'''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
'''
import numpy as np
from statsmodels.regression.linear_model import OLS
from statsmodels.sandbox.regression.predstd import wls_prediction_std
from . import utils
__all__ = ['plot_fit', 'plot_regress_exog', 'plot_partregress', 'plot_ccpr',
'plot_regress_exog']
[docs]def plot_fit(res, exog_idx, exog_name='', y_true=None, ax=None, fontsize='small'):
"""Plot fit against one regressor.
This creates one graph with the scatterplot of observed values compared to
fitted values.
Parameters
----------
res : result instance
result instance with resid, model.endog and model.exog as attributes
exog_idx : int
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.
Returns
-------
fig : Matplotlib figure instance
If `ax` is None, the created figure. Otherwise the figure to which
`ax` is connected.
Notes
-----
This is currently very simple, no options or varnames yet.
"""
fig, ax = utils.create_mpl_ax(ax)
if exog_name == '':
exog_name = 'variable %d' % exog_idx
#maybe add option for wendog, wexog
y = res.model.endog
x1 = res.model.exog[:, exog_idx]
x1_argsort = np.argsort(x1)
y = y[x1_argsort]
x1 = x1[x1_argsort]
ax.plot(x1, y, 'bo', label='observed')
if not y_true is None:
ax.plot(x1, y_true[x1_argsort], 'b-', label='true')
title = 'fitted versus regressor %s' % exog_name
else:
title = 'fitted versus regressor %s' % exog_name
prstd, iv_l, iv_u = wls_prediction_std(res)
ax.plot(x1, res.fittedvalues[x1_argsort], 'k-', label='fitted') #'k-o')
#ax.plot(x1, iv_u, 'r--')
#ax.plot(x1, iv_l, 'r--')
ax.fill_between(x1, iv_l[x1_argsort], iv_u[x1_argsort], alpha=0.1, color='k')
ax.set_title(title, fontsize=fontsize)
return fig
[docs]def plot_regress_exog(res, exog_idx, exog_name='', 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
----------
res : 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
Notes
-----
This is currently very simple, no options or varnames yet.
"""
fig = utils.create_mpl_fig(fig)
if exog_name == '':
exog_name = 'variable %d' % exog_idx
#maybe add option for wendog, wexog
#y = res.endog
x1 = res.model.exog[:,exog_idx]
ax = fig.add_subplot(2,2,1)
#namestr = ' for %s' % self.name if self.name else ''
ax.plot(x1, res.model.endog, 'o')
ax.set_title('endog versus exog', fontsize='small')# + namestr)
ax = fig.add_subplot(2,2,2)
#namestr = ' for %s' % self.name if self.name else ''
ax.plot(x1, res.resid, 'o')
ax.axhline(y=0)
ax.set_title('residuals versus exog', fontsize='small')# + namestr)
ax = fig.add_subplot(2,2,3)
#namestr = ' for %s' % self.name if self.name else ''
ax.plot(x1, res.fittedvalues, 'o')
ax.set_title('Fitted versus exog', fontsize='small')# + namestr)
ax = fig.add_subplot(2,2,4)
#namestr = ' for %s' % self.name if self.name else ''
ax.plot(x1, res.fittedvalues + res.resid, 'o')
ax.set_title('Fitted plus residuals versus exog', fontsize='small')# + namestr)
fig.suptitle('Regression Plots for %s' % exog_name)
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)
def plot_partregress_ax(endog, exog_i, exog_others, varname='',
title_fontsize=None, ax=None):
"""Plot partial regression for a single regressor.
Parameters
----------
endog : ndarray
endogenous or response variable
exog_i : ndarray
exogenous, explanatory variable
exog_others : ndarray
other exogenous, explanatory variables, the effect of these variables
will be removed by OLS regression
varname : str
name of the variable used in the title
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.
See Also
--------
plot_partregress : Plot partial regression for a set of regressors.
"""
fig, ax = utils.create_mpl_ax(ax)
res1a = OLS(endog, exog_others).fit()
res1b = OLS(exog_i, exog_others).fit()
ax.plot(res1b.resid, res1a.resid, 'o')
res1c = OLS(res1a.resid, res1b.resid).fit()
ax.plot(res1b.resid, res1c.fittedvalues, '-', color='k')
ax.set_title('Partial Regression plot %s' % varname,
fontsize=title_fontsize)# + namestr)
return fig
[docs]def plot_partregress(endog, exog, exog_idx=None, grid=None, fig=None):
"""Plot partial regression for a set of regressors.
Parameters
----------
endog : ndarray
endogenous or response variable
exog : ndarray
exogenous, regressor variables
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 `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_ax : Plot partial regression for a single regressor.
plot_ccpr
References
----------
See http://www.itl.nist.gov/div898/software/dataplot/refman1/auxillar/partregr.htm
"""
fig = utils.create_mpl_fig(fig)
#maybe add option for using wendog, wexog instead
y = endog
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_fontsize = 'small'
else:
nrows = len(exog_idx)
ncols = 1
title_fontsize = None
k_vars = exog.shape[1]
#this function doesn't make sense if k_vars=1
for i,idx in enumerate(exog_idx):
others = range(k_vars)
others.pop(idx)
exog_others = exog[:, others]
ax = fig.add_subplot(nrows, ncols, i+1)
plot_partregress_ax(y, exog[:, idx], exog_others, ax=ax)
return fig
def plot_ccpr_ax(res, exog_idx=None, ax=None):
"""Plot CCPR against one regressor.
Generates a CCPR (component and component-plus-residual) plot.
Parameters
----------
res : result instance
uses exog and params of the result instance
exog_idx : int
(column) index of the exog used in the plot
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.
See Also
--------
plot_ccpr : Creates CCPR plot for multiple regressors in a plot grid.
References
----------
See http://www.itl.nist.gov/div898/software/dataplot/refman1/auxillar/ccpr.htm
"""
fig, ax = utils.create_mpl_ax(ax)
x1 = res.model.exog[:,exog_idx]
#namestr = ' for %s' % self.name if self.name else ''
x1beta = x1*res.params[1]
ax.plot(x1, x1beta + res.resid, 'o')
ax.plot(x1, x1beta, '-')
ax.set_title('X_%d beta_%d plus residuals versus exog (CCPR)' % \
(exog_idx, exog_idx))
return fig
[docs]def plot_ccpr(res, 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
----------
res : 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_ax : 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)
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
for i, idx in enumerate(exog_idx):
ax = fig.add_subplot(nrows, ncols, i+1)
plot_ccpr_ax(res, exog_idx=idx, ax=ax)
return fig
if __name__ == '__main__':
import numpy as np
import statsmodels.api as sm
import matplotlib.pyplot as plt
from statsmodels.sandbox.regression.predstd import wls_prediction_std
#example from tut.ols with changes
#fix a seed for these examples
np.random.seed(9876789)
# OLS non-linear curve but linear in parameters
# ---------------------------------------------
nsample = 100
sig = 0.5
x1 = np.linspace(0, 20, nsample)
x2 = 5 + 3* np.random.randn(nsample)
X = np.c_[x1, x2, np.sin(0.5*x1), (x2-5)**2, np.ones(nsample)]
beta = [0.5, 0.5, 1, -0.04, 5.]
y_true = np.dot(X, beta)
y = y_true + sig * np.random.normal(size=nsample)
#estimate only linear function, misspecified because of non-linear terms
exog0 = sm.add_constant(np.c_[x1, x2], prepend=False)
# plt.figure()
# plt.plot(x1, y, 'o', x1, y_true, 'b-')
res = sm.OLS(y, exog0).fit()
#print res.params
#print res.bse
plot_old = 0 #True
if plot_old:
#current bug predict requires call to model.results
#print res.model.predict
prstd, iv_l, iv_u = wls_prediction_std(res)
plt.plot(x1, res.fittedvalues, 'r-o')
plt.plot(x1, iv_u, 'r--')
plt.plot(x1, iv_l, 'r--')
plt.title('blue: true, red: OLS')
plt.figure()
plt.plot(res.resid, 'o')
plt.title('Residuals')
fig2 = plt.figure()
ax = fig2.add_subplot(2,1,1)
#namestr = ' for %s' % self.name if self.name else ''
plt.plot(x1, res.resid, 'o')
ax.set_title('residuals versus exog')# + namestr)
ax = fig2.add_subplot(2,1,2)
plt.plot(x2, res.resid, 'o')
fig3 = plt.figure()
ax = fig3.add_subplot(2,1,1)
#namestr = ' for %s' % self.name if self.name else ''
plt.plot(x1, res.fittedvalues, 'o')
ax.set_title('Fitted values versus exog')# + namestr)
ax = fig3.add_subplot(2,1,2)
plt.plot(x2, res.fittedvalues, 'o')
fig4 = plt.figure()
ax = fig4.add_subplot(2,1,1)
#namestr = ' for %s' % self.name if self.name else ''
plt.plot(x1, res.fittedvalues + res.resid, 'o')
ax.set_title('Fitted values plus residuals versus exog')# + namestr)
ax = fig4.add_subplot(2,1,2)
plt.plot(x2, res.fittedvalues + res.resid, 'o')
# see http://www.itl.nist.gov/div898/software/dataplot/refman1/auxillar/partregr.htm
fig5 = plt.figure()
ax = fig5.add_subplot(2,1,1)
#namestr = ' for %s' % self.name if self.name else ''
res1a = sm.OLS(y, exog0[:,[0,2]]).fit()
res1b = sm.OLS(x1, exog0[:,[0,2]]).fit()
plt.plot(res1b.resid, res1a.resid, 'o')
res1c = sm.OLS(res1a.resid, res1b.resid).fit()
plt.plot(res1b.resid, res1c.fittedvalues, '-')
ax.set_title('Partial Regression plot')# + namestr)
ax = fig5.add_subplot(2,1,2)
#plt.plot(x2, res.fittedvalues + res.resid, 'o')
res2a = sm.OLS(y, exog0[:,[0,1]]).fit()
res2b = sm.OLS(x2, exog0[:,[0,1]]).fit()
plt.plot(res2b.resid, res2a.resid, 'o')
res2c = sm.OLS(res2a.resid, res2b.resid).fit()
plt.plot(res2b.resid, res2c.fittedvalues, '-')
# see http://www.itl.nist.gov/div898/software/dataplot/refman1/auxillar/ccpr.htm
fig6 = plt.figure()
ax = fig6.add_subplot(2,1,1)
#namestr = ' for %s' % self.name if self.name else ''
x1beta = x1*res.params[1]
x2beta = x2*res.params[2]
plt.plot(x1, x1beta + res.resid, 'o')
plt.plot(x1, x1beta, '-')
ax.set_title('X_i beta_i plus residuals versus exog (CCPR)')# + namestr)
ax = fig6.add_subplot(2,1,2)
plt.plot(x2, x2beta + res.resid, 'o')
plt.plot(x2, x2beta, '-')
#print res.summary()
doplots = 1
if doplots:
plot_fit(res, 0, y_true=None)
plot_fit(res, 1, y_true=None)
plot_partregress(y, exog0, exog_idx=[0,1])
plot_regress_exog(res, exog_idx=[0])
plot_ccpr(res, exog_idx=[0])
plot_ccpr(res, exog_idx=[0,1])
tp = TestPlot()
tp.test_plot_fit()
#plt.show()