) new_range = size**2 - 8**2 psize = (psize - psize.min()) * new_range/old_range + 8**2 leverage = infl.hat_matrix_diag if external: resids = infl.resid_studentized_external else: resids = infl.resid_studentized from scipy import stats cutoff = stats.t.ppf(1.-alpha/2, results.df_resid) large_resid = np.abs(resids) > cutoff large_leverage = leverage > _high_leverage(results) large_points = np.logical_or(large_resid, large_leverage) ax.scatter(leverage, resids, s=psize, alpha=plot_alpha) # add point labels labels = results.model.data.row_labels if labels is None: labels = lrange(len(resids)) ax = utils.annotate_axes(np.where(large_points)[0], labels, lzip(leverage, resids), lzip(-(psize/2)**.5, (psize/2)**.5), "x-large", ax) #TODO: make configurable or let people do it ex-post? font = {"fontsize" : 16, "color" : "black"} ax.set_ylabel("Studentized Residuals", **font) ax.set_xlabel("H Leverage", **font) ax.set_title("Influence Plot", **font) return fig _influence_plot.__doc__ = _plot_influence_doc.format({ 'extra_params_doc' : "results: object\n\tResults for a fitted regression model\n" "influence: instance\n instance of Influence for model"})
[docs]def influence_plot(results, external=True, alpha=.05, criterion="cooks", size=48, plot_alpha=.75, ax=None, **kwargs): infl = results.get_influence() res = _influence_plot(results, infl, external=external, alpha=alpha, criterion=criterion, size=size, plot_alpha=plot_alpha, ax=ax, **kwargs) return res
influence_plot.__doc__ = _plot_influence_doc.format({ 'extra_params_doc' : "results: object\n" " Results for a fitted regression model"}) def _plot_leverage_resid2(results, influence, alpha=.05, ax=None, **kwargs): from scipy.stats import zscore, norm fig, ax = utils.create_mpl_ax(ax) infl = influence leverage = infl.hat_matrix_diag resid = zscore(infl.resid) ax.plot(resid**2, leverage, 'o', **kwargs) ax.set_xlabel("Normalized residuals**2") ax.set_ylabel("Leverage") ax.set_title("Leverage vs. Normalized residuals squared") large_leverage = leverage > _high_leverage(results) #norm or t here if standardized? cutoff = norm.ppf(1.-alpha/2) large_resid = np.abs(resid) > cutoff labels = results.model.data.row_labels if labels is None: labels = lrange(int(results.nobs)) index = np.where(np.logical_or(large_leverage, large_resid))[0] ax = utils.annotate_axes(index, labels, lzip(resid**2, leverage), [(0, 5)]*int(results.nobs), "large", ax=ax, ha="center", va="bottom") ax.margins(.075, .075) return fig _plot_leverage_resid2.__doc__ = _plot_leverage_resid2_doc.format({ 'extra_params_doc' : "results: object\n\tResults for a fitted regression model\n" "influence: instance\n instance of Influence for model"})
[docs]def plot_leverage_resid2(results, alpha=.05, ax=None, **kwargs): infl = results.get_influence() res = _plot_leverage_resid2(results, infl, alpha=.05, ax=None, **kwargs) return res
plot_leverage_resid2.__doc__ = _plot_leverage_resid2_doc.format({ 'extra_params_doc' : "results: object\n" " Results for a fitted regression model"}) def plot_added_variable(results, focus_exog, resid_type=None, use_glm_weights=True, fit_kwargs=None, ax=None): # Docstring attached below model = results.model fig, ax = utils.create_mpl_ax(ax) endog_resid, focus_exog_resid =\ added_variable_resids(results, focus_exog, resid_type=resid_type, use_glm_weights=use_glm_weights, fit_kwargs=fit_kwargs) ax.plot(focus_exog_resid, endog_resid, 'o', alpha=0.6) ax.set_title('Added variable plot', fontsize='large') if type(focus_exog) is str: xname = focus_exog else: xname = model.exog_names[focus_exog] ax.set_xlabel(xname, size=15) ax.set_ylabel(model.endog_names + " residuals", size=15) return fig plot_added_variable.__doc__ = _plot_added_variable_doc % { 'extra_params_doc' : "results: object\n\tResults for a fitted regression model"} def plot_partial_residuals(results, focus_exog, ax=None): # Docstring attached below model = results.model focus_exog, focus_col = utils.maybe_name_or_idx(focus_exog, model) pr = partial_resids(results, focus_exog) focus_exog_vals = results.model.exog[:, focus_col] fig, ax = utils.create_mpl_ax(ax) ax.plot(focus_exog_vals, pr, 'o', alpha=0.6) ax.set_title('Partial residuals plot', fontsize='large') if type(focus_exog) is str: xname = focus_exog else: xname = model.exog_names[focus_exog] ax.set_xlabel(xname, size=15) ax.set_ylabel("Component plus residual", size=15) return fig plot_partial_residuals.__doc__ = _plot_partial_residuals_doc % { 'extra_params_doc' : "results: object\n\tResults for a fitted regression model"} def plot_ceres_residuals(results, focus_exog, frac=0.66, cond_means=None, ax=None): # Docstring attached below model = results.model focus_exog, focus_col = utils.maybe_name_or_idx(focus_exog, model) presid = ceres_resids(results, focus_exog, frac=frac, cond_means=cond_means) focus_exog_vals = model.exog[:, focus_col] fig, ax = utils.create_mpl_ax(ax) ax.plot(focus_exog_vals, presid, 'o', alpha=0.6) ax.set_title('CERES residuals plot', fontsize='large') ax.set_xlabel(focus_exog, size=15) ax.set_ylabel("Component plus residual", size=15) return fig plot_ceres_residuals.__doc__ = _plot_ceres_residuals_doc % { 'extra_params_doc' : "results: object\n\tResults for a fitted regression model"} def ceres_resids(results, focus_exog, frac=0.66, cond_means=None): """ Calculate the CERES residuals (Conditional Expectation Partial Residuals) for a fitted model. Parameters ---------- results : model results instance The fitted model for which the CERES residuals are calculated. focus_exog : int The column of results.model.exog used as the 'focus variable'. frac : float, optional Lowess smoothing parameter for estimating the conditional means. Not used if `cond_means` is provided. cond_means : array-like, optional If provided, the columns of this array are the conditional means E[exog | focus exog], where exog ranges over some or all of the columns of exog other than focus exog. If this is an empty nx0 array, the conditional means are treated as being zero. If None, the conditional means are estimated. Returns ------- An array containing the CERES residuals. Notes ----- If `cond_means` is not provided, it is obtained by smoothing each column of exog (except the focus column) against the focus column. Currently only supports GLM, GEE, and OLS models. """ model = results.model if not isinstance(model, (GLM, GEE, OLS)): raise ValueError("ceres residuals not available for %s" % model.__class__.__name__) focus_exog, focus_col = utils.maybe_name_or_idx(focus_exog, model) # Indices of non-focus columns ix_nf = range(len(results.params)) ix_nf = list(ix_nf) ix_nf.pop(focus_col) nnf = len(ix_nf) # Estimate the conditional means if not provided. if cond_means is None: # Below we calculate E[x | focus] where x is each column other # than the focus column. We don't want the intercept when we do # this so we remove it here. pexog = model.exog[:, ix_nf] pexog -= pexog.mean(0) u, s, vt = np.linalg.svd(pexog, 0) ii = np.flatnonzero(s > 1e-6) pexog = u[:, ii] fcol = model.exog[:, focus_col] cond_means = np.empty((len(fcol), pexog.shape[1])) for j in range(pexog.shape[1]): # Get the fitted values for column i given the other # columns (skip the intercept). y0 = pexog[:, j] cf = lowess(y0, fcol, frac=frac, return_sorted=False) cond_means[:, j] = cf new_exog = np.concatenate((model.exog[:, ix_nf], cond_means), axis=1) # Refit the model using the adjusted exog values klass = model.__class__ init_kwargs = model._get_init_kwds() new_model = klass(model.endog, new_exog, **init_kwargs) new_result = new_model.fit() # The partial residual, with respect to l(x2) (notation of Cook 1998) presid = model.endog - new_result.fittedvalues if isinstance(model, (GLM, GEE)): presid *= model.family.link.deriv(new_result.fittedvalues) if new_exog.shape[1] > nnf: presid += np.dot(new_exog[:, nnf:], new_result.params[nnf:]) return presid def partial_resids(results, focus_exog): """ Returns partial residuals for a fitted model with respect to a 'focus predictor'. Parameters ---------- results : results instance A fitted regression model. focus col : int The column index of model.exog with respect to which the partial residuals are calculated. Returns ------- An array of partial residuals. References ---------- RD Cook and R Croos-Dabrera (1998). Partial residual plots in generalized linear models. Journal of the American Statistical Association, 93:442. """ # TODO: could be a method of results # TODO: see Cook et al (1998) for a more general definition # The calculation follows equation (8) from Cook's paper. model = results.model resid = model.endog - results.predict() if isinstance(model, (GLM, GEE)): resid *= model.family.link.deriv(results.fittedvalues) elif isinstance(model, (OLS, GLS, WLS)): pass # No need to do anything else: raise ValueError("Partial residuals for '%s' not implemented." % type(model)) if type(focus_exog) is str: focus_col = model.exog_names.index(focus_exog) else: focus_col = focus_exog focus_val = results.params[focus_col] * model.exog[:, focus_col] return focus_val + resid def added_variable_resids(results, focus_exog, resid_type=None, use_glm_weights=True, fit_kwargs=None): """ Residualize the endog variable and a 'focus' exog variable in a regression model with respect to the other exog variables. Parameters ---------- results : regression results instance A fitted model including the focus exog and all other predictors of interest. focus_exog : integer or string The column of results.model.exog or a variable name that is to be residualized against the other predictors. resid_type : string The type of residuals to use for the dependent variable. If None, uses `resid_deviance` for GLM/GEE and `resid` otherwise. use_glm_weights : bool Only used if the model is a GLM or GEE. If True, the residuals for the focus predictor are computed using WLS, with the weights obtained from the IRLS calculations for fitting the GLM. If False, unweighted regression is used. fit_kwargs : dict, optional Keyword arguments to be passed to fit when refitting the model. Returns ------- endog_resid : array-like The residuals for the original exog focus_exog_resid : array-like The residuals for the focus predictor Notes ----- The 'focus variable' residuals are always obtained using linear regression. Currently only GLM, GEE, and OLS models are supported. """ model = results.model if not isinstance(model, (GEE, GLM, OLS)): raise ValueError("model type %s not supported for added variable residuals" % model.__class__.__name__) exog = model.exog endog = model.endog focus_exog, focus_col = utils.maybe_name_or_idx(focus_exog, model) focus_exog_vals = exog[:, focus_col] # Default residuals if resid_type is None: if isinstance(model, (GEE, GLM)): resid_type = "resid_deviance" else: resid_type = "resid" ii = range(exog.shape[1]) ii = list(ii) ii.pop(focus_col) reduced_exog = exog[:, ii] start_params = results.params[ii] klass = model.__class__ kwargs = model._get_init_kwds() new_model = klass(endog, reduced_exog, **kwargs) args = {"start_params": start_params} if fit_kwargs is not None: args.update(fit_kwargs) new_result = new_model.fit(**args) if not new_result.converged: raise ValueError("fit did not converge when calculating added variable residuals") try: endog_resid = getattr(new_result, resid_type) except AttributeError: raise ValueError("'%s' residual type not available" % resid_type) import statsmodels.regression.linear_model as lm if isinstance(model, (GLM, GEE)) and use_glm_weights: weights = model.family.weights(results.fittedvalues) if hasattr(model, "data_weights"): weights = weights * model.data_weights lm_results = lm.WLS(focus_exog_vals, reduced_exog, weights).fit() else: lm_results = lm.OLS(focus_exog_vals, reduced_exog).fit() focus_exog_resid = lm_results.resid return endog_resid, focus_exog_resid