# Source code for statsmodels.graphics.regressionplots

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

Author: Josef Perktold
Created: 2011-01-23

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

'''
from statsmodels.compat.pandas import Appender
from statsmodels.compat.python import lrange, lzip

import numpy as np
import pandas as pd
from patsy import dmatrix

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

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

__all__ = ['plot_fit', 'plot_regress_exog', 'plot_partregress', 'plot_ccpr',
'plot_regress_exog', 'plot_partregress_grid', 'plot_ccpr_grid',
'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 : AxesSubplot
The Axes to which to add the plot
lines_idx : int
This is the line on the existing plot to which you want to add
a smoothed lowess line.
frac : float
The fraction of the points to use when doing the lowess fit.
lowess_kwargs
Additional keyword arguments are passes to lowess.

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

[docs]
def plot_fit(results, exog_idx, y_true=None, ax=None, vlines=True, **kwargs):
"""
Plot fit against one regressor.

This creates one graph with the scatterplot of observed values
compared to fitted values.

Parameters
----------
results : Results
A result instance with resid, model.endog and model.exog as
attributes.
exog_idx : {int, str}
Name or index of regressor in exog matrix.
y_true : array_like. optional
If this is not None, then the array is added to the plot.
ax : AxesSubplot, optional
If given, this subplot is used to plot in instead of a new figure being
created.
vlines : bool, optional
If this not True, then the uncertainty (pointwise prediction intervals) of the fit is not
plotted.
**kwargs
The keyword arguments are passed to the plot command for the fitted
values points.

Returns
-------
Figure
If `ax` is None, the created figure.  Otherwise the figure to which
`ax` is connected.

Examples
--------
Load the Statewide Crime data set and perform linear regression with
`poverty` and `hs_grad` as variables and `murder` as the response

>>> import statsmodels.api as sm
>>> import matplotlib.pyplot as plt

>>> data = sm.datasets.statecrime.load_pandas().data
>>> murder = data['murder']
>>> X = data[['poverty', 'hs_grad']]

>>> X["constant"] = 1
>>> y = murder
>>> model = sm.OLS(y, X)
>>> results = model.fit()

Create a plot just for the variable 'Poverty.'
Note that vertical bars representing uncertainty are plotted since vlines is true

>>> fig, ax = plt.subplots()
>>> fig = sm.graphics.plot_fit(results, 0, ax=ax)
>>> ax.set_ylabel("Murder Rate")
>>> ax.set_xlabel("Poverty Level")
>>> ax.set_title("Linear Regression")

>>> plt.show()

.. plot:: plots/graphics_plot_fit_ex.py
"""

fig, ax = utils.create_mpl_ax(ax)

exog_name, exog_idx = utils.maybe_name_or_idx(exog_idx, results.model)
results = maybe_unwrap_results(results)

#maybe add option for wendog, wexog
y = results.model.endog
x1 = results.model.exog[:, exog_idx]
x1_argsort = np.argsort(x1)
y = y[x1_argsort]
x1 = x1[x1_argsort]

ax.plot(x1, y, 'bo', label=results.model.endog_names)
if y_true is not None:
ax.plot(x1, y_true[x1_argsort], 'b-', label='True values')
title = 'Fitted values versus %s' % exog_name

ax.plot(x1, results.fittedvalues[x1_argsort], 'D', color='r',
label='fitted', **kwargs)
if vlines is True:
_, iv_l, iv_u = wls_prediction_std(results)
ax.vlines(x1, iv_l[x1_argsort], iv_u[x1_argsort], linewidth=1,
color='k', alpha=.7)
#ax.fill_between(x1, iv_l[x1_argsort], iv_u[x1_argsort], alpha=0.1,
#                    color='k')
ax.set_title(title)
ax.set_xlabel(exog_name)
ax.set_ylabel(results.model.endog_names)
ax.legend(loc='best', numpoints=1)

return fig

[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
A result instance with resid, model.endog and model.exog as attributes.
exog_idx : int or str
Name or index of regressor in exog matrix.
fig : Figure, optional
If given, this figure is simply returned.  Otherwise a new figure is
created.

Returns
-------
Figure
The value of `fig` if provided. Otherwise a new instance.

Examples
--------
Load the Statewide Crime data set and build a model with regressors
including the rate of high school graduation (hs_grad), population in urban
areas (urban), households below poverty line (poverty), and single person
households (single).  Outcome variable is the murder rate (murder).

Build a 2 by 2 figure based on poverty showing fitted versus actual murder
rate, residuals versus the poverty rate, partial regression plot of poverty,
and CCPR plot for poverty rate.

>>> import statsmodels.api as sm
>>> import matplotlib.pyplot as plt
>>> import statsmodels.formula.api as smf

>>> fig = plt.figure(figsize=(8, 6))
>>> crime_data = sm.datasets.statecrime.load_pandas()
>>> results = smf.ols('murder ~ hs_grad + urban + poverty + single',
...                   data=crime_data.data).fit()
>>> sm.graphics.plot_regress_exog(results, 'poverty', fig=fig)
>>> plt.show()

.. plot:: plots/graphics_regression_regress_exog.py
"""

fig = utils.create_mpl_fig(fig)

exog_name, exog_idx = utils.maybe_name_or_idx(exog_idx, results.model)
results = maybe_unwrap_results(results)

#maybe add option for wendog, wexog
y_name = results.model.endog_names
x1 = results.model.exog[:, exog_idx]
prstd, iv_l, iv_u = wls_prediction_std(results)

ax = fig.add_subplot(2, 2, 1)
ax.plot(x1, results.model.endog, 'o', color='b', alpha=0.9, label=y_name)
ax.plot(x1, results.fittedvalues, 'D', color='r', label='fitted',
alpha=.5)
ax.vlines(x1, iv_l, iv_u, linewidth=1, color='k', alpha=.7)
ax.set_title('Y and Fitted vs. X', fontsize='large')
ax.set_xlabel(exog_name)
ax.set_ylabel(y_name)
ax.legend(loc='best')

ax = fig.add_subplot(2, 2, 2)
ax.plot(x1, results.resid, 'o')
ax.axhline(y=0, color='black')
ax.set_title('Residuals versus %s' % exog_name, fontsize='large')
ax.set_xlabel(exog_name)
ax.set_ylabel("resid")

ax = fig.add_subplot(2, 2, 3)
exog_noti = np.ones(results.model.exog.shape[1], bool)
exog_noti[exog_idx] = False
exog_others = results.model.exog[:, exog_noti]
from pandas import Series
fig = plot_partregress(results.model.data.orig_endog,
Series(x1, name=exog_name,
index=results.model.data.row_labels),
exog_others, obs_labels=False, ax=ax)
ax.set_title('Partial regression plot', fontsize='large')
#ax.set_ylabel("Fitted values")
#ax.set_xlabel(exog_name)

ax = fig.add_subplot(2, 2, 4)
fig = plot_ccpr(results, exog_idx, ax=ax)
ax.set_title('CCPR Plot', fontsize='large')
#ax.set_xlabel(exog_name)
#ax.set_ylabel("Fitted values + resids")

fig.suptitle('Regression Plots for %s' % exog_name, fontsize="large")

fig.tight_layout()

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 does not appear to be used.
res1a = OLS(endog, exog_others).fit()
res1b = OLS(exog_i, exog_others).fit()
res1c = OLS(res1a.resid, res1b.resid).fit()

return res1c, (res1a, res1b)

[docs]
def plot_partregress(endog, exog_i, exog_others, data=None,
title_kwargs={}, obs_labels=True, label_kwargs={},
ax=None, ret_coords=False, eval_env=1, **kwargs):
"""Plot partial regression for a single regressor.

Parameters
----------
endog : {ndarray, str}
The endogenous or response variable. If string is given, you can use a
arbitrary translations as with a formula.
exog_i : {ndarray, str}
The exogenous, explanatory variable. If string is given, you can use a
arbitrary translations as with a formula.
exog_others : {ndarray, list[str]}
Any other exogenous, explanatory variables. If a list of strings is
given, each item is a term in formula. You can use a arbitrary
translations as with a formula. The effect of these variables will be
removed by OLS regression.
data : {DataFrame, dict}
Some kind of data structure with names if the other variables are
given as strings.
title_kwargs : dict
Keyword arguments to pass on for the title. The key to control the
fonts is fontdict.
obs_labels : {bool, array_like}
Whether or not to annotate the plot points with their observation
labels. If obs_labels is a boolean, the point labels will try to do
the right thing. First it will try to use the index of data, then
fall back to the index of exog_i. Alternatively, you may give an
array-like object corresponding to the observation numbers.
label_kwargs : dict
Keyword arguments that control annotate for the observation labels.
ax : AxesSubplot, optional
If given, this subplot is used to plot in instead of a new figure being
created.
ret_coords : bool
If True will return the coordinates of the points in the plot. You
can use this to add your own annotations.
eval_env : int
Patsy eval environment if user functions and formulas are used in
defining endog or exog.
**kwargs
The keyword arguments passed to plot for the points.

Returns
-------
fig : Figure
If `ax` is None, the created figure.  Otherwise the figure to which
`ax` is connected.
coords : list, optional
If ret_coords is True, return a tuple of arrays (x_coords, y_coords).

--------
plot_partregress_grid : Plot partial regression for a set of regressors.

Notes
-----
The slope of the fitted line is the that of `exog_i` in the full
multiple regression. The individual points can be used to assess the
influence of points on the estimated coefficient.

Examples
--------
Load the Statewide Crime data set and plot partial regression of the rate
of high school graduation (hs_grad) on the murder rate(murder).

The effects of the percent of the population living in urban areas (urban),
below the poverty line (poverty) , and in a single person household (single)
are removed by OLS regression.

>>> import statsmodels.api as sm
>>> import matplotlib.pyplot as plt

>>> crime_data = sm.datasets.statecrime.load_pandas()
...                              exog_others=['urban', 'poverty', 'single'],
...                              data=crime_data.data, obs_labels=False)
>>> plt.show()

.. plot:: plots/graphics_regression_partregress.py

More detailed examples can be found in the Regression Plots notebook
on the examples page.
"""
#NOTE: there is no interaction between possible missing data and
#obs_labels yet, so this will need to be tweaked a bit for this case
fig, ax = utils.create_mpl_ax(ax)

# strings, use patsy to transform to data
if isinstance(endog, str):
endog = dmatrix(endog + "-1", data, eval_env=eval_env)

if isinstance(exog_others, str):
RHS = dmatrix(exog_others, data, eval_env=eval_env)
elif isinstance(exog_others, list):
RHS = "+".join(exog_others)
RHS = dmatrix(RHS, data, eval_env=eval_env)
else:
RHS = exog_others
RHS_isemtpy = False
if isinstance(RHS, np.ndarray) and RHS.size==0:
RHS_isemtpy = True
elif isinstance(RHS, pd.DataFrame) and RHS.empty:
RHS_isemtpy = True
if isinstance(exog_i, str):
exog_i = dmatrix(exog_i + "-1", data, eval_env=eval_env)

# all arrays or pandas-like

if RHS_isemtpy:
endog = np.asarray(endog)
exog_i = np.asarray(exog_i)
ax.plot(endog, exog_i, 'o', **kwargs)
fitted_line = OLS(endog, exog_i).fit()
x_axis_endog_name = 'x' if isinstance(exog_i, np.ndarray) else exog_i.name
y_axis_endog_name = 'y' if isinstance(endog, np.ndarray) else endog.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, np.asarray(fitted_line.params)[0], color='k', ax=ax)

if x_axis_endog_name == 'y':  # for no names regression will just get a y
x_axis_endog_name = 'x'  # this is misleading, so use x
ax.set_xlabel("e(%s | X)" % x_axis_endog_name)
ax.set_ylabel("e(%s | X)" % y_axis_endog_name)
ax.set_title('Partial Regression Plot', **title_kwargs)

# NOTE: if we want to get super fancy, we could annotate if a point is
# clicked using this widget
# http://stackoverflow.com/questions/4652439/
# is-there-a-matplotlib-equivalent-of-matlabs-datacursormode/
# 4674445#4674445
if obs_labels is True:
if data is not None:
obs_labels = data.index
elif hasattr(exog_i, "index"):
obs_labels = exog_i.index
else:
obs_labels = res_xaxis.model.data.row_labels
#NOTE: row_labels can be None.
#Maybe we should fix this to never be the case.
if obs_labels is None:
obs_labels = lrange(len(exog_i))

if obs_labels is not False:  # could be array_like
if len(obs_labels) != len(exog_i):
raise ValueError("obs_labels does not match length of exog_i")
label_kwargs.update(dict(ha="center", va="bottom"))
ax = utils.annotate_axes(lrange(len(obs_labels)), obs_labels,
lzip(res_xaxis.resid, res_yaxis.resid),
[(0, 5)] * len(obs_labels), "x-large", ax=ax,
**label_kwargs)

if ret_coords:
return fig, (res_xaxis.resid, res_yaxis.resid)
else:
return fig

[docs]
def plot_partregress_grid(results, exog_idx=None, grid=None, fig=None):
"""
Plot partial regression for a set of regressors.

Parameters
----------
results : Results instance
A regression model results instance.
exog_idx : {None, list[int], list[str]}
The indices  or column names of the exog used in the plot, default is
all.
grid : {None, tuple[int]}
If grid is given, then it is used for the arrangement of the subplots.
The format of grid is  (nrows, ncols). If grid is None, then ncol is
one, if there are only 2 subplots, and the number of columns is two
otherwise.
fig : Figure, optional
If given, this figure is simply returned.  Otherwise a new figure is
created.

Returns
-------
Figure
If `fig` is None, the created figure.  Otherwise `fig` itself.

--------
plot_partregress : Plot partial regression for a single regressor.
plot_ccpr : Plot CCPR against one regressor

Notes
-----
A subplot is created for each explanatory variable given by exog_idx.
The partial regression plot shows the relationship between the response
and the given explanatory variable after removing the effect of all other
explanatory variables in exog.

References
----------
See http://www.itl.nist.gov/div898/software/dataplot/refman1/auxillar/partregr.htm

Examples
--------
Using the state crime dataset separately plot the effect of the each
variable on the on the outcome, murder rate while accounting for the effect
of all other variables in the model visualized with a grid of partial
regression plots.

>>> from statsmodels.graphics.regressionplots import plot_partregress_grid
>>> import statsmodels.api as sm
>>> import matplotlib.pyplot as plt
>>> import statsmodels.formula.api as smf

>>> fig = plt.figure(figsize=(8, 6))
>>> crime_data = sm.datasets.statecrime.load_pandas()
>>> results = smf.ols('murder ~ hs_grad + urban + poverty + single',
...                   data=crime_data.data).fit()
>>> plot_partregress_grid(results, fig=fig)
>>> plt.show()

.. plot:: plots/graphics_regression_partregress_grid.py
"""
import pandas
fig = utils.create_mpl_fig(fig)

exog_name, exog_idx = utils.maybe_name_or_idx(exog_idx, results.model)

# TODO: maybe add option for using wendog, wexog instead
y = pandas.Series(results.model.endog, name=results.model.endog_names)
exog = results.model.exog

k_vars = exog.shape[1]
# this function does not make sense if k_vars=1

nrows = (len(exog_idx) + 1) // 2
ncols = 1 if nrows == len(exog_idx) else 2
if grid is not None:
nrows, ncols = grid
if ncols > 1:
title_kwargs = {"fontdict": {"fontsize": 'small'}}

# for indexing purposes
other_names = np.array(results.model.exog_names)
for i, idx in enumerate(exog_idx):
others = lrange(k_vars)
others.pop(idx)
exog_others = pandas.DataFrame(exog[:, others],
columns=other_names[others])
ax = fig.add_subplot(nrows, ncols, i + 1)
plot_partregress(y, pandas.Series(exog[:, idx],
name=other_names[idx]),
exog_others, ax=ax, title_kwargs=title_kwargs,
obs_labels=False)
ax.set_title("")

fig.suptitle("Partial Regression Plot", fontsize="large")
fig.tight_layout()

return fig

[docs]
def plot_ccpr(results, exog_idx, ax=None):
"""
Plot CCPR against one regressor.

Generates a component and component-plus-residual (CCPR) plot.

Parameters
----------
results : result instance
A regression results instance.
exog_idx : {int, str}
Exogenous, explanatory variable. If string is given, it should
be the variable name that you want to use, and you can use arbitrary
translations as with a formula.
ax : AxesSubplot, optional
If given, it is used to plot in instead of a new figure being
created.

Returns
-------
Figure
If `ax` is None, the created figure.  Otherwise the figure to which
`ax` is connected.

--------
plot_ccpr_grid : Creates CCPR plot for multiple regressors in a plot grid.

Notes
-----
The CCPR plot provides a way to judge the effect of one regressor on the
response variable by taking into account the effects of the other
independent variables. The partial residuals plot is defined as
Residuals + B_i*X_i versus X_i. The component adds the B_i*X_i versus
X_i to show where the fitted line would lie. Care should be taken if X_i
is highly correlated with any of the other independent variables. If this
is the case, the variance evident in the plot will be an underestimate of
the true variance.

References
----------
http://www.itl.nist.gov/div898/software/dataplot/refman1/auxillar/ccpr.htm

Examples
--------
Using the state crime dataset plot the effect of the rate of single
households ('single') on the murder rate while accounting for high school
graduation rate ('hs_grad'), percentage of people in an urban area, and rate
of poverty ('poverty').

>>> import statsmodels.api as sm
>>> import matplotlib.pyplot as plt
>>> import statsmodels.formula.api as smf

>>> crime_data = sm.datasets.statecrime.load_pandas()
>>> results = smf.ols('murder ~ hs_grad + urban + poverty + single',
...                   data=crime_data.data).fit()
>>> sm.graphics.plot_ccpr(results, 'single')
>>> plt.show()

.. plot:: plots/graphics_regression_ccpr.py
"""
fig, ax = utils.create_mpl_ax(ax)

exog_name, exog_idx = utils.maybe_name_or_idx(exog_idx, results.model)
results = maybe_unwrap_results(results)

x1 = results.model.exog[:, exog_idx]
#namestr = ' for %s' % self.name if self.name else ''
x1beta = x1*results.params[exog_idx]
ax.plot(x1, x1beta + results.resid, 'o')
from statsmodels.tools.tools import add_constant
mod = OLS(x1beta, add_constant(x1)).fit()
params = mod.params
fig = abline_plot(*params, **dict(ax=ax))
#ax.plot(x1, x1beta, '-')
ax.set_title('Component and component plus residual plot')
ax.set_ylabel("Residual + %s*beta_%d" % (exog_name, exog_idx))
ax.set_xlabel("%s" % exog_name)

return fig

[docs]
def plot_ccpr_grid(results, exog_idx=None, grid=None, fig=None):
"""
Generate CCPR plots against a set of regressors, plot in a grid.

Generates a grid of component and component-plus-residual (CCPR) plots.

Parameters
----------
results : result instance
A results instance with exog and params.
exog_idx : None or list of int
The indices or column names of the exog used in the plot.
grid : None or tuple of int (nrows, ncols)
If grid is given, then it is used for the arrangement of the subplots.
If grid is None, then ncol is one, if there are only 2 subplots, and
the number of columns is two otherwise.
fig : Figure, optional
If given, this figure is simply returned.  Otherwise a new figure is
created.

Returns
-------
Figure
If `ax` is None, the created figure.  Otherwise the figure to which
`ax` is connected.

--------
plot_ccpr : Creates CCPR plot for a single regressor.

Notes
-----
Partial residual plots are formed as::

Res + Betahat(i)*Xi versus Xi

Betahat(i)*Xi versus Xi

References
----------
See http://www.itl.nist.gov/div898/software/dataplot/refman1/auxillar/ccpr.htm

Examples
--------
Using the state crime dataset separately plot the effect of the each
variable on the on the outcome, murder rate while accounting for the effect
of all other variables in the model.

>>> import statsmodels.api as sm
>>> import matplotlib.pyplot as plt
>>> import statsmodels.formula.api as smf

>>> fig = plt.figure(figsize=(8, 8))
>>> crime_data = sm.datasets.statecrime.load_pandas()
>>> results = smf.ols('murder ~ hs_grad + urban + poverty + single',
...                   data=crime_data.data).fit()
>>> sm.graphics.plot_ccpr_grid(results, fig=fig)
>>> plt.show()

.. plot:: plots/graphics_regression_ccpr_grid.py
"""
fig = utils.create_mpl_fig(fig)

exog_name, exog_idx = utils.maybe_name_or_idx(exog_idx, results.model)

if grid is not None:
nrows, ncols = grid
else:
if len(exog_idx) > 2:
nrows = int(np.ceil(len(exog_idx)/2.))
ncols = 2
else:
nrows = len(exog_idx)
ncols = 1

seen_constant = 0
for i, idx in enumerate(exog_idx):
if results.model.exog[:, idx].var() == 0:
seen_constant = 1
continue

ax = fig.add_subplot(nrows, ncols, i+1-seen_constant)
fig = plot_ccpr(results, exog_idx=idx, ax=ax)
ax.set_title("")

fig.suptitle("Component-Component Plus Residual Plot", fontsize="large")

fig.tight_layout()

return fig

[docs]
def abline_plot(intercept=None, slope=None, horiz=None, vert=None,
model_results=None, ax=None, **kwargs):
"""
Plot a line given an intercept and slope.

Parameters
----------
intercept : float
The intercept of the line.
slope : float
The slope of the line.
horiz : float or array_like
Data for horizontal lines on the y-axis.
vert : array_like
Data for verterical lines on the x-axis.
model_results : statsmodels results instance
Any object that has a two-value `params` attribute. Assumed that it
is (intercept, slope).
ax : axes, optional
Matplotlib axes instance.
**kwargs
Options passed to matplotlib.pyplot.plt.

Returns
-------
Figure
The figure given by `ax.figure` or a new instance.

Examples
--------
>>> import numpy as np
>>> import statsmodels.api as sm

>>> np.random.seed(12345)
>>> X = sm.add_constant(np.random.normal(0, 20, size=30))
>>> y = np.dot(X, [25, 3.5]) + np.random.normal(0, 30, size=30)
>>> mod = sm.OLS(y,X).fit()
>>> fig = sm.graphics.abline_plot(model_results=mod)
>>> ax = fig.axes[0]
>>> ax.scatter(X[:,1], y)
>>> ax.margins(.1)
>>> import matplotlib.pyplot as plt
>>> plt.show()

.. plot:: plots/graphics_regression_abline.py
"""
if ax is not None:  # get axis limits first thing, do not change these
x = ax.get_xlim()
else:
x = None

fig, ax = utils.create_mpl_ax(ax)

if model_results:
intercept, slope = model_results.params
if x is None:
x = [model_results.model.exog[:, 1].min(),
model_results.model.exog[:, 1].max()]
else:
if not (intercept is not None and slope is not None):
raise ValueError("specify slope and intercepty or model_results")
if x is None:
x = ax.get_xlim()

data_y = [x[0]*slope+intercept, x[1]*slope+intercept]
ax.set_xlim(x)
#ax.set_ylim(y)

from matplotlib.lines import Line2D

class ABLine2D(Line2D):
def __init__(self, *args, **kwargs):
super(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)
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

@Appender(_plot_influence_doc.format(**{
'extra_params_doc': "results: object\n"
"        Results for a fitted regression model.\n"
"    influence: instance\n"
"        The instance of Influence for model."}))
def _influence_plot(results, influence, external=True, alpha=.05,
criterion="cooks", size=48, plot_alpha=.75, ax=None,
leverage=None, resid=None,
**kwargs):
# leverage and resid kwds are used only internally for MLEInfluence
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

if leverage is None:
leverage = infl.hat_matrix_diag
if resid is None:
ylabel = "Studentized Residuals"
if external:
resid = infl.resid_studentized_external
else:
resid = infl.resid_studentized
else:
resid = np.asarray(resid)
ylabel = "Residuals"

from scipy import stats

cutoff = stats.t.ppf(1.-alpha/2, results.df_resid)
large_resid = np.abs(resid) > cutoff
large_leverage = leverage > _high_leverage(results)
large_points = np.logical_or(large_resid, large_leverage)

ax.scatter(leverage, resid, s=psize, alpha=plot_alpha)

# add point labels
labels = results.model.data.row_labels
if labels is None:
labels = lrange(len(resid))
ax = utils.annotate_axes(np.where(large_points)[0], labels,
lzip(leverage, resid),
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(ylabel, **font)
ax.set_xlabel("Leverage", **font)
ax.set_title("Influence Plot", **font)
return fig

[docs]
@Appender(_plot_influence_doc.format(**{
'extra_params_doc': "results : Results\n"
"        Results for a fitted regression model."}))
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

@Appender(_plot_leverage_resid2_doc.format({
'extra_params_doc': "results: object\n"
"    Results for a fitted regression model\n"
"influence: instance\n"
"    instance of Influence for model"}))
def _plot_leverage_resid2(results, influence, alpha=.05, ax=None,
**kwargs):

from scipy.stats import norm, zscore
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

[docs]
@Appender(_plot_leverage_resid2_doc.format({
'extra_params_doc': "results : object\n"
"    Results for a fitted regression model"}))
def plot_leverage_resid2(results, alpha=.05, ax=None, **kwargs):

infl = results.get_influence()
return _plot_leverage_resid2(results, infl, alpha=alpha, ax=ax, **kwargs)

'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):

model = results.model

fig, ax = utils.create_mpl_ax(ax)

endog_resid, focus_exog_resid =\
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 isinstance(focus_exog, 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

@Appender(_plot_partial_residuals_doc % {
'extra_params_doc': "results : object\n"
"    Results 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 isinstance(focus_exog, 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

[docs]
@Appender(_plot_ceres_residuals_doc % {
'extra_params_doc': "results : Results\n"
"        Results instance of a fitted regression "
"model."})
def plot_ceres_residuals(results, focus_exog, frac=0.66, cond_means=None,
ax=None):

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

def ceres_resids(results, focus_exog, frac=0.66, cond_means=None):
"""
Calculate the CERES residuals (Conditional Expectation Partial
Residuals) for a fitted model.

Parameters
----------
results : model results instance
The fitted model for which the CERES residuals are calculated.
focus_exog : int
The column of results.model.exog used as the 'focus variable'.
frac : float, optional
Lowess smoothing parameter for estimating the conditional
means.  Not used if `cond_means` is provided.
cond_means : array_like, optional
If provided, the columns of this array are the conditional
means E[exog | focus exog], where exog ranges over some
or all of the columns of exog other than focus exog.  If
this is an empty nx0 array, the conditional means are
treated as being zero.  If None, the conditional means are
estimated.

Returns
-------
An array containing the CERES residuals.

Notes
-----
If `cond_means` is not provided, it is obtained by smoothing each
column of exog (except the focus column) against the focus column.

Currently only supports GLM, GEE, and OLS models.
"""

model = results.model

if not isinstance(model, (GLM, GEE, OLS)):
raise ValueError("ceres residuals not available for %s" %
model.__class__.__name__)

focus_exog, focus_col = utils.maybe_name_or_idx(focus_exog, model)

# Indices of non-focus columns
ix_nf = range(len(results.params))
ix_nf = list(ix_nf)
ix_nf.pop(focus_col)
nnf = len(ix_nf)

# Estimate the conditional means if not provided.
if cond_means is None:

# Below we calculate E[x | focus] where x is each column other
# than the focus column.  We do not want the intercept when we do
# this so we remove it here.
pexog = model.exog[:, ix_nf]
pexog -= pexog.mean(0)
u, s, vt = np.linalg.svd(pexog, 0)
ii = np.flatnonzero(s > 1e-6)
pexog = u[:, ii]

fcol = model.exog[:, focus_col]
cond_means = np.empty((len(fcol), pexog.shape[1]))
for j in range(pexog.shape[1]):

# Get the fitted values for column i given the other
# columns (skip the intercept).
y0 = pexog[:, j]

cf = lowess(y0, fcol, frac=frac, return_sorted=False)

cond_means[:, j] = cf

new_exog = np.concatenate((model.exog[:, ix_nf], cond_means), axis=1)

# Refit the model using the adjusted exog values
klass = model.__class__
init_kwargs = model._get_init_kwds()
new_model = klass(model.endog, new_exog, **init_kwargs)
new_result = new_model.fit()

# The partial residual, with respect to l(x2) (notation of Cook 1998)
presid = model.endog - new_result.fittedvalues
if isinstance(model, (GLM, GEE)):
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)):
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 : {int, str}
The column of results.model.exog or a variable name that is
to be residualized against the other predictors.
resid_type : str
The type of residuals to use for the dependent variable.  If
None, uses `resid_deviance` for GLM/GEE and `resid` otherwise.
use_glm_weights : bool
Only used if the model is a GLM or GEE.  If True, the
residuals for the focus predictor are computed using WLS, with
the weights obtained from the IRLS calculations for fitting
the GLM.  If False, unweighted regression is used.
fit_kwargs : dict, optional
Keyword arguments to be passed to fit when refitting the
model.

Returns
-------
endog_resid : array_like
The residuals for the original exog
focus_exog_resid : array_like
The residuals for the focus predictor

Notes
-----
The 'focus variable' residuals are always obtained using linear
regression.

Currently only GLM, GEE, and OLS models are supported.
"""

model = results.model
if not isinstance(model, (GEE, GLM, OLS)):
raise ValueError("model type %s not supported for added variable residuals" %
model.__class__.__name__)

exog = model.exog
endog = model.endog

focus_exog, focus_col = utils.maybe_name_or_idx(focus_exog, model)

focus_exog_vals = exog[:, focus_col]

# Default residuals
if resid_type is None:
if isinstance(model, (GEE, GLM)):
resid_type = "resid_deviance"
else:
resid_type = "resid"

ii = range(exog.shape[1])
ii = list(ii)
ii.pop(focus_col)
reduced_exog = exog[:, ii]
start_params = results.params[ii]

klass = model.__class__

kwargs = model._get_init_kwds()
new_model = klass(endog, reduced_exog, **kwargs)
args = {"start_params": start_params}
if fit_kwargs is not None:
args.update(fit_kwargs)
new_result = new_model.fit(**args)
if not getattr(new_result, "converged", True):
raise ValueError("fit did not converge when calculating added variable residuals")

try:
endog_resid = getattr(new_result, resid_type)
except AttributeError:
raise ValueError("'%s' residual type not available" % resid_type)

import statsmodels.regression.linear_model as lm

if isinstance(model, (GLM, GEE)) and use_glm_weights:
weights = model.family.weights(results.fittedvalues)
if hasattr(model, "data_weights"):
weights = weights * model.data_weights
lm_results = lm.WLS(focus_exog_vals, reduced_exog, weights).fit()
else:
lm_results = lm.OLS(focus_exog_vals, reduced_exog).fit()
focus_exog_resid = lm_results.resid

return endog_resid, focus_exog_resid
``````

Last update: Dec 14, 2023