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)
x1 = results.model.exog[:, exog_idx]
#namestr = ' for %s' % self.name if self.name else ''
x1beta = x1*results._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_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
def plot_rsquare(self, ncomp=None, ax=None):
"""
Box plots of the individual series R-square against the number of PCs
Parameters
----------
ncomp : int, optional
Number of components ot include in the plot. If None, will
plot the minimum of 10 or the number of computed components
ax : Matplotlib axes instance, optional
An axes on which to draw the graph. If omitted, new a figure
is created
Returns
-------
fig : figure
Handle to the figure
"""
import statsmodels.graphics.utils as gutils
fig, ax = gutils.create_mpl_ax(ax)
ncomp = 10 if ncomp is None else ncomp
ncomp = min(ncomp, self._ncomp)
# R2s in rows, series in columns
r2s = 1.0 - self._ess_indiv / self._tss_indiv
r2s = r2s[1:]
r2s = r2s[:ncomp]
ax.boxplot(r2s.T)
ax.set_title('Individual Input $R^2$')
ax.set_ylabel('$R^2$')
ax.set_xlabel('Number of Included Principal Components')
return fig
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
def _plot_index(self, y, ylabel, threshold=None, title=None, ax=None,**kwds):
from statsmodels.graphics import utils
fig, ax = utils.create_mpl_ax(ax)
if title is None:
title = "Index Plot"
nobs = len(self.endog)
index = np.arange(nobs)
ax.scatter(index, y, **kwds)
if threshold == 'all':
large_points = np.ones(nobs, np.bool_)
else:
large_points = np.abs(y) > threshold
psize = 3 * np.ones(nobs)
# add point labels
labels = self.results.model.data.row_labels
if labels is None:
labels = np.arange(nobs)
ax = utils.annotate_axes(np.where(large_points)[0], labels,
lzip(index, y),
lzip(-psize, psize), "large",
ax)
font = {"fontsize" : 16, "color" : "black"}
ax.set_ylabel(ylabel, **font)
ax.set_xlabel("Observation", **font)
ax.set_title(title, **font)
return fig
def seasonal_plot(grouped_x, xticklabels, ylabel=None, ax=None):
"""
Consider using one of month_plot or quarter_plot unless you need
irregular plotting.
Parameters
----------
grouped_x : iterable of DataFrames
Should be a GroupBy object (or similar pair of group_names and groups
as DataFrames) with a DatetimeIndex or PeriodIndex
"""
fig, ax = utils.create_mpl_ax(ax)
start = 0
ticks = []
for season, df in grouped_x:
df = df.copy() # or sort balks for series. may be better way
sort_values(df, inplace=True)
nobs = len(df)
x_plot = np.arange(start, start + nobs)
ticks.append(x_plot.mean())
ax.plot(x_plot, df.values, 'k')
ax.hlines(df.values.mean(), x_plot[0], x_plot[-1], colors='k')
start += nobs
ax.set_xticks(ticks)
ax.set_xticklabels(xticklabels)
ax.set_ylabel(ylabel)
ax.margins(.1, .05)
return fig
def plot_scree(self, ncomp=None, log_scale=True,
cumulative=False, ax=None):
"""
Plot of the ordered eigenvalues
Parameters
----------
ncomp : int, optional
Number of components ot include in the plot. If None, will
included the same as the number of components computed
log_scale : boot, optional
Flag indicating whether ot use a log scale for the y-axis
cumulative : bool, optional
Flag indicating whether to plot the eigenvalues or cumulative
eigenvalues
ax : Matplotlib axes instance, optional
An axes on which to draw the graph. If omitted, new a figure
is created
Returns
-------
fig : figure
Handle to the figure
"""
import statsmodels.graphics.utils as gutils
fig, ax = gutils.create_mpl_ax(ax)
ncomp = self._ncomp if ncomp is None else ncomp
vals = np.asarray(self.eigenvals)
vals = vals[:self._ncomp]
if cumulative:
vals = np.cumsum(vals)
if log_scale:
ax.set_yscale('log')
ax.plot(np.arange(ncomp), vals[: ncomp], 'bo')
ax.autoscale(tight=True)
xlim = np.array(ax.get_xlim())
sp = xlim[1] - xlim[0]
xlim += 0.02 * np.array([-sp, sp])
ax.set_xlim(xlim)
ylim = np.array(ax.get_ylim())
scale = 0.02
if log_scale:
sp = np.log(ylim[1] / ylim[0])
ylim = np.exp(np.array([np.log(ylim[0]) - scale * sp,
np.log(ylim[1]) + scale * sp]))
else:
sp = ylim[1] - ylim[0]
ylim += scale * np.array([-sp, sp])
ax.set_ylim(ylim)
ax.set_title('Scree Plot')
ax.set_ylabel('Eigenvalue')
ax.set_xlabel('Component Number')
fig.tight_layout()
return fig
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.
"""
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')
return fig
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
def plot_partial(self, smooth_index, plot_se=True, cpr=False,
include_constant=True, ax=None):
"""plot the contribution of a smooth term to the linear prediction
Parameters
----------
smooth_index : int
index of the smooth term within list of smooth terms
plot_se : book
If plot_se is true, then the confidence interval for the linear
prediction will be added to the plot.
cpr : bool
If cpr (component plus residual) is true, the a scatter plot of
the partial working residuals will be added to the plot.
include_constant : bool
If true, then the estimated intercept is added to the prediction
and its standard errors. This avoids that the confidence interval
has zero width at the imposed identification constraint, e.g.
either at a reference point or at the mean.
ax : None or matplotlib axis instance
If ax is not None, then the plot will be added to it.
Returns
-------
fig : matplotlib Figure instance
"""
from statsmodels.graphics.utils import _import_mpl, create_mpl_ax
_import_mpl()
variable = smooth_index
y_est, se = self.partial_values(variable,
include_constant=include_constant)
smoother = self.model.smoother
x = smoother.smoothers[variable].x
sort_index = np.argsort(x)
x = x[sort_index]
y_est = y_est[sort_index]
se = se[sort_index]
fig, ax = create_mpl_ax(ax)
ax.plot(x, y_est, c='blue', lw=2)
if plot_se:
ax.plot(x, y_est + 1.96 * se, '-', c='blue')
ax.plot(x, y_est - 1.96 * se, '-', c='blue')
if cpr:
# TODO: resid_response doesn't make sense with nonlinear link
# use resid_working ?
cpr_ = y_est + self.resid_working
ax.plot(x, cpr_, '.', lw=2)
ax.set_xlabel(smoother.smoothers[variable].variable_name)
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
def plot_contour(self, mu_low, mu_high, var_low, var_high, mu_step,
var_step,
levs=[.2, .1, .05, .01, .001]):
"""
Returns a plot of the confidence region for a univariate
mean and variance.
Parameters
----------
mu_low : float
Lowest value of the mean to plot
mu_high : float
Highest value of the mean to plot
var_low : float
Lowest value of the variance to plot
var_high : float
Highest value of the variance to plot
mu_step : float
Increments to evaluate the mean
var_step : float
Increments to evaluate the mean
levs : list
Which values of significance the contour lines will be drawn.
Default is [.2, .1, .05, .01, .001]
Returns
-------
fig : matplotlib figure instance
The contour plot
"""
fig, ax = utils.create_mpl_ax()
ax.set_ylabel('Variance')
ax.set_xlabel('Mean')
mu_vect = list(np.arange(mu_low, mu_high, mu_step))
var_vect = list(np.arange(var_low, var_high, var_step))
z = []
for sig0 in var_vect:
self.sig2_0 = sig0
for mu0 in mu_vect:
z.append(self._opt_var(mu0, pval=True))
z = np.asarray(z).reshape(len(var_vect), len(mu_vect))
ax.contour(mu_vect, var_vect, z, levels=levs)
return fig
def plot_leverage_resid2(results, alpha=.05, label_kwargs={}, ax=None,
**kwargs):
"""
Plots leverage statistics vs. normalized residuals squared
Parameters
----------
results : results instance
A regression results instance
alpha : float
Specifies the cut-off for large-standardized residuals. Residuals
are assumed to be distributed N(0, 1) with alpha=alpha.
label_kwargs : dict
The keywords to pass to annotate for the labels.
ax : Axes instance
Matplotlib Axes instance
Returns
-------
fig : matplotlib Figure
A matplotlib figure instance.
"""
from scipy.stats import zscore, norm, t
fig, ax = utils.create_mpl_ax(ax)
infl = results.get_influence()
leverage = infl.hat_matrix_diag
resid = zscore(results.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 = range(results.nobs)
index = np.where(np.logical_or(large_leverage, large_resid))[0]
ax = utils.annotate_axes(index, labels, zip(resid**2, leverage),
[(0, 5)]*int(results.nobs), "large",
ax=ax, ha="center", va="bottom")
ax.margins(.075, .075)
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
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
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
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
def seasonal_plot(grouped_x, xticklabels, ylabel=None, ax=None):
"""
Consider using one of month_plot or quarter_plot unless you need
irregular plotting.
Parameters
----------
grouped_x : iterable of DataFrames
Should be a GroupBy object (or similar pair of group_names and groups
as DataFrames) with a DatetimeIndex or PeriodIndex
xticklabels : list of str
List of season labels, one for each group.
ylabel : str
Lable for y axis
ax : Matplotlib AxesSubplot instance, optional
If given, this subplot is used to plot in instead of a new figure being
created.
"""
fig, ax = utils.create_mpl_ax(ax)
start = 0
ticks = []
for season, df in grouped_x:
df = df.copy() # or sort balks for series. may be better way
df.sort_index()
nobs = len(df)
x_plot = np.arange(start, start + nobs)
ticks.append(x_plot.mean())
ax.plot(x_plot, df.values, 'k')
ax.hlines(df.values.mean(), x_plot[0], x_plot[-1], colors='r',
linewidth=3)
start += nobs
ax.set_xticks(ticks)
ax.set_xticklabels(xticklabels)
ax.set_ylabel(ylabel)
ax.margins(.1, .05)
return fig
def plot_acf(x,
ax=None,
lags=None,
*,
alpha=.05,
use_vlines=True,
adjusted=False,
fft=False,
missing='none',
title='Autocorrelation',
zero=True,
vlines_kwargs=None,
**kwargs):
"""
Plot the autocorrelation function
Plots lags on the horizontal and the correlations on vertical axis.
Parameters
----------
x : array_like
Array of time-series values
ax : AxesSubplot, optional
If given, this subplot is used to plot in instead of a new figure being
created.
lags : {int, array_like}, optional
An int or array of lag values, used on horizontal axis. Uses
np.arange(lags) when lags is an int. If not provided,
``lags=np.arange(len(corr))`` is used.
alpha : scalar, optional
If a number is given, the confidence intervals for the given level are
returned. For instance if alpha=.05, 95 % confidence intervals are
returned where the standard deviation is computed according to
Bartlett's formula. If None, no confidence intervals are plotted.
use_vlines : bool, optional
If True, vertical lines and markers are plotted.
If False, only markers are plotted. The default marker is 'o'; it can
be overridden with a ``marker`` kwarg.
adjusted : bool
If True, then denominators for autocovariance are n-k, otherwise n
fft : bool, optional
If True, computes the ACF via FFT.
missing : str, optional
A string in ['none', 'raise', 'conservative', 'drop'] specifying how
the NaNs are to be treated.
title : str, optional
Title to place on plot. Default is 'Autocorrelation'
zero : bool, optional
Flag indicating whether to include the 0-lag autocorrelation.
Default is True.
vlines_kwargs : dict, optional
Optional dictionary of keyword arguments that are passed to vlines.
**kwargs : kwargs, optional
Optional keyword arguments that are directly passed on to the
Matplotlib ``plot`` and ``axhline`` functions.
Returns
-------
Figure
If `ax` is None, the created figure. Otherwise the figure to which
`ax` is connected.
See Also
--------
matplotlib.pyplot.xcorr
matplotlib.pyplot.acorr
Notes
-----
Adapted from matplotlib's `xcorr`.
Data are plotted as ``plot(lags, corr, **kwargs)``
kwargs is used to pass matplotlib optional arguments to both the line
tracing the autocorrelations and for the horizontal line at 0. These
options must be valid for a Line2D object.
vlines_kwargs is used to pass additional optional arguments to the
vertical lines connecting each autocorrelation to the axis. These options
must be valid for a LineCollection object.
Examples
--------
>>> import pandas as pd
>>> import matplotlib.pyplot as plt
>>> import statsmodels.api as sm
>>> dta = sm.datasets.sunspots.load_pandas().data
>>> dta.index = pd.Index(sm.tsa.datetools.dates_from_range('1700', '2008'))
>>> del dta["YEAR"]
>>> sm.graphics.tsa.plot_acf(dta.values.squeeze(), lags=40)
>>> plt.show()
.. plot:: plots/graphics_tsa_plot_acf.py
"""
fig, ax = utils.create_mpl_ax(ax)
lags, nlags, irregular = _prepare_data_corr_plot(x, lags, zero)
vlines_kwargs = {} if vlines_kwargs is None else vlines_kwargs
confint = None
# acf has different return type based on alpha
acf_x = acf(x,
nlags=nlags,
alpha=alpha,
fft=fft,
adjusted=adjusted,
missing=missing)
if alpha is not None:
acf_x, confint = acf_x
_plot_corr(ax, title, acf_x, confint, lags, irregular, use_vlines,
vlines_kwargs, **kwargs)
return fig
def interaction_plot(x,
trace,
response,
func=np.mean,
ax=None,
plottype='b',
xlabel=None,
ylabel=None,
colors=None,
markers=None,
linestyles=None,
legendloc='best',
legendtitle=None,
**kwargs):
"""
Interaction plot for factor level statistics.
Note. If categorial factors are supplied levels will be internally
recoded to integers. This ensures matplotlib compatibility. Uses
a DataFrame to calculate an `aggregate` statistic for each level of the
factor or group given by `trace`.
Parameters
----------
x : array_like
The `x` factor levels constitute the x-axis. If a `pandas.Series` is
given its name will be used in `xlabel` if `xlabel` is None.
trace : array_like
The `trace` factor levels will be drawn as lines in the plot.
If `trace` is a `pandas.Series` its name will be used as the
`legendtitle` if `legendtitle` is None.
response : array_like
The reponse or dependent variable. If a `pandas.Series` is given
its name will be used in `ylabel` if `ylabel` is None.
func : function
Anything accepted by `pandas.DataFrame.aggregate`. This is applied to
the response variable grouped by the trace levels.
ax : axes, optional
Matplotlib axes instance
plottype : str {'line', 'scatter', 'both'}, optional
The type of plot to return. Can be 'l', 's', or 'b'
xlabel : str, optional
Label to use for `x`. Default is 'X'. If `x` is a `pandas.Series` it
will use the series names.
ylabel : str, optional
Label to use for `response`. Default is 'func of response'. If
`response` is a `pandas.Series` it will use the series names.
colors : list, optional
If given, must have length == number of levels in trace.
markers : list, optional
If given, must have length == number of levels in trace
linestyles : list, optional
If given, must have length == number of levels in trace.
legendloc : {None, str, int}
Location passed to the legend command.
legendtitle : {None, str}
Title of the legend.
**kwargs
These will be passed to the plot command used either plot or scatter.
If you want to control the overall plotting options, use kwargs.
Returns
-------
Figure
The figure given by `ax.figure` or a new instance.
Examples
--------
>>> import numpy as np
>>> np.random.seed(12345)
>>> weight = np.random.randint(1,4,size=60)
>>> duration = np.random.randint(1,3,size=60)
>>> days = np.log(np.random.randint(1,30, size=60))
>>> fig = interaction_plot(weight, duration, days,
... colors=['red','blue'], markers=['D','^'], ms=10)
>>> import matplotlib.pyplot as plt
>>> plt.show()
.. plot::
import numpy as np
from statsmodels.graphics.factorplots import interaction_plot
np.random.seed(12345)
weight = np.random.randint(1,4,size=60)
duration = np.random.randint(1,3,size=60)
days = np.log(np.random.randint(1,30, size=60))
fig = interaction_plot(weight, duration, days,
colors=['red','blue'], markers=['D','^'], ms=10)
import matplotlib.pyplot as plt
#plt.show()
"""
from pandas import DataFrame
fig, ax = utils.create_mpl_ax(ax)
response_name = ylabel or getattr(response, 'name', 'response')
ylabel = '%s of %s' % (func.__name__, response_name)
xlabel = xlabel or getattr(x, 'name', 'X')
legendtitle = legendtitle or getattr(trace, 'name', 'Trace')
ax.set_ylabel(ylabel)
ax.set_xlabel(xlabel)
x_values = x_levels = None
if isinstance(x[0], str):
x_levels = [l for l in np.unique(x)]
x_values = lrange(len(x_levels))
x = _recode(x, dict(zip(x_levels, x_values)))
data = DataFrame(dict(x=x, trace=trace, response=response))
plot_data = data.groupby(['trace', 'x']).aggregate(func).reset_index()
# return data
# check plot args
n_trace = len(plot_data['trace'].unique())
linestyles = ['-'] * n_trace if linestyles is None else linestyles
markers = ['.'] * n_trace if markers is None else markers
colors = rainbow(n_trace) if colors is None else colors
if len(linestyles) != n_trace:
raise ValueError("Must be a linestyle for each trace level")
if len(markers) != n_trace:
raise ValueError("Must be a marker for each trace level")
if len(colors) != n_trace:
raise ValueError("Must be a color for each trace level")
if plottype == 'both' or plottype == 'b':
for i, (values, group) in enumerate(plot_data.groupby(['trace'])):
# trace label
label = str(group['trace'].values[0])
ax.plot(group['x'],
group['response'],
color=colors[i],
marker=markers[i],
label=label,
linestyle=linestyles[i],
**kwargs)
elif plottype == 'line' or plottype == 'l':
for i, (values, group) in enumerate(plot_data.groupby(['trace'])):
# trace label
label = str(group['trace'].values[0])
ax.plot(group['x'],
group['response'],
color=colors[i],
label=label,
linestyle=linestyles[i],
**kwargs)
elif plottype == 'scatter' or plottype == 's':
for i, (values, group) in enumerate(plot_data.groupby(['trace'])):
# trace label
label = str(group['trace'].values[0])
ax.scatter(group['x'],
group['response'],
color=colors[i],
label=label,
marker=markers[i],
**kwargs)
else:
raise ValueError("Plot type %s not understood" % plottype)
ax.legend(loc=legendloc, title=legendtitle)
ax.margins(.1)
if all([x_levels, x_values]):
ax.set_xticks(x_values)
ax.set_xticklabels(x_levels)
return fig
def plot_acf(x,
ax=None,
lags=None,
alpha=.05,
use_vlines=True,
unbiased=False,
fft=False,
**kwargs):
"""Plot the autocorrelation function
Plots lags on the horizontal and the correlations on vertical axis.
Parameters
----------
x : array_like
Array of time-series values
ax : Matplotlib AxesSubplot instance, optional
If given, this subplot is used to plot in instead of a new figure being
created.
lags : array_like, optional
Array of lag values, used on horizontal axis.
If not given, ``lags=np.arange(len(corr))`` is used.
alpha : scalar, optional
If a number is given, the confidence intervals for the given level are
returned. For instance if alpha=.05, 95 % confidence intervals are
returned where the standard deviation is computed according to
Bartlett's formula. If None, no confidence intervals are plotted.
use_vlines : bool, optional
If True, vertical lines and markers are plotted.
If False, only markers are plotted. The default marker is 'o'; it can
be overridden with a ``marker`` kwarg.
unbiased : bool
If True, then denominators for autocovariance are n-k, otherwise n
fft : bool, optional
If True, computes the ACF via FFT.
**kwargs : kwargs, optional
Optional keyword arguments that are directly passed on to the
Matplotlib ``plot`` and ``axhline`` functions.
Returns
-------
fig : Matplotlib figure instance
If `ax` is None, the created figure. Otherwise the figure to which
`ax` is connected.
See Also
--------
matplotlib.pyplot.xcorr
matplotlib.pyplot.acorr
mpl_examples/pylab_examples/xcorr_demo.py
Notes
-----
Adapted from matplotlib's `xcorr`.
Data are plotted as ``plot(lags, corr, **kwargs)``
"""
fig, ax = utils.create_mpl_ax(ax)
if lags is None:
lags = np.arange(len(x))
nlags = len(lags) - 1
else:
nlags = lags
lags = np.arange(lags + 1) # +1 for zero lag
confint = None
# acf has different return type based on alpha
if alpha is None:
acf_x = acf(x, nlags=nlags, alpha=alpha, fft=fft, unbiased=unbiased)
else:
acf_x, confint = acf(x,
nlags=nlags,
alpha=alpha,
fft=fft,
unbiased=unbiased)
if use_vlines:
ax.vlines(lags, [0], acf_x, **kwargs)
ax.axhline(**kwargs)
kwargs.setdefault('marker', 'o')
kwargs.setdefault('markersize', 5)
kwargs.setdefault('linestyle', 'None')
ax.margins(.05)
ax.plot(lags, acf_x, **kwargs)
ax.set_title("Autocorrelation")
if confint is not None:
# center the confidence interval TODO: do in acf?
ax.fill_between(lags,
confint[:, 0] - acf_x,
confint[:, 1] - acf_x,
alpha=.25)
return fig
def plot_fit_obs(self, col_name, lowess_args=None,
lowess_min_n=40, jitter=None,
plot_points=True, ax=None):
"""
Plot fitted versus imputed or observed values as a scatterplot.
Parameters
----------
col_name : string
The variable to be plotted on the horizontal axis.
lowess_args : dict-like
Keyword arguments passed to lowess fit. A dictionary of
dictionaries, keys are 'o' and 'i' denoting 'observed' and
'imputed', respectively.
lowess_min_n : integer
Minimum sample size to plot a lowess fit
jitter : float or tuple
Standard deviation for jittering points in the plot.
Either a single scalar applied to both axes, or a tuple
containing x-axis jitter and y-axis jitter, respectively.
plot_points : bool
If True, the data points are plotted.
ax : matplotlib axes object
Axes on which to plot, created if not provided.
Returns
-------
The matplotlib figure on which the plot is drawn.
"""
from statsmodels.graphics import utils as gutils
from statsmodels.nonparametric.smoothers_lowess import lowess
if lowess_args is None:
lowess_args = {}
if ax is None:
fig, ax = gutils.create_mpl_ax(ax)
else:
fig = ax.get_figure()
ax.set_position([0.1, 0.1, 0.7, 0.8])
ixi = self.ix_miss[col_name]
ixo = self.ix_obs[col_name]
vec1 = np.asarray(self.data[col_name])
# Fitted values
formula = self.conditional_formula[col_name]
endog, exog = patsy.dmatrices(formula, self.data,
return_type="dataframe")
results = self.results[col_name]
vec2 = results.predict(exog=exog)
vec2 = self._get_predicted(vec2)
if jitter is not None:
if np.isscalar(jitter):
jitter = (jitter, jitter)
vec1 += jitter[0] * np.random.normal(size=len(vec1))
vec2 += jitter[1] * np.random.normal(size=len(vec2))
# Plot the points
keys = ['o', 'i']
ixs = {'o': ixo, 'i': ixi}
lak = {'o': 'obs', 'i': 'imp'}
color = {'o': 'orange', 'i': 'lime'}
if plot_points:
for ky in keys:
ix = ixs[ky]
ax.plot(vec1[ix], vec2[ix], 'o', color=color[ky],
label=lak[ky], alpha=0.6)
# Plot the lowess fits
for ky in keys:
ix = ixs[ky]
if len(ix) < lowess_min_n:
continue
if ky in lowess_args:
la = lowess_args[ky]
else:
la = {}
ix = ixs[ky]
lfit = lowess(vec2[ix], vec1[ix], **la)
ax.plot(lfit[:, 0], lfit[:, 1], '-', color=color[ky],
alpha=0.6, lw=4, label=lak[ky])
ha, la = ax.get_legend_handles_labels()
leg = fig.legend(ha, la, 'center right', numpoints=1)
leg.draw_frame(False)
ax.set_xlabel(col_name + " observed or imputed")
ax.set_ylabel(col_name + " fitted")
return fig
def plot_missing_pattern(self, ax=None, row_order="pattern",
column_order="pattern",
hide_complete_rows=False,
hide_complete_columns=False,
color_row_patterns=True):
"""
Generate an image showing the missing data pattern.
Parameters
----------
ax : matplotlib axes
Axes on which to draw the plot.
row_order : string
The method for ordering the rows. Must be one of 'pattern',
'proportion', or 'raw'.
column_order : string
The method for ordering the columns. Must be one of 'pattern',
'proportion', or 'raw'.
hide_complete_rows : boolean
If True, rows with no missing values are not drawn.
hide_complete_columns : boolean
If True, columns with no missing values are not drawn.
color_row_patterns : boolean
If True, color the unique row patterns, otherwise use grey
and white as colors.
Returns
-------
A figure containing a plot of the missing data pattern.
"""
# Create an indicator matrix for missing values.
miss = np.zeros(self.data.shape)
cols = self.data.columns
for j, col in enumerate(cols):
ix = self.ix_miss[col]
miss[ix, j] = 1
# Order the columns as requested
if column_order == "proportion":
ix = np.argsort(miss.mean(0))
elif column_order == "pattern":
cv = np.cov(miss.T)
u, s, vt = np.linalg.svd(cv, 0)
ix = np.argsort(cv[:, 0])
elif column_order == "raw":
ix = np.arange(len(cols))
else:
raise ValueError(
column_order + " is not an allowed value for `column_order`.")
miss = miss[:, ix]
cols = [cols[i] for i in ix]
# Order the rows as requested
if row_order == "proportion":
ix = np.argsort(miss.mean(1))
elif row_order == "pattern":
x = 2**np.arange(miss.shape[1])
rky = np.dot(miss, x)
ix = np.argsort(rky)
elif row_order == "raw":
ix = np.arange(miss.shape[0])
else:
raise ValueError(
row_order + " is not an allowed value for `row_order`.")
miss = miss[ix, :]
if hide_complete_rows:
ix = np.flatnonzero((miss == 1).any(1))
miss = miss[ix, :]
if hide_complete_columns:
ix = np.flatnonzero((miss == 1).any(0))
miss = miss[:, ix]
cols = [cols[i] for i in ix]
from statsmodels.graphics import utils as gutils
from matplotlib.colors import LinearSegmentedColormap
if ax is None:
fig, ax = gutils.create_mpl_ax(ax)
else:
fig = ax.get_figure()
if color_row_patterns:
x = 2**np.arange(miss.shape[1])
rky = np.dot(miss, x)
_, rcol = np.unique(rky, return_inverse=True)
miss *= 1 + rcol[:, None]
ax.imshow(miss, aspect="auto", interpolation="nearest",
cmap='gist_ncar_r')
else:
cmap = LinearSegmentedColormap.from_list("_",
["white", "darkgrey"])
ax.imshow(miss, aspect="auto", interpolation="nearest",
cmap=cmap)
ax.set_ylabel("Cases")
ax.set_xticks(range(len(cols)))
ax.set_xticklabels(cols, rotation=90)
return fig
def plot_predict(
result,
start=None,
end=None,
dynamic=False,
alpha=0.05,
ax=None,
**predict_kwargs,
):
"""
Parameters
----------
result : Result
Any model result supporting ``get_prediction``.
start : int, str, or datetime, optional
Zero-indexed observation number at which to start forecasting,
i.e., the first forecast is start. Can also be a date string to
parse or a datetime type. Default is the the zeroth observation.
end : int, str, or datetime, optional
Zero-indexed observation number at which to end forecasting, i.e.,
the last forecast is end. Can also be a date string to
parse or a datetime type. However, if the dates index does not
have a fixed frequency, end must be an integer index if you
want out of sample prediction. Default is the last observation in
the sample.
dynamic : bool, int, str, or datetime, optional
Integer offset relative to `start` at which to begin dynamic
prediction. Can also be an absolute date string to parse or a
datetime type (these are not interpreted as offsets).
Prior to this observation, true endogenous values will be used for
prediction; starting with this observation and continuing through
the end of prediction, forecasted endogenous values will be used
instead.
alpha : {float, None}
The tail probability not covered by the confidence interval. Must
be in (0, 1). Confidence interval is constructed assuming normally
distributed shocks. If None, figure will not show the confidence
interval.
ax : AxesSubplot
matplotlib Axes instance to use
**predict_kwargs
Any additional keyword arguments to pass to ``result.get_prediction``.
Returns
-------
Figure
matplotlib Figure containing the prediction plot
"""
from statsmodels.graphics.utils import _import_mpl, create_mpl_ax
_ = _import_mpl()
fig, ax = create_mpl_ax(ax)
from statsmodels.tsa.base.prediction import PredictionResults
# use predict so you set dates
pred: PredictionResults = result.get_prediction(start=start,
end=end,
dynamic=dynamic,
**predict_kwargs)
mean = pred.predicted_mean
if isinstance(mean, (pd.Series, pd.DataFrame)):
x = mean.index
mean.plot(ax=ax, label="forecast")
else:
x = np.arange(mean.shape[0])
ax.plot(x, mean)
if alpha is not None:
label = f"{1-alpha:.0%} confidence interval"
ci = pred.conf_int(alpha)
conf_int = np.asarray(ci)
ax.fill_between(
x,
conf_int[:, 0],
conf_int[:, 1],
color="gray",
alpha=0.5,
label=label,
)
ax.legend(loc="best")
return fig
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 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':
>>> 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
def plot_missing_pattern(self, ax=None, row_order="pattern",
column_order="pattern",
hide_complete_rows=False,
hide_complete_columns=False,
color_row_patterns=True):
"""
Generate an image showing the missing data pattern.
Parameters
----------
ax : matplotlib axes
Axes on which to draw the plot.
row_order : string
The method for ordering the rows. Must be one of 'pattern',
'proportion', or 'raw'.
column_order : string
The method for ordering the columns. Must be one of 'pattern',
'proportion', or 'raw'.
hide_complete_rows : boolean
If True, rows with no missing values are not drawn.
hide_complete_columns : boolean
If True, columns with no missing values are not drawn.
color_row_patterns : boolean
If True, color the unique row patterns, otherwise use grey
and white as colors.
Returns
-------
A figure containing a plot of the missing data pattern.
"""
# Create an indicator matrix for missing values.
miss = np.zeros(self.data.shape)
cols = self.data.columns
for j, col in enumerate(cols):
ix = self.ix_miss[col]
miss[ix, j] = 1
# Order the columns as requested
if column_order == "proportion":
ix = np.argsort(miss.mean(0))
elif column_order == "pattern":
cv = np.cov(miss.T)
u, s, vt = np.linalg.svd(cv, 0)
ix = np.argsort(cv[:, 0])
elif column_order == "raw":
ix = np.arange(len(cols))
else:
raise ValueError(column_order + " is not an allowed value for `column_order`.")
miss = miss[:, ix]
cols = [cols[i] for i in ix]
# Order the rows as requested
if row_order == "proportion":
ix = np.argsort(miss.mean(1))
elif row_order == "pattern":
x = 2**np.arange(miss.shape[1])
rky = np.dot(miss, x)
ix = np.argsort(rky)
elif row_order == "raw":
ix = np.arange(miss.shape[0])
else:
raise ValueError(row_order + " is not an allowed value for `row_order`.")
miss = miss[ix, :]
if hide_complete_rows:
ix = np.flatnonzero((miss == 1).any(1))
miss = miss[ix, :]
if hide_complete_columns:
ix = np.flatnonzero((miss == 1).any(0))
miss = miss[:, ix]
cols = [cols[i] for i in ix]
from statsmodels.graphics import utils as gutils
from matplotlib.colors import LinearSegmentedColormap
if ax is None:
fig, ax = gutils.create_mpl_ax(ax)
else:
fig = ax.get_figure()
if color_row_patterns:
x = 2**np.arange(miss.shape[1])
rky = np.dot(miss, x)
_, rcol = np.unique(rky, return_inverse=True)
miss *= 1 + rcol[:, None]
ax.imshow(miss, aspect="auto", interpolation="nearest",
cmap='gist_ncar_r')
else:
cmap = LinearSegmentedColormap.from_list("_",
["white", "darkgrey"])
ax.imshow(miss, aspect="auto", interpolation="nearest",
cmap=cmap)
ax.set_ylabel("Cases")
ax.set_xticks(range(len(cols)))
ax.set_xticklabels(cols, rotation=90)
return fig
def plot_pacf(x,
ax=None,
lags=None,
alpha=.05,
method='ywunbiased',
use_vlines=True,
title='Partial Autocorrelation',
zero=True,
**kwargs):
"""
Plot the partial autocorrelation function
Parameters
----------
x : array_like
Array of time-series values
ax : Matplotlib AxesSubplot instance, optional
If given, this subplot is used to plot in instead of a new figure being
created.
lags : int or array_like, optional
int or Array of lag values, used on horizontal axis. Uses
np.arange(lags) when lags is an int. If not provided,
``lags=np.arange(len(corr))`` is used.
alpha : float, optional
If a number is given, the confidence intervals for the given level are
returned. For instance if alpha=.05, 95 % confidence intervals are
returned where the standard deviation is computed according to
1/sqrt(len(x))
method : {'ywunbiased', 'ywmle', 'ols'}
Specifies which method for the calculations to use:
- yw or ywunbiased : yule walker with bias correction in denominator
for acovf. Default.
- ywm or ywmle : yule walker without bias correction
- ols - regression of time series on lags of it and on constant
- ld or ldunbiased : Levinson-Durbin recursion with bias correction
- ldb or ldbiased : Levinson-Durbin recursion without bias correction
use_vlines : bool, optional
If True, vertical lines and markers are plotted.
If False, only markers are plotted. The default marker is 'o'; it can
be overridden with a ``marker`` kwarg.
title : str, optional
Title to place on plot. Default is 'Partial Autocorrelation'
zero : bool, optional
Flag indicating whether to include the 0-lag autocorrelation.
Default is True.
**kwargs : kwargs, optional
Optional keyword arguments that are directly passed on to the
Matplotlib ``plot`` and ``axhline`` functions.
Returns
-------
fig : Matplotlib figure instance
If `ax` is None, the created figure. Otherwise the figure to which
`ax` is connected.
See Also
--------
matplotlib.pyplot.xcorr
matplotlib.pyplot.acorr
mpl_examples/pylab_examples/xcorr_demo.py
Notes
-----
Plots lags on the horizontal and the correlations on vertical axis.
Adapted from matplotlib's `xcorr`.
Data are plotted as ``plot(lags, corr, **kwargs)``
"""
fig, ax = utils.create_mpl_ax(ax)
lags, nlags, irregular = _prepare_data_corr_plot(x, lags, zero)
confint = None
if alpha is None:
acf_x = pacf(x, nlags=nlags, alpha=alpha, method=method)
else:
acf_x, confint = pacf(x, nlags=nlags, alpha=alpha, method=method)
_plot_corr(ax, title, acf_x, confint, lags, irregular, use_vlines,
**kwargs)
return fig
def plot_acf(x,
ax=None,
lags=None,
alpha=.05,
use_vlines=True,
unbiased=False,
fft=False,
title='Autocorrelation',
zero=True,
**kwargs):
"""Plot the autocorrelation function
Plots lags on the horizontal and the correlations on vertical axis.
Parameters
----------
x : array_like
Array of time-series values
ax : Matplotlib AxesSubplot instance, optional
If given, this subplot is used to plot in instead of a new figure being
created.
lags : int or array_like, optional
int or Array of lag values, used on horizontal axis. Uses
np.arange(lags) when lags is an int. If not provided,
``lags=np.arange(len(corr))`` is used.
alpha : scalar, optional
If a number is given, the confidence intervals for the given level are
returned. For instance if alpha=.05, 95 % confidence intervals are
returned where the standard deviation is computed according to
Bartlett's formula. If None, no confidence intervals are plotted.
use_vlines : bool, optional
If True, vertical lines and markers are plotted.
If False, only markers are plotted. The default marker is 'o'; it can
be overridden with a ``marker`` kwarg.
unbiased : bool
If True, then denominators for autocovariance are n-k, otherwise n
fft : bool, optional
If True, computes the ACF via FFT.
title : str, optional
Title to place on plot. Default is 'Autocorrelation'
zero : bool, optional
Flag indicating whether to include the 0-lag autocorrelation.
Default is True.
**kwargs : kwargs, optional
Optional keyword arguments that are directly passed on to the
Matplotlib ``plot`` and ``axhline`` functions.
Returns
-------
fig : Matplotlib figure instance
If `ax` is None, the created figure. Otherwise the figure to which
`ax` is connected.
See Also
--------
matplotlib.pyplot.xcorr
matplotlib.pyplot.acorr
mpl_examples/pylab_examples/xcorr_demo.py
Notes
-----
Adapted from matplotlib's `xcorr`.
Data are plotted as ``plot(lags, corr, **kwargs)``
"""
fig, ax = utils.create_mpl_ax(ax)
lags, nlags, irregular = _prepare_data_corr_plot(x, lags, zero)
confint = None
# acf has different return type based on alpha
if alpha is None:
acf_x = acf(x, nlags=nlags, alpha=alpha, fft=fft, unbiased=unbiased)
else:
acf_x, confint = acf(x,
nlags=nlags,
alpha=alpha,
fft=fft,
unbiased=unbiased)
_plot_corr(ax, title, acf_x, confint, lags, irregular, use_vlines,
**kwargs)
return fig
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
def plot_ccf(x,
y,
ax=None,
lags=None,
*,
alpha=.05,
use_vlines=True,
unbiased=False,
title='Cross-correlation',
vlines_kwargs=None,
**kwargs):
"""
Plot the cross-correlation function
Plots lags on the horizontal and the correlations on vertical axis.
Parameters
----------
x : array_like
Array of time-series values
y: array_like
Array of time-series values
ax : AxesSubplot, optional
If given, this subplot is used to plot in instead of a new figure being
created.
lags : {int, array_like}, optional
An int or array of lag values, used on horizontal axis. Uses
np.arange(lags) when lags is an int. If not provided,
``lags=np.arange(len(corr))`` is used.
alpha : scalar, optional
If a number is given, the confidence intervals for the given level are
returned. For instance if alpha=.05, 95 % confidence intervals are
returned where the standard deviation is computed according to
Bartlett's formula. If None, no confidence intervals are plotted.
use_vlines : bool, optional
If True, vertical lines and markers are plotted.
If False, only markers are plotted. The default marker is 'o'; it can
be overridden with a ``marker`` kwarg.
unbiased : bool
If True, then denominators for autocovariance are n-k, otherwise n
title : str, optional
Title to place on plot. Default is 'Cross-correlation'
vlines_kwargs : dict, optional
Optional dictionary of keyword arguments that are passed to vlines.
**kwargs : kwargs, optional
Optional keyword arguments that are directly passed on to the
Matplotlib ``plot`` and ``axhline`` functions.
Returns
-------
Figure
If `ax` is None, the created figure. Otherwise the figure to which
`ax` is connected.
See Also
--------
matplotlib.pyplot.xcorr
matplotlib.pyplot.acorr
Notes
-----
Adapted from
https://github.com/statsmodels/statsmodels/blob/master/statsmodels/graphics/tsaplots.py
"""
fig, ax = utils.create_mpl_ax(ax)
lags, nlags, irregular = _prepare_data_corr_plot_ccf(x, lags)
vlines_kwargs = {} if vlines_kwargs is None else vlines_kwargs
confint = None
ccf_data = ccf(y, x, lag_max=nlags)
if alpha is not None:
z = norm.ppf(1 - alpha / 2)
sl = z / np.sqrt(len(x))
confint = np.empty((2 * nlags + 1, 2))
confint[:, 0] = ccf_data - sl
confint[:, 1] = ccf_data + sl
_plot_corr(ax, title, ccf_data, confint, lags, irregular, use_vlines,
vlines_kwargs, **kwargs)
return fig
def mv_mean_contour(self,
mu1_low,
mu1_upp,
mu2_low,
mu2_upp,
step1,
step2,
levs=(.001, .01, .05, .1, .2),
var1_name=None,
var2_name=None,
plot_dta=False):
"""
Creates a confidence region plot for the mean of bivariate data
Parameters
----------
m1_low : float
Minimum value of the mean for variable 1
m1_upp : float
Maximum value of the mean for variable 1
mu2_low : float
Minimum value of the mean for variable 2
mu2_upp : float
Maximum value of the mean for variable 2
step1 : float
Increment of evaluations for variable 1
step2 : float
Increment of evaluations for variable 2
levs : list
Levels to be drawn on the contour plot.
Default = (.001, .01, .05, .1, .2)
plot_dta : bool
If True, makes a scatter plot of the data on
top of the contour plot. Defaultis False.
var1_name : str
Name of variable 1 to be plotted on the x-axis
var2_name : str
Name of variable 2 to be plotted on the y-axis
Notes
-----
The smaller the step size, the more accurate the intervals
will be
If the function returns optimization failed, consider narrowing
the boundaries of the plot
Examples
--------
>>> import statsmodels.api as sm
>>> two_rvs = np.random.standard_normal((20,2))
>>> el_analysis = sm.emplike.DescStat(two_rvs)
>>> contourp = el_analysis.mv_mean_contour(-2, 2, -2, 2, .1, .1)
>>> contourp.show()
"""
if self.endog.shape[1] != 2:
raise ValueError('Data must contain exactly two variables')
fig, ax = utils.create_mpl_ax()
if var2_name is None:
ax.set_ylabel('Variable 2')
else:
ax.set_ylabel(var2_name)
if var1_name is None:
ax.set_xlabel('Variable 1')
else:
ax.set_xlabel(var1_name)
x = np.arange(mu1_low, mu1_upp, step1)
y = np.arange(mu2_low, mu2_upp, step2)
pairs = itertools.product(x, y)
z = []
for i in pairs:
z.append(self.mv_test_mean(np.asarray(i))[0])
X, Y = np.meshgrid(x, y)
z = np.asarray(z)
z = z.reshape(X.shape[1], Y.shape[0])
ax.contour(x, y, z.T, levels=levs)
if plot_dta:
ax.plot(self.endog[:, 0], self.endog[:, 1], 'bo')
return fig
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
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)
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 plot_fit_obs(self, col_name, lowess_args=None,
lowess_min_n=40, jitter=None,
plot_points=True, ax=None):
"""
Plot fitted versus imputed or observed values as a scatterplot.
Parameters
----------
col_name : string
The variable to be plotted on the horizontal axis.
lowess_args : dict-like
Keyword arguments passed to lowess fit. A dictionary of
dictionaries, keys are 'o' and 'i' denoting 'observed' and
'imputed', respectively.
lowess_min_n : integer
Minimum sample size to plot a lowess fit
jitter : float or tuple
Standard deviation for jittering points in the plot.
Either a single scalar applied to both axes, or a tuple
containing x-axis jitter and y-axis jitter, respectively.
plot_points : bool
If True, the data points are plotted.
ax : matplotlib axes object
Axes on which to plot, created if not provided.
Returns
-------
The matplotlib figure on which the plot is drawn.
"""
from statsmodels.graphics import utils as gutils
from statsmodels.nonparametric.smoothers_lowess import lowess
import pandas as pd
if lowess_args is None:
lowess_args = {}
if ax is None:
fig, ax = gutils.create_mpl_ax(ax)
else:
fig = ax.get_figure()
ax.set_position([0.1, 0.1, 0.7, 0.8])
ixi = self.ix_miss[col_name]
ixo = self.ix_obs[col_name]
vec1 = np.asarray(self.data[col_name])
# Fitted values
formula = self.conditional_formula[col_name]
endog, exog = patsy.dmatrices(formula, self.data,
return_type="dataframe")
results = self.results[col_name]
vec2 = results.predict(exog=exog)
vec2 = self._get_predicted(vec2)
if jitter is not None:
if np.isscalar(jitter):
jitter = (jitter, jitter)
vec1 += jitter[0] * np.random.normal(size=len(vec1))
vec2 += jitter[1] * np.random.normal(size=len(vec2))
# Plot the points
keys = ['o', 'i']
ixs = {'o': ixo, 'i': ixi}
lak = {'o': 'obs', 'i': 'imp'}
color = {'o': 'orange', 'i': 'lime'}
if plot_points:
for ky in keys:
ix = ixs[ky]
ax.plot(vec1[ix], vec2[ix], 'o', color=color[ky],
label=lak[ky], alpha=0.6)
# Plot the lowess fits
for ky in keys:
ix = ixs[ky]
if len(ix) < lowess_min_n:
continue
if ky in lowess_args:
la = lowess_args[ky]
else:
la = {}
ix = ixs[ky]
lfit = lowess(vec2[ix], vec1[ix], **la)
ax.plot(lfit[:, 0], lfit[:, 1], '-', color=color[ky],
alpha=0.6, lw=4, label=lak[ky])
ha, la = ax.get_legend_handles_labels()
leg = fig.legend(ha, la, 'center right', numpoints=1)
leg.draw_frame(False)
ax.set_xlabel(col_name + " observed or imputed")
ax.set_ylabel(col_name + " fitted")
return fig
def split_plot3(grouped_x,
keyOrder,
ydim,
labdim,
xticklabels=None,
ylabel=None,
ax=None,
label=False,
keyHighlight=None,
ylim=None):
fig, ax = utils.create_mpl_ax(ax)
start = 0
ticks = []
tmpxlabels = []
for key in keyOrder:
df = grouped_x.get_group(key)
nobs = len(df)
x_plot = arange(start, start + nobs)
ticks.append(x_plot.mean())
#Third parameter is color; 'k' is black
ax.plot(x_plot, df[ydim], 'g', linestyle='--')
#named colors: http://matplotlib.org/examples/color/named_colors.html
highlightColors = [
'mistyrose', 'lightsalmon', 'salmon', 'tomato', 'orangered'
]
baseColors = [
'silver', 'lightblue', 'paleturquoise', 'lightcyan', 'lightgreen'
]
if key == keyHighlight:
colors = highlightColors
else:
colors = baseColors
for i in range(0, nobs):
if ylim is not None and (df[ydim].iloc[i] <= ylim[0]
or df[ydim].iloc[i] >= ylim[1]):
continue
if label:
if nobs <= len(colors):
if keyHighlight == 'leader':
if int(df[labdim].iloc[i]) == 1:
color = highlightColors[i - nobs]
else:
color = baseColors[i - nobs]
else:
color = colors[i - nobs]
else:
color = 'pink'
ax.text(x_plot[i],
df[ydim].iloc[i],
int(df[labdim].iloc[i]),
bbox=dict(boxstyle='round,pad=0.3', color=color))
#elif df[ydim].iloc[i]>self.RC1SIZE:
# ax.text(x_plot[i]-1, df[ydim].iloc[i], int(df[labdim].iloc[i]),
# bbox=dict( boxstyle='round,pad=0.3',color='pink')) #facecolor='none',edgecolor='black',
else:
ax.plot(x_plot[i], df[labdim].iloc[i], 'or')
#ax.hlines(df.values.mean(), x_plot[0], x_plot[-1], colors='k')
start += nobs
tmpxlabels.append(key)
if xticklabels is None:
xticklabels = tmpxlabels
elif isinstance(xticklabels, dict):
xticklabels = [
xticklabels[x] if x in xticklabels else x for x in tmpxlabels
]
ax.set_xticks(ticks)
ax.set_xticklabels(xticklabels)
if ylabel is not None: ax.set_ylabel(ylabel)
ax.margins(.1, .05)
return fig
def plot_survfunc(survfuncs, ax=None):
"""
Plot one or more survivor functions.
Parameters
----------
survfuncs : object or array-like
A single SurvfuncRight object, or a list or SurvfuncRight
objects that are plotted together.
Returns
-------
A figure instance on which the plot was drawn.
Examples
--------
Add a legend:
>>> import statsmodels.api as sm
>>> from statsmodels.duration.survfunc import plot_survfunc
>>> data = sm.datasets.get_rdataset("flchain", "survival").data
>>> df = data.loc[data.sex == "F", :]
>>> sf0 = sm.SurvfuncRight(df["futime"], df["death"])
>>> sf1 = sm.SurvfuncRight(3.0 * df["futime"], df["death"])
>>> fig = plot_survfunc([sf0, sf1])
>>> ax = fig.get_axes()[0]
>>> ax.set_position([0.1, 0.1, 0.64, 0.8])
>>> ha, lb = ax.get_legend_handles_labels()
>>> leg = fig.legend((ha[0], ha[1]), (lb[0], lb[1]), 'center right')
Change the line colors:
>>> fig = plot_survfunc([sf0, sf1])
>>> ax = fig.get_axes()[0]
>>> ax.set_position([0.1, 0.1, 0.64, 0.8])
>>> ha, lb = ax.get_legend_handles_labels()
>>> ha[0].set_color('purple')
>>> ha[1].set_color('orange')
"""
fig, ax = utils.create_mpl_ax(ax)
# If we have only a single survival function to plot, put it into
# a list.
try:
assert(type(survfuncs[0]) is SurvfuncRight)
except:
survfuncs = [survfuncs]
for gx, sf in enumerate(survfuncs):
# The estimated survival function does not include a point at
# time 0, include it here for plotting.
surv_times = np.concatenate(([0], sf.surv_times))
surv_prob = np.concatenate(([1], sf.surv_prob))
# If the final times are censoring times they are not included
# in the survival function so we add them here
mxt = max(sf.time)
if mxt > surv_times[-1]:
surv_times = np.concatenate((surv_times, [mxt]))
surv_prob = np.concatenate((surv_prob, [surv_prob[-1]]))
label = getattr(sf, "title", "Group %d" % (gx + 1))
li, = ax.step(surv_times, surv_prob, '-', label=label, lw=2,
where='post')
# Plot the censored points.
ii = np.flatnonzero(np.logical_not(sf.status))
ti = sf.time[ii]
jj = np.searchsorted(surv_times, ti) - 1
sp = surv_prob[jj]
ax.plot(ti, sp, '+', ms=12, color=li.get_color(),
label=label + " points")
ax.set_ylim(0, 1.01)
return fig
def plot_acf(
x,
ax=None,
lags=None,
*,
alpha=0.05,
use_vlines=True,
adjusted=False,
fft=False,
missing="none",
title="Autocorrelation",
zero=True,
auto_ylims=False,
bartlett_confint=True,
vlines_kwargs=None,
**kwargs,
):
"""
Plot the autocorrelation function
Plots lags on the horizontal and the correlations on vertical axis.
Parameters
----------
x : array_like
Array of time-series values
ax : AxesSubplot, optional
If given, this subplot is used to plot in instead of a new figure being
created.
lags : {int, array_like}, optional
An int or array of lag values, used on horizontal axis. Uses
np.arange(lags) when lags is an int. If not provided,
``lags=np.arange(len(corr))`` is used.
alpha : scalar, optional
If a number is given, the confidence intervals for the given level are
returned. For instance if alpha=.05, 95 % confidence intervals are
returned where the standard deviation is computed according to
Bartlett's formula. If None, no confidence intervals are plotted.
use_vlines : bool, optional
If True, vertical lines and markers are plotted.
If False, only markers are plotted. The default marker is 'o'; it can
be overridden with a ``marker`` kwarg.
adjusted : bool
If True, then denominators for autocovariance are n-k, otherwise n
fft : bool, optional
If True, computes the ACF via FFT.
missing : str, optional
A string in ['none', 'raise', 'conservative', 'drop'] specifying how
the NaNs are to be treated.
title : str, optional
Title to place on plot. Default is 'Autocorrelation'
zero : bool, optional
Flag indicating whether to include the 0-lag autocorrelation.
Default is True.
auto_ylims : bool, optional
If True, adjusts automatically the y-axis limits to ACF values.
bartlett_confint : bool, default True
Confidence intervals for ACF values are generally placed at 2
standard errors around r_k. The formula used for standard error
depends upon the situation. If the autocorrelations are being used
to test for randomness of residuals as part of the ARIMA routine,
the standard errors are determined assuming the residuals are white
noise. The approximate formula for any lag is that standard error
of each r_k = 1/sqrt(N). See section 9.4 of [1] for more details on
the 1/sqrt(N) result. For more elementary discussion, see section
5.3.2 in [2].
For the ACF of raw data, the standard error at a lag k is
found as if the right model was an MA(k-1). This allows the
possible interpretation that if all autocorrelations past a
certain lag are within the limits, the model might be an MA of
order defined by the last significant autocorrelation. In this
case, a moving average model is assumed for the data and the
standard errors for the confidence intervals should be
generated using Bartlett's formula. For more details on
Bartlett formula result, see section 7.2 in [1].
vlines_kwargs : dict, optional
Optional dictionary of keyword arguments that are passed to vlines.
**kwargs : kwargs, optional
Optional keyword arguments that are directly passed on to the
Matplotlib ``plot`` and ``axhline`` functions.
Returns
-------
Figure
If `ax` is None, the created figure. Otherwise the figure to which
`ax` is connected.
See Also
--------
matplotlib.pyplot.xcorr
matplotlib.pyplot.acorr
Notes
-----
Adapted from matplotlib's `xcorr`.
Data are plotted as ``plot(lags, corr, **kwargs)``
kwargs is used to pass matplotlib optional arguments to both the line
tracing the autocorrelations and for the horizontal line at 0. These
options must be valid for a Line2D object.
vlines_kwargs is used to pass additional optional arguments to the
vertical lines connecting each autocorrelation to the axis. These options
must be valid for a LineCollection object.
References
----------
[1] Brockwell and Davis, 1987. Time Series Theory and Methods
[2] Brockwell and Davis, 2010. Introduction to Time Series and
Forecasting, 2nd edition.
Examples
--------
>>> import pandas as pd
>>> import matplotlib.pyplot as plt
>>> import statsmodels.api as sm
>>> dta = sm.datasets.sunspots.load_pandas().data
>>> dta.index = pd.Index(sm.tsa.datetools.dates_from_range('1700', '2008'))
>>> del dta["YEAR"]
>>> sm.graphics.tsa.plot_acf(dta.values.squeeze(), lags=40)
>>> plt.show()
.. plot:: plots/graphics_tsa_plot_acf.py
"""
fig, ax = utils.create_mpl_ax(ax)
lags, nlags, irregular = _prepare_data_corr_plot(x, lags, zero)
vlines_kwargs = {} if vlines_kwargs is None else vlines_kwargs
confint = None
# acf has different return type based on alpha
acf_x = acf(
x,
nlags=nlags,
alpha=alpha,
fft=fft,
bartlett_confint=bartlett_confint,
adjusted=adjusted,
missing=missing,
)
if alpha is not None:
acf_x, confint = acf_x[:2]
_plot_corr(
ax,
title,
acf_x,
confint,
lags,
irregular,
use_vlines,
vlines_kwargs,
auto_ylims=auto_ylims,
**kwargs,
)
return fig
def plot_acf(x, ax=None, lags=None, alpha=.05, use_vlines=True, unbiased=False,
fft=False, **kwargs):
"""Plot the autocorrelation function
Plots lags on the horizontal and the correlations on vertical axis.
Parameters
----------
x : array_like
Array of time-series values
ax : Matplotlib AxesSubplot instance, optional
If given, this subplot is used to plot in instead of a new figure being
created.
lags : array_like, optional
Array of lag values, used on horizontal axis.
If not given, ``lags=np.arange(len(corr))`` is used.
alpha : scalar, optional
If a number is given, the confidence intervals for the given level are
returned. For instance if alpha=.05, 95 % confidence intervals are
returned where the standard deviation is computed according to
Bartlett's formula. If None, no confidence intervals are plotted.
use_vlines : bool, optional
If True, vertical lines and markers are plotted.
If False, only markers are plotted. The default marker is 'o'; it can
be overridden with a ``marker`` kwarg.
unbiased : bool
If True, then denominators for autocovariance are n-k, otherwise n
fft : bool, optional
If True, computes the ACF via FFT.
**kwargs : kwargs, optional
Optional keyword arguments that are directly passed on to the
Matplotlib ``plot`` and ``axhline`` functions.
Returns
-------
fig : Matplotlib figure instance
If `ax` is None, the created figure. Otherwise the figure to which
`ax` is connected.
See Also
--------
matplotlib.pyplot.xcorr
matplotlib.pyplot.acorr
mpl_examples/pylab_examples/xcorr_demo.py
Notes
-----
Adapted from matplotlib's `xcorr`.
Data are plotted as ``plot(lags, corr, **kwargs)``
"""
fig, ax = utils.create_mpl_ax(ax)
if lags is None:
lags = np.arange(len(x))
nlags = len(lags) - 1
else:
nlags = lags
lags = np.arange(lags + 1) # +1 for zero lag
acf_x, confint = acf(x, nlags=nlags, alpha=alpha, fft=fft,
unbiased=unbiased)
if use_vlines:
ax.vlines(lags, [0], acf_x, **kwargs)
ax.axhline(**kwargs)
# center the confidence interval TODO: do in acf?
confint = confint - confint.mean(1)[:,None]
kwargs.setdefault('marker', 'o')
kwargs.setdefault('markersize', 5)
kwargs.setdefault('linestyle', 'None')
ax.margins(.05)
ax.plot(lags, acf_x, **kwargs)
ax.fill_between(lags, confint[:,0], confint[:,1], alpha=.25)
ax.set_title("Autocorrelation")
return fig
def plot_bivariate(self, col1_name, col2_name,
lowess_args=None, lowess_min_n=40,
jitter=None, plot_points=True, ax=None):
"""
Plot observed and imputed values for two variables.
Displays a scatterplot of one variable against another. The
points are colored according to whether the values are
observed or imputed.
Parameters
----------
col1_name : string
The variable to be plotted on the horizontal axis.
col2_name : string
The variable to be plotted on the vertical axis.
lowess_args : dictionary
A dictionary of dictionaries, keys are 'ii', 'io', 'oi'
and 'oo', where 'o' denotes 'observed' and 'i' denotes
imputed. See Notes for details.
lowess_min_n : integer
Minimum sample size to plot a lowess fit
jitter : float or tuple
Standard deviation for jittering points in the plot.
Either a single scalar applied to both axes, or a tuple
containing x-axis jitter and y-axis jitter, respectively.
plot_points : bool
If True, the data points are plotted.
ax : matplotlib axes object
Axes on which to plot, created if not provided.
Returns
-------
The matplotlib figure on which the plot id drawn.
"""
from statsmodels.graphics import utils as gutils
from statsmodels.nonparametric.smoothers_lowess import lowess
if lowess_args is None:
lowess_args = {}
if ax is None:
fig, ax = gutils.create_mpl_ax(ax)
else:
fig = ax.get_figure()
ax.set_position([0.1, 0.1, 0.7, 0.8])
ix1i = self.ix_miss[col1_name]
ix1o = self.ix_obs[col1_name]
ix2i = self.ix_miss[col2_name]
ix2o = self.ix_obs[col2_name]
ix_ii = np.intersect1d(ix1i, ix2i)
ix_io = np.intersect1d(ix1i, ix2o)
ix_oi = np.intersect1d(ix1o, ix2i)
ix_oo = np.intersect1d(ix1o, ix2o)
vec1 = np.asarray(self.data[col1_name])
vec2 = np.asarray(self.data[col2_name])
if jitter is not None:
if np.isscalar(jitter):
jitter = (jitter, jitter)
vec1 += jitter[0] * np.random.normal(size=len(vec1))
vec2 += jitter[1] * np.random.normal(size=len(vec2))
# Plot the points
keys = ['oo', 'io', 'oi', 'ii']
lak = {'i': 'imp', 'o': 'obs'}
ixs = {'ii': ix_ii, 'io': ix_io, 'oi': ix_oi, 'oo': ix_oo}
color = {'oo': 'grey', 'ii': 'red', 'io': 'orange',
'oi': 'lime'}
if plot_points:
for ky in keys:
ix = ixs[ky]
lab = lak[ky[0]] + "/" + lak[ky[1]]
ax.plot(vec1[ix], vec2[ix], 'o', color=color[ky],
label=lab, alpha=0.6)
# Plot the lowess fits
for ky in keys:
ix = ixs[ky]
if len(ix) < lowess_min_n:
continue
if ky in lowess_args:
la = lowess_args[ky]
else:
la = {}
ix = ixs[ky]
lfit = lowess(vec2[ix], vec1[ix], **la)
if plot_points:
ax.plot(lfit[:, 0], lfit[:, 1], '-', color=color[ky],
alpha=0.6, lw=4)
else:
lab = lak[ky[0]] + "/" + lak[ky[1]]
ax.plot(lfit[:, 0], lfit[:, 1], '-', color=color[ky],
alpha=0.6, lw=4, label=lab)
ha, la = ax.get_legend_handles_labels()
pad = 0.0001 if plot_points else 0.5
leg = fig.legend(ha, la, 'center right', numpoints=1,
handletextpad=pad)
leg.draw_frame(False)
ax.set_xlabel(col1_name)
ax.set_ylabel(col2_name)
return fig
def mosaic(data, index=None, ax=None, horizontal=True, gap=0.005,
properties=lambda key: None, labelizer=None,
title='', statistic=False, axes_label=True,
label_rotation=0.0):
"""Create a mosaic plot from a contingency table.
It allows to visualize multivariate categorical data in a rigorous
and informative way.
Parameters
----------
data : dict, pandas.Series, np.ndarray, pandas.DataFrame
The contingency table that contains the data.
Each category should contain a non-negative number
with a tuple as index. It expects that all the combination
of keys to be representes; if that is not true, will
automatically consider the missing values as 0. The order
of the keys will be the same as the one of insertion.
If a dict of a Series (or any other dict like object)
is used, it will take the keys as labels. If a
np.ndarray is provided, it will generate a simple
numerical labels.
index: list, optional
Gives the preferred order for the category ordering. If not specified
will default to the given order. It doesn't support named indexes
for hierarchical Series. If a DataFrame is provided, it expects
a list with the name of the columns.
ax : matplotlib.Axes, optional
The graph where display the mosaic. If not given, will
create a new figure
horizontal : bool, optional (default True)
The starting direction of the split (by default along
the horizontal axis)
gap : float or array of floats
The list of gaps to be applied on each subdivision.
If the lenght of the given array is less of the number
of subcategories (or if it's a single number) it will extend
it with exponentially decreasing gaps
labelizer : function (key) -> string, optional
A function that generate the text to display at the center of
each tile base on the key of that tile
properties : function (key) -> dict, optional
A function that for each tile in the mosaic take the key
of the tile and returns the dictionary of properties
of the generated Rectangle, like color, hatch or similar.
A default properties set will be provided fot the keys whose
color has not been defined, and will use color variation to help
visually separates the various categories. It should return None
to indicate that it should use the default property for the tile.
A dictionary of the properties for each key can be passed,
and it will be internally converted to the correct function
statistic: bool, optional (default False)
if true will use a crude statistical model to give colors to the plot.
If the tile has a containt that is more than 2 standard deviation
from the expected value under independence hipotesys, it will
go from green to red (for positive deviations, blue otherwise) and
will acquire an hatching when crosses the 3 sigma.
title: string, optional
The title of the axis
axes_label: boolean, optional
Show the name of each value of each category
on the axis (default) or hide them.
label_rotation: float or list of float
the rotation of the axis label (if present). If a list is given
each axis can have a different rotation
Returns
----------
fig : matplotlib.Figure
The generate figure
rects : dict
A dictionary that has the same keys of the original
dataset, that holds a reference to the coordinates of the
tile and the Rectangle that represent it
See Also
----------
A Brief History of the Mosaic Display
Michael Friendly, York University, Psychology Department
Journal of Computational and Graphical Statistics, 2001
Mosaic Displays for Loglinear Models.
Michael Friendly, York University, Psychology Department
Proceedings of the Statistical Graphics Section, 1992, 61-68.
Mosaic displays for multi-way contingecy tables.
Michael Friendly, York University, Psychology Department
Journal of the american statistical association
March 1994, Vol. 89, No. 425, Theory and Methods
Examples
----------
The most simple use case is to take a dictionary and plot the result
>>> data = {'a': 10, 'b': 15, 'c': 16}
>>> mosaic(data, title='basic dictionary')
>>> pylab.show()
A more useful example is given by a dictionary with multiple indices.
In this case we use a wider gap to a better visual separation of the
resulting plot
>>> data = {('a', 'b'): 1, ('a', 'c'): 2, ('d', 'b'): 3, ('d', 'c'): 4}
>>> mosaic(data, gap=0.05, title='complete dictionary')
>>> pylab.show()
The same data can be given as a simple or hierarchical indexed Series
>>> rand = np.random.random
>>> from itertools import product
>>>
>>> tuples = list(product(['bar', 'baz', 'foo', 'qux'], ['one', 'two']))
>>> index = pd.MultiIndex.from_tuples(tuples, names=['first', 'second'])
>>> data = pd.Series(rand(8), index=index)
>>> mosaic(data, title='hierarchical index series')
>>> pylab.show()
The third accepted data structureis the np array, for which a
very simple index will be created.
>>> rand = np.random.random
>>> data = 1+rand((2,2))
>>> mosaic(data, title='random non-labeled array')
>>> pylab.show()
If you need to modify the labeling and the coloring you can give
a function tocreate the labels and one with the graphical properties
starting from the key tuple
>>> data = {'a': 10, 'b': 15, 'c': 16}
>>> props = lambda key: {'color': 'r' if 'a' in key else 'gray'}
>>> labelizer = lambda k: {('a',): 'first', ('b',): 'second',
('c',): 'third'}[k]
>>> mosaic(data, title='colored dictionary',
properties=props, labelizer=labelizer)
>>> pylab.show()
Using a DataFrame as source, specifying the name of the columns of interest
>>> gender = ['male', 'male', 'male', 'female', 'female', 'female']
>>> pet = ['cat', 'dog', 'dog', 'cat', 'dog', 'cat']
>>> data = pandas.DataFrame({'gender': gender, 'pet': pet})
>>> mosaic(data, ['pet', 'gender'])
>>> pylab.show()
"""
from pylab import Rectangle
fig, ax = utils.create_mpl_ax(ax)
# normalize the data to a dict with tuple of strings as keys
data = _normalize_data(data, index)
# split the graph into different areas
rects = _hierarchical_split(data, horizontal=horizontal, gap=gap)
# if there is no specified way to create the labels
# create a default one
if labelizer is None:
labelizer = lambda k: "\n".join(k)
if statistic:
default_props = _statistical_coloring(data)
else:
default_props = _create_default_properties(data)
if isinstance(properties, dict):
color_dict = properties
properties = lambda key: color_dict.get(key, None)
for k, v in list(rects.items()):
# create each rectangle and put a label on it
x, y, w, h = v
conf = properties(k)
props = conf if conf else default_props[k]
text = labelizer(k)
Rect = Rectangle((x, y), w, h, label=text, **props)
ax.add_patch(Rect)
ax.text(x + w / 2, y + h / 2, text, ha='center',
va='center', size='smaller')
#creating the labels on the axis
#o clearing it
if axes_label:
if np.iterable(label_rotation):
rotation = label_rotation
else:
rotation = [label_rotation] * 4
labels = _create_labels(rects, horizontal, ax, rotation)
else:
ax.set_xticks([])
ax.set_xticklabels([])
ax.set_yticks([])
ax.set_yticklabels([])
ax.set_title(title)
return fig, rects
def plot_imputed_hist(self, col_name, ax=None, imp_hist_args=None,
obs_hist_args=None, all_hist_args=None):
"""
Display imputed values for one variable as a histogram.
Parameters
----------
col_name : string
The name of the variable to be plotted.
ax : matplotlib axes
An axes on which to draw the histograms. If not provided,
one is created.
imp_hist_args : dict
Keyword arguments to be passed to pyplot.hist when
creating the histogram for imputed values.
obs_hist_args : dict
Keyword arguments to be passed to pyplot.hist when
creating the histogram for observed values.
all_hist_args : dict
Keyword arguments to be passed to pyplot.hist when
creating the histogram for all values.
Returns
-------
The matplotlib figure on which the histograms were drawn
"""
from statsmodels.graphics import utils as gutils
if imp_hist_args is None:
imp_hist_args = {}
if obs_hist_args is None:
obs_hist_args = {}
if all_hist_args is None:
all_hist_args = {}
if ax is None:
fig, ax = gutils.create_mpl_ax(ax)
else:
fig = ax.get_figure()
ax.set_position([0.1, 0.1, 0.7, 0.8])
ixm = self.ix_miss[col_name]
ixo = self.ix_obs[col_name]
imp = self.data[col_name].iloc[ixm]
obs = self.data[col_name].iloc[ixo]
for di in imp_hist_args, obs_hist_args, all_hist_args:
if 'histtype' not in di:
di['histtype'] = 'step'
ha, la = [], []
if len(imp) > 0:
h = ax.hist(np.asarray(imp), **imp_hist_args)
ha.append(h[-1][0])
la.append("Imp")
h1 = ax.hist(np.asarray(obs), **obs_hist_args)
h2 = ax.hist(np.asarray(self.data[col_name]), **all_hist_args)
ha.extend([h1[-1][0], h2[-1][0]])
la.extend(["Obs", "All"])
leg = fig.legend(ha, la, 'center right', numpoints=1)
leg.draw_frame(False)
ax.set_xlabel(col_name)
ax.set_ylabel("Frequency")
return fig
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), prepend=True)
>>> y = np.dot(X, [25, 3.5]) + np.random.normal(0, 30, size=30)
>>> mod = sm.OLS(y,X).fit()
>>> fig = abline_plot(model_results=mod)
>>> ax = fig.axes
>>> 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()
y = ax.get_ylim()
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 update_datalim(self, ax):
ax.set_autoscale_on(False)
children = ax.get_children()
abline = [children[i] for i in range(len(children))
if isinstance(children[i], ABLine2D)][0]
x = ax.get_xlim()
y = [x[0]*slope+intercept, x[1]*slope+intercept]
abline.set_data(x,y)
ax.figure.canvas.draw()
line = ABLine2D(x, data_y, **kwargs)
ax.add_line(line)
ax.callbacks.connect('xlim_changed', line.update_datalim)
ax.callbacks.connect('ylim_changed', line.update_datalim)
if horiz:
ax.hline(horiz)
if vert:
ax.vline(vert)
return fig
def plot_power(self, dep_var='nobs', nobs=None, effect_size=None,
alpha=0.05, ax=None, title=None, plt_kwds=None, **kwds):
'''plot power with number of observations or effect size on x-axis
Parameters
----------
dep_var : string in ['nobs', 'effect_size', 'alpha']
This specifies which variable is used for the horizontal axis.
If dep_var='nobs' (default), then one curve is created for each
value of ``effect_size``. If dep_var='effect_size' or alpha, then
one curve is created for each value of ``nobs``.
nobs : scalar or array_like
specifies the values of the number of observations in the plot
effect_size : scalar or array_like
specifies the values of the effect_size in the plot
alpha : float or array_like
The significance level (type I error) used in the power
calculation. Can only be more than a scalar, if ``dep_var='alpha'``
ax : None or axis instance
If ax is None, than a matplotlib figure is created. If ax is a
matplotlib axis instance, then it is reused, and the plot elements
are created with it.
title : string
title for the axis. Use an empty string, ``''``, to avoid a title.
plt_kwds : None or dict
not used yet
kwds : optional keywords for power function
These remaining keyword arguments are used as arguments to the
power function. Many power function support ``alternative`` as a
keyword argument, two-sample test support ``ratio``.
Returns
-------
fig : matplotlib figure instance
Notes
-----
This works only for classes where the ``power`` method has
``effect_size``, ``nobs`` and ``alpha`` as the first three arguments.
If the second argument is ``nobs1``, then the number of observations
in the plot are those for the first sample.
TODO: fix this for FTestPower and GofChisquarePower
TODO: maybe add line variable, if we want more than nobs and effectsize
'''
#if pwr_kwds is None:
# pwr_kwds = {}
from statsmodels.graphics import utils
from statsmodels.graphics.plottools import rainbow
fig, ax = utils.create_mpl_ax(ax)
import matplotlib.pyplot as plt
colormap = plt.cm.Dark2 #pylint: disable-msg=E1101
plt_alpha = 1 #0.75
lw = 2
if dep_var == 'nobs':
colors = rainbow(len(effect_size))
colors = [colormap(i) for i in np.linspace(0, 0.9, len(effect_size))]
for ii, es in enumerate(effect_size):
power = self.power(es, nobs, alpha, **kwds)
ax.plot(nobs, power, lw=lw, alpha=plt_alpha,
color=colors[ii], label='es=%4.2F' % es)
xlabel = 'Number of Observations'
elif dep_var in ['effect size', 'effect_size', 'es']:
colors = rainbow(len(nobs))
colors = [colormap(i) for i in np.linspace(0, 0.9, len(nobs))]
for ii, n in enumerate(nobs):
power = self.power(effect_size, n, alpha, **kwds)
ax.plot(effect_size, power, lw=lw, alpha=plt_alpha,
color=colors[ii], label='N=%4.2F' % n)
xlabel = 'Effect Size'
elif dep_var in ['alpha']:
# experimental nobs as defining separate lines
colors = rainbow(len(nobs))
for ii, n in enumerate(nobs):
power = self.power(effect_size, n, alpha, **kwds)
ax.plot(alpha, power, lw=lw, alpha=plt_alpha,
color=colors[ii], label='N=%4.2F' % n)
xlabel = 'alpha'
else:
raise ValueError('depvar not implemented')
if title is None:
title = 'Power of Test'
ax.set_xlabel(xlabel)
ax.set_title(title)
ax.legend(loc='lower right')
return fig
yhat=phi1*np.hstack((0,y[0:(n-1)]))
sigma=np.var(y,ddof=1)
nu=np.hstack((sigma,sigma*(1-phi1**(2))[1:n]))
tau=nu/sigma
sigmahat=np.mean((y-yhat)**2/tau)
nuhat=sigmahat*(1-phi1**(2))
nuhat2=np.sqrt(nuhat)
ciar=(1-phi1**(2))
nuhat3=np.sqrt(sigma*ciar)
####Fitting Regular Models
arma_mod10 = sm.tsa.ARMA(y, (1,0)).fit(trend='nc')
#arma_mod10.summary()
syar=arma_mod10.sigma2/(1-arma_mod10.params[0]**2)
car=(1-arma_mod10.params[0]**2)
sear=np.sqrt(sigma*car)
pdf = matplotlib.backends.backend_pdf.PdfPages("outputAR.pdf")
ax=None
fig, ax = utils.create_mpl_ax(ax)
ax.vlines(sT[1:100], ymin=np.zeros(100), ymax=nuhat3[1:100])
ax.scatter(sT[1:100],nuhat3[1:100],c='green')
ax.axhline(np.sqrt(sigma),color='red')
ax.axhline(sear,color='blue')
ax.axhline(np.mean(nuhat3[1:100]),color='black')
ax.set_ylim([0, 1])
pdf.savefig(1)
pdf.close()
def plot_pacf(x,
ax=None,
lags=None,
alpha=.05,
method='ywadjusted',
use_vlines=True,
title='Partial Autocorrelation',
zero=True,
vlines_kwargs=None,
**kwargs):
"""
Plot the partial autocorrelation function
Parameters
----------
x : array_like
Array of time-series values
ax : AxesSubplot, optional
If given, this subplot is used to plot in instead of a new figure being
created.
lags : {int, array_like}, optional
An int or array of lag values, used on horizontal axis. Uses
np.arange(lags) when lags is an int. If not provided,
``lags=np.arange(len(corr))`` is used.
alpha : float, optional
If a number is given, the confidence intervals for the given level are
returned. For instance if alpha=.05, 95 % confidence intervals are
returned where the standard deviation is computed according to
1/sqrt(len(x))
method : {'ywunbiased', 'ywmle', 'ols'}
Specifies which method for the calculations to use:
- yw or ywunbiased : yule walker with bias correction in denominator
for acovf. Default.
- ywm or ywmle : yule walker without bias correction
- ols - regression of time series on lags of it and on constant
- ld or ldunbiased : Levinson-Durbin recursion with bias correction
- ldb or ldbiased : Levinson-Durbin recursion without bias correction
use_vlines : bool, optional
If True, vertical lines and markers are plotted.
If False, only markers are plotted. The default marker is 'o'; it can
be overridden with a ``marker`` kwarg.
title : str, optional
Title to place on plot. Default is 'Partial Autocorrelation'
zero : bool, optional
Flag indicating whether to include the 0-lag autocorrelation.
Default is True.
vlines_kwargs : dict, optional
Optional dictionary of keyword arguments that are passed to vlines.
**kwargs : kwargs, optional
Optional keyword arguments that are directly passed on to the
Matplotlib ``plot`` and ``axhline`` functions.
Returns
-------
Figure
If `ax` is None, the created figure. Otherwise the figure to which
`ax` is connected.
See Also
--------
matplotlib.pyplot.xcorr
matplotlib.pyplot.acorr
Notes
-----
Plots lags on the horizontal and the correlations on vertical axis.
Adapted from matplotlib's `xcorr`.
Data are plotted as ``plot(lags, corr, **kwargs)``
kwargs is used to pass matplotlib optional arguments to both the line
tracing the autocorrelations and for the horizontal line at 0. These
options must be valid for a Line2D object.
vlines_kwargs is used to pass additional optional arguments to the
vertical lines connecting each autocorrelation to the axis. These options
must be valid for a LineCollection object.
Examples
--------
>>> import pandas as pd
>>> import matplotlib.pyplot as plt
>>> import statsmodels.api as sm
>>> dta = sm.datasets.sunspots.load_pandas().data
>>> dta.index = pd.Index(sm.tsa.datetools.dates_from_range('1700', '2008'))
>>> del dta["YEAR"]
>>> sm.graphics.tsa.plot_acf(dta.values.squeeze(), lags=40)
>>> plt.show()
.. plot:: plots/graphics_tsa_plot_pacf.py
"""
fig, ax = utils.create_mpl_ax(ax)
vlines_kwargs = {} if vlines_kwargs is None else vlines_kwargs
lags, nlags, irregular = _prepare_data_corr_plot(x, lags, zero)
confint = None
if alpha is None:
acf_x = pacf(x, nlags=nlags, alpha=alpha, method=method)
else:
acf_x, confint = pacf(x, nlags=nlags, alpha=alpha, method=method)
_plot_corr(ax, title, acf_x, confint, lags, irregular, use_vlines,
vlines_kwargs, **kwargs)
return fig
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).
See Also
--------
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()
>>> sm.graphics.plot_partregress(endog='murder', exog_i='hs_grad',
... 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)
print("eval_env:", eval_env)
# 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, 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_power(self,
dep_var='nobs',
nobs=None,
effect_size=None,
alpha=0.05,
ax=None,
title=None,
plt_kwds=None,
**kwds):
'''plot power with number of observations or effect size on x-axis
Parameters
----------
dep_var : string in ['nobs', 'effect_size', 'alpha']
This specifies which variable is used for the horizontal axis.
If dep_var='nobs' (default), then one curve is created for each
value of ``effect_size``. If dep_var='effect_size' or alpha, then
one curve is created for each value of ``nobs``.
nobs : scalar or array_like
specifies the values of the number of observations in the plot
effect_size : scalar or array_like
specifies the values of the effect_size in the plot
alpha : float or array_like
The significance level (type I error) used in the power
calculation. Can only be more than a scalar, if ``dep_var='alpha'``
ax : None or axis instance
If ax is None, than a matplotlib figure is created. If ax is a
matplotlib axis instance, then it is reused, and the plot elements
are created with it.
title : string
title for the axis. Use an empty string, ``''``, to avoid a title.
plt_kwds : None or dict
not used yet
kwds : optional keywords for power function
These remaining keyword arguments are used as arguments to the
power function. Many power function support ``alternative`` as a
keyword argument, two-sample test support ``ratio``.
Returns
-------
fig : matplotlib figure instance
Notes
-----
This works only for classes where the ``power`` method has
``effect_size``, ``nobs`` and ``alpha`` as the first three arguments.
If the second argument is ``nobs1``, then the number of observations
in the plot are those for the first sample.
TODO: fix this for FTestPower and GofChisquarePower
TODO: maybe add line variable, if we want more than nobs and effectsize
'''
#if pwr_kwds is None:
# pwr_kwds = {}
from statsmodels.graphics import utils
from statsmodels.graphics.plottools import rainbow
fig, ax = utils.create_mpl_ax(ax)
import matplotlib.pyplot as plt
colormap = plt.cm.Dark2 #pylint: disable-msg=E1101
plt_alpha = 1 #0.75
lw = 2
if dep_var == 'nobs':
colors = rainbow(len(effect_size))
colors = [
colormap(i) for i in np.linspace(0, 0.9, len(effect_size))
]
for ii, es in enumerate(effect_size):
power = self.power(es, nobs, alpha, **kwds)
ax.plot(nobs,
power,
lw=lw,
alpha=plt_alpha,
color=colors[ii],
label='es=%4.2F' % es)
xlabel = 'Number of Observations'
elif dep_var in ['effect size', 'effect_size', 'es']:
colors = rainbow(len(nobs))
colors = [colormap(i) for i in np.linspace(0, 0.9, len(nobs))]
for ii, n in enumerate(nobs):
power = self.power(effect_size, n, alpha, **kwds)
ax.plot(effect_size,
power,
lw=lw,
alpha=plt_alpha,
color=colors[ii],
label='N=%4.2F' % n)
xlabel = 'Effect Size'
elif dep_var in ['alpha']:
# experimental nobs as defining separate lines
colors = rainbow(len(nobs))
for ii, n in enumerate(nobs):
power = self.power(effect_size, n, alpha, **kwds)
ax.plot(alpha,
power,
lw=lw,
alpha=plt_alpha,
color=colors[ii],
label='N=%4.2F' % n)
xlabel = 'alpha'
else:
raise ValueError('depvar not implemented')
if title is None:
title = 'Power of Test'
ax.set_xlabel(xlabel)
ax.set_title(title)
ax.legend(loc='lower right')
return fig
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.
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
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 plot
>>> 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
def plot_bivariate(self, col1_name, col2_name,
lowess_args=None, lowess_min_n=40,
jitter=None, plot_points=True, ax=None):
"""
Plot observed and imputed values for two variables.
Displays a scatterplot of one variable against another. The
points are colored according to whether the values are
observed or imputed.
Parameters
----------
col1_name : string
The variable to be plotted on the horizontal axis.
col2_name : string
The variable to be plotted on the vertical axis.
lowess_args : dictionary
A dictionary of dictionaries, keys are 'ii', 'io', 'oi'
and 'oo', where 'o' denotes 'observed' and 'i' denotes
imputed. See Notes for details.
lowess_min_n : integer
Minimum sample size to plot a lowess fit
jitter : float or tuple
Standard deviation for jittering points in the plot.
Either a single scalar applied to both axes, or a tuple
containing x-axis jitter and y-axis jitter, respectively.
plot_points : bool
If True, the data points are plotted.
ax : matplotlib axes object
Axes on which to plot, created if not provided.
Returns
-------
The matplotlib figure on which the plot id drawn.
"""
from statsmodels.graphics import utils as gutils
from statsmodels.nonparametric.smoothers_lowess import lowess
if lowess_args is None:
lowess_args = {}
if ax is None:
fig, ax = gutils.create_mpl_ax(ax)
else:
fig = ax.get_figure()
ax.set_position([0.1, 0.1, 0.7, 0.8])
ix1i = self.ix_miss[col1_name]
ix1o = self.ix_obs[col1_name]
ix2i = self.ix_miss[col2_name]
ix2o = self.ix_obs[col2_name]
ix_ii = np.intersect1d(ix1i, ix2i)
ix_io = np.intersect1d(ix1i, ix2o)
ix_oi = np.intersect1d(ix1o, ix2i)
ix_oo = np.intersect1d(ix1o, ix2o)
vec1 = np.asarray(self.data[col1_name])
vec2 = np.asarray(self.data[col2_name])
if jitter is not None:
if np.isscalar(jitter):
jitter = (jitter, jitter)
vec1 += jitter[0] * np.random.normal(size=len(vec1))
vec2 += jitter[1] * np.random.normal(size=len(vec2))
# Plot the points
keys = ['oo', 'io', 'oi', 'ii']
lak = {'i': 'imp', 'o': 'obs'}
ixs = {'ii': ix_ii, 'io': ix_io, 'oi': ix_oi, 'oo': ix_oo}
color = {'oo': 'grey', 'ii': 'red', 'io': 'orange',
'oi': 'lime'}
if plot_points:
for ky in keys:
ix = ixs[ky]
lab = lak[ky[0]] + "/" + lak[ky[1]]
ax.plot(vec1[ix], vec2[ix], 'o', color=color[ky],
label=lab, alpha=0.6)
# Plot the lowess fits
for ky in keys:
ix = ixs[ky]
if len(ix) < lowess_min_n:
continue
if ky in lowess_args:
la = lowess_args[ky]
else:
la = {}
ix = ixs[ky]
lfit = lowess(vec2[ix], vec1[ix], **la)
if plot_points:
ax.plot(lfit[:, 0], lfit[:, 1], '-', color=color[ky],
alpha=0.6, lw=4)
else:
lab = lak[ky[0]] + "/" + lak[ky[1]]
ax.plot(lfit[:, 0], lfit[:, 1], '-', color=color[ky],
alpha=0.6, lw=4, label=lab)
ha, la = ax.get_legend_handles_labels()
pad = 0.0001 if plot_points else 0.5
leg = fig.legend(ha, la, 'center right', numpoints=1,
handletextpad=pad)
leg.draw_frame(False)
ax.set_xlabel(col1_name)
ax.set_ylabel(col2_name)
return fig
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
if isinstance(exog_i, string_types):
exog_i = dmatrix(exog_i + "-1", data)
# all arrays or pandas-like
res_yaxis = OLS(endog, RHS).fit()
res_xaxis = OLS(exog_i, RHS).fit()
ax.plot(res_xaxis.resid, res_yaxis.resid, 'o', **kwargs)
fitted_line = OLS(res_yaxis.resid, res_xaxis.resid).fit()
fig = abline_plot(0, fitted_line.params[0], color='k', ax=ax)
x_axis_endog_name = res_xaxis.model.endog_names
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)" % res_yaxis.model.endog_names)
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_imputed_hist(self, col_name, ax=None, imp_hist_args=None,
obs_hist_args=None, all_hist_args=None):
"""
Display imputed values for one variable as a histogram.
Parameters
----------
col_name : string
The name of the variable to be plotted.
ax : matplotlib axes
An axes on which to draw the histograms. If not provided,
one is created.
imp_hist_args : dict
Keyword arguments to be passed to pyplot.hist when
creating the histogram for imputed values.
obs_hist_args : dict
Keyword arguments to be passed to pyplot.hist when
creating the histogram for observed values.
all_hist_args : dict
Keyword arguments to be passed to pyplot.hist when
creating the histogram for all values.
Returns
-------
The matplotlib figure on which the histograms were drawn
"""
from statsmodels.graphics import utils as gutils
from matplotlib.colors import LinearSegmentedColormap
if imp_hist_args is None:
imp_hist_args = {}
if obs_hist_args is None:
obs_hist_args = {}
if all_hist_args is None:
all_hist_args = {}
if ax is None:
fig, ax = gutils.create_mpl_ax(ax)
else:
fig = ax.get_figure()
ax.set_position([0.1, 0.1, 0.7, 0.8])
ixm = self.ix_miss[col_name]
ixo = self.ix_obs[col_name]
imp = self.data[col_name].iloc[ixm]
obs = self.data[col_name].iloc[ixo]
for di in imp_hist_args, obs_hist_args, all_hist_args:
if 'histtype' not in di:
di['histtype'] = 'step'
ha, la = [], []
if len(imp) > 0:
h = ax.hist(np.asarray(imp), **imp_hist_args)
ha.append(h[-1][0])
la.append("Imp")
h1 = ax.hist(np.asarray(obs), **obs_hist_args)
h2 = ax.hist(np.asarray(self.data[col_name]), **all_hist_args)
ha.extend([h1[-1][0], h2[-1][0]])
la.extend(["Obs", "All"])
leg = fig.legend(ha, la, 'center right', numpoints=1)
leg.draw_frame(False)
ax.set_xlabel(col_name)
ax.set_ylabel("Frequency")
return fig
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_pacf(x,
ax=None,
lags=None,
alpha=.05,
method='ywm',
use_vlines=True,
**kwargs):
"""Plot the partial autocorrelation function
Plots lags on the horizontal and the correlations on vertical axis.
Parameters
----------
x : array_like
Array of time-series values
ax : Matplotlib AxesSubplot instance, optional
If given, this subplot is used to plot in instead of a new figure being
created.
lags : array_like, optional
Array of lag values, used on horizontal axis.
If not given, ``lags=np.arange(len(corr))`` is used.
alpha : scalar, optional
If a number is given, the confidence intervals for the given level are
returned. For instance if alpha=.05, 95 % confidence intervals are
returned where the standard deviation is computed according to
1/sqrt(len(x))
method : 'ywunbiased' (default) or 'ywmle' or 'ols'
specifies which method for the calculations to use:
- yw or ywunbiased : yule walker with bias correction in denominator
for acovf
- ywm or ywmle : yule walker without bias correction
- ols - regression of time series on lags of it and on constant
- ld or ldunbiased : Levinson-Durbin recursion with bias correction
- ldb or ldbiased : Levinson-Durbin recursion without bias correction
use_vlines : bool, optional
If True, vertical lines and markers are plotted.
If False, only markers are plotted. The default marker is 'o'; it can
be overridden with a ``marker`` kwarg.
**kwargs : kwargs, optional
Optional keyword arguments that are directly passed on to the
Matplotlib ``plot`` and ``axhline`` functions.
Returns
-------
fig : Matplotlib figure instance
If `ax` is None, the created figure. Otherwise the figure to which
`ax` is connected.
See Also
--------
matplotlib.pyplot.xcorr
matplotlib.pyplot.acorr
mpl_examples/pylab_examples/xcorr_demo.py
Notes
-----
Adapted from matplotlib's `xcorr`.
Data are plotted as ``plot(lags, corr, **kwargs)``
"""
fig, ax = utils.create_mpl_ax(ax)
if lags is None:
lags = np.arange(len(x))
nlags = len(lags) - 1
else:
nlags = lags
lags = np.arange(lags + 1) # +1 for zero lag
confint = None
if alpha is None:
acf_x = pacf(x, nlags=nlags, alpha=alpha, method=method)
else:
acf_x, confint = pacf(x, nlags=nlags, alpha=alpha, method=method)
if use_vlines:
ax.vlines(lags, [0], acf_x, **kwargs)
ax.axhline(**kwargs)
# center the confidence interval TODO: do in acf?
kwargs.setdefault('marker', 'o')
kwargs.setdefault('markersize', 5)
kwargs.setdefault('linestyle', 'None')
ax.margins(.05)
ax.plot(lags, acf_x, **kwargs)
ax.set_title("Partial Autocorrelation")
if confint is not None:
# center the confidence interval TODO: do in acf?
ax.fill_between(lags,
confint[:, 0] - acf_x,
confint[:, 1] - acf_x,
alpha=.25)
return fig
def influence_plot(results, external=True, alpha=.05, criterion="cooks",
size=48, plot_alpha=.75, ax=None, **kwargs):
"""
Plot of influence in regression. Plots studentized resids vs. leverage.
Parameters
----------
results : results instance
A fitted model.
external : bool
Whether to use externally or internally studentized residuals. It is
recommended to leave external as True.
alpha : float
The alpha value to identify large studentized residuals. Large means
abs(resid_studentized) > t.ppf(1-alpha/2, dof=results.df_resid)
criterion : str {'DFFITS', 'Cooks'}
Which criterion to base the size of the points on. Options are
DFFITS or Cook's D.
size : float
The range of `criterion` is mapped to 10**2 - size**2 in points.
plot_alpha : float
The `alpha` of the plotted points.
ax : matplotlib Axes instance
An instance of a matplotlib Axes.
Returns
-------
fig : matplotlib figure
The matplotlib figure that contains the Axes.
Notes
-----
Row labels for the observations in which the leverage, measured by the
diagonal of the hat matrix, is high or the residuals are large, as the
combination of large residuals and a high influence value indicates an
influence point. The value of large residuals can be controlled using the
`alpha` parameter. Large leverage points are identified as
hat_i > 2 * (df_model + 1)/nobs.
"""
fig, ax = utils.create_mpl_ax(ax)
infl = results.get_influence()
if criterion.lower().startswith('dff'):
psize = infl.cooks_distance[0]
elif criterion.lower().startswith('coo'):
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_internal
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
def plot_pacf(x, ax=None, lags=None, alpha=.05, method='ywm',
use_vlines=True, **kwargs):
"""Plot the partial autocorrelation function
Plots lags on the horizontal and the correlations on vertical axis.
Parameters
----------
x : array_like
Array of time-series values
ax : Matplotlib AxesSubplot instance, optional
If given, this subplot is used to plot in instead of a new figure being
created.
lags : array_like, optional
Array of lag values, used on horizontal axis.
If not given, ``lags=np.arange(len(corr))`` is used.
alpha : scalar, optional
If a number is given, the confidence intervals for the given level are
returned. For instance if alpha=.05, 95 % confidence intervals are
returned where the standard deviation is computed according to
1/sqrt(len(x))
method : 'ywunbiased' (default) or 'ywmle' or 'ols'
specifies which method for the calculations to use:
- yw or ywunbiased : yule walker with bias correction in denominator
for acovf
- ywm or ywmle : yule walker without bias correction
- ols - regression of time series on lags of it and on constant
- ld or ldunbiased : Levinson-Durbin recursion with bias correction
- ldb or ldbiased : Levinson-Durbin recursion without bias correction
use_vlines : bool, optional
If True, vertical lines and markers are plotted.
If False, only markers are plotted. The default marker is 'o'; it can
be overridden with a ``marker`` kwarg.
**kwargs : kwargs, optional
Optional keyword arguments that are directly passed on to the
Matplotlib ``plot`` and ``axhline`` functions.
Returns
-------
fig : Matplotlib figure instance
If `ax` is None, the created figure. Otherwise the figure to which
`ax` is connected.
See Also
--------
matplotlib.pyplot.xcorr
matplotlib.pyplot.acorr
mpl_examples/pylab_examples/xcorr_demo.py
Notes
-----
Adapted from matplotlib's `xcorr`.
Data are plotted as ``plot(lags, corr, **kwargs)``
"""
fig, ax = utils.create_mpl_ax(ax)
if lags is None:
lags = np.arange(len(x))
nlags = len(lags) - 1
else:
nlags = lags
lags = np.arange(lags + 1) # +1 for zero lag
acf_x, confint = pacf(x, nlags=nlags, alpha=alpha, method=method)
if use_vlines:
ax.vlines(lags, [0], acf_x, **kwargs)
ax.axhline(**kwargs)
# center the confidence interval TODO: do in acf?
confint = confint - confint.mean(1)[:,None]
kwargs.setdefault('marker', 'o')
kwargs.setdefault('markersize', 5)
kwargs.setdefault('linestyle', 'None')
ax.margins(.05)
ax.plot(lags, acf_x, **kwargs)
ax.fill_between(lags, confint[:,0], confint[:,1], alpha=.25)
ax.set_title("Partial Autocorrelation")
return fig
def mosaic(data,
index=None,
ax=None,
horizontal=True,
gap=0.005,
properties=lambda key: None,
labelizer=None,
title='',
statistic=False,
axes_label=True,
label_rotation=0.0):
"""Create a mosaic plot from a contingency table.
It allows to visualize multivariate categorical data in a rigorous
and informative way.
Parameters
----------
data : {dict, Series, ndarray, DataFrame}
The contingency table that contains the data.
Each category should contain a non-negative number
with a tuple as index. It expects that all the combination
of keys to be represents; if that is not true, will
automatically consider the missing values as 0. The order
of the keys will be the same as the one of insertion.
If a dict of a Series (or any other dict like object)
is used, it will take the keys as labels. If a
np.ndarray is provided, it will generate a simple
numerical labels.
index : list, optional
Gives the preferred order for the category ordering. If not specified
will default to the given order. It does not support named indexes
for hierarchical Series. If a DataFrame is provided, it expects
a list with the name of the columns.
ax : Axes, optional
The graph where display the mosaic. If not given, will
create a new figure
horizontal : bool, optional
The starting direction of the split (by default along
the horizontal axis)
gap : {float, sequence[float]}
The list of gaps to be applied on each subdivision.
If the length of the given array is less of the number
of subcategories (or if it's a single number) it will extend
it with exponentially decreasing gaps
properties : dict[str, callable], optional
A function that for each tile in the mosaic take the key
of the tile and returns the dictionary of properties
of the generated Rectangle, like color, hatch or similar.
A default properties set will be provided fot the keys whose
color has not been defined, and will use color variation to help
visually separates the various categories. It should return None
to indicate that it should use the default property for the tile.
A dictionary of the properties for each key can be passed,
and it will be internally converted to the correct function
labelizer : dict[str, callable], optional
A function that generate the text to display at the center of
each tile base on the key of that tile
title : str, optional
The title of the axis
statistic : bool, optional
If true will use a crude statistical model to give colors to the plot.
If the tile has a constraint that is more than 2 standard deviation
from the expected value under independence hypothesis, it will
go from green to red (for positive deviations, blue otherwise) and
will acquire an hatching when crosses the 3 sigma.
axes_label : bool, optional
Show the name of each value of each category
on the axis (default) or hide them.
label_rotation : {float, list[float]}
The rotation of the axis label (if present). If a list is given
each axis can have a different rotation
Returns
---------
fig : Figure
The figure containing the plot.
rects : dict
A dictionary that has the same keys of the original
dataset, that holds a reference to the coordinates of the
tile and the Rectangle that represent it.
References
----------
A Brief History of the Mosaic Display
Michael Friendly, York University, Psychology Department
Journal of Computational and Graphical Statistics, 2001
Mosaic Displays for Loglinear Models.
Michael Friendly, York University, Psychology Department
Proceedings of the Statistical Graphics Section, 1992, 61-68.
Mosaic displays for multi-way contingency tables.
Michael Friendly, York University, Psychology Department
Journal of the american statistical association
March 1994, Vol. 89, No. 425, Theory and Methods
Examples
----------
>>> import numpy as np
>>> import pandas as pd
>>> import matplotlib.pyplot as plt
>>> from statsmodels.graphics.mosaicplot import mosaic
The most simple use case is to take a dictionary and plot the result
>>> data = {'a': 10, 'b': 15, 'c': 16}
>>> mosaic(data, title='basic dictionary')
>>> plt.show()
A more useful example is given by a dictionary with multiple indices.
In this case we use a wider gap to a better visual separation of the
resulting plot
>>> data = {('a', 'b'): 1, ('a', 'c'): 2, ('d', 'b'): 3, ('d', 'c'): 4}
>>> mosaic(data, gap=0.05, title='complete dictionary')
>>> plt.show()
The same data can be given as a simple or hierarchical indexed Series
>>> rand = np.random.random
>>> from itertools import product
>>> tuples = list(product(['bar', 'baz', 'foo', 'qux'], ['one', 'two']))
>>> index = pd.MultiIndex.from_tuples(tuples, names=['first', 'second'])
>>> data = pd.Series(rand(8), index=index)
>>> mosaic(data, title='hierarchical index series')
>>> plt.show()
The third accepted data structure is the np array, for which a
very simple index will be created.
>>> rand = np.random.random
>>> data = 1+rand((2,2))
>>> mosaic(data, title='random non-labeled array')
>>> plt.show()
If you need to modify the labeling and the coloring you can give
a function tocreate the labels and one with the graphical properties
starting from the key tuple
>>> data = {'a': 10, 'b': 15, 'c': 16}
>>> props = lambda key: {'color': 'r' if 'a' in key else 'gray'}
>>> labelizer = lambda k: {('a',): 'first', ('b',): 'second',
... ('c',): 'third'}[k]
>>> mosaic(data, title='colored dictionary', properties=props,
... labelizer=labelizer)
>>> plt.show()
Using a DataFrame as source, specifying the name of the columns of interest
>>> gender = ['male', 'male', 'male', 'female', 'female', 'female']
>>> pet = ['cat', 'dog', 'dog', 'cat', 'dog', 'cat']
>>> data = pd.DataFrame({'gender': gender, 'pet': pet})
>>> mosaic(data, ['pet', 'gender'], title='DataFrame as Source')
>>> plt.show()
.. plot :: plots/graphics_mosaicplot_mosaic.py
"""
if isinstance(data, DataFrame) and index is None:
raise ValueError("You must pass an index if data is a DataFrame."
" See examples.")
from matplotlib.patches import Rectangle
#from pylab import Rectangle
fig, ax = utils.create_mpl_ax(ax)
# normalize the data to a dict with tuple of strings as keys
data = _normalize_data(data, index)
# split the graph into different areas
rects = _hierarchical_split(data, horizontal=horizontal, gap=gap)
# if there is no specified way to create the labels
# create a default one
if labelizer is None:
labelizer = lambda k: "\n".join(k)
if statistic:
default_props = _statistical_coloring(data)
else:
default_props = _create_default_properties(data)
if isinstance(properties, dict):
color_dict = properties
properties = lambda key: color_dict.get(key, None)
for k, v in rects.items():
# create each rectangle and put a label on it
x, y, w, h = v
conf = properties(k)
props = conf if conf else default_props[k]
text = labelizer(k)
Rect = Rectangle((x, y), w, h, label=text, **props)
ax.add_patch(Rect)
ax.text(x + w / 2,
y + h / 2,
text,
ha='center',
va='center',
size='smaller')
#creating the labels on the axis
#o clearing it
if axes_label:
if np.iterable(label_rotation):
rotation = label_rotation
else:
rotation = [label_rotation] * 4
labels = _create_labels(rects, horizontal, ax, rotation)
else:
ax.set_xticks([])
ax.set_xticklabels([])
ax.set_yticks([])
ax.set_yticklabels([])
ax.set_title(title)
return fig, rects
def plot_pacf(x, ax=None, lags=None, alpha=.05, method='ywm', use_vlines=True,
title='Partial Autocorrelation', zero=True, **kwargs):
"""Plot the partial autocorrelation function
Plots lags on the horizontal and the correlations on vertical axis.
Parameters
----------
x : array_like
Array of time-series values
ax : Matplotlib AxesSubplot instance, optional
If given, this subplot is used to plot in instead of a new figure being
created.
lags : int or array_like, optional
int or Array of lag values, used on horizontal axis. Uses
np.arange(lags) when lags is an int. If not provided,
``lags=np.arange(len(corr))`` is used.
alpha : scalar, optional
If a number is given, the confidence intervals for the given level are
returned. For instance if alpha=.05, 95 % confidence intervals are
returned where the standard deviation is computed according to
1/sqrt(len(x))
method : 'ywunbiased' (default) or 'ywmle' or 'ols'
specifies which method for the calculations to use:
- yw or ywunbiased : yule walker with bias correction in denominator
for acovf
- ywm or ywmle : yule walker without bias correction
- ols - regression of time series on lags of it and on constant
- ld or ldunbiased : Levinson-Durbin recursion with bias correction
- ldb or ldbiased : Levinson-Durbin recursion without bias correction
use_vlines : bool, optional
If True, vertical lines and markers are plotted.
If False, only markers are plotted. The default marker is 'o'; it can
be overridden with a ``marker`` kwarg.
title : str, optional
Title to place on plot. Default is 'Partial Autocorrelation'
zero : bool, optional
Flag indicating whether to include the 0-lag autocorrelation.
Default is True.
**kwargs : kwargs, optional
Optional keyword arguments that are directly passed on to the
Matplotlib ``plot`` and ``axhline`` functions.
Returns
-------
fig : Matplotlib figure instance
If `ax` is None, the created figure. Otherwise the figure to which
`ax` is connected.
See Also
--------
matplotlib.pyplot.xcorr
matplotlib.pyplot.acorr
mpl_examples/pylab_examples/xcorr_demo.py
Notes
-----
Adapted from matplotlib's `xcorr`.
Data are plotted as ``plot(lags, corr, **kwargs)``
"""
fig, ax = utils.create_mpl_ax(ax)
lags, nlags, irregular = _prepare_data_corr_plot(x, lags, zero)
confint = None
if alpha is None:
acf_x = pacf(x, nlags=nlags, alpha=alpha, method=method)
else:
acf_x, confint = pacf(x, nlags=nlags, alpha=alpha, method=method)
_plot_corr(ax, title, acf_x, confint, lags, irregular, use_vlines, **kwargs)
return fig
def plot_scree(self,
ncomp=None,
log_scale=True,
cumulative=False,
ax=None):
"""
Plot of the ordered eigenvalues
Parameters
----------
ncomp : int, optional
Number of components ot include in the plot. If None, will
included the same as the number of components computed
log_scale : boot, optional
Flag indicating whether ot use a log scale for the y-axis
cumulative : bool, optional
Flag indicating whether to plot the eigenvalues or cumulative
eigenvalues
ax : Matplotlib axes instance, optional
An axes on which to draw the graph. If omitted, new a figure
is created
Returns
-------
fig : figure
Handle to the figure
"""
import statsmodels.graphics.utils as gutils
fig, ax = gutils.create_mpl_ax(ax)
ncomp = self._ncomp if ncomp is None else ncomp
vals = np.asarray(self.eigenvals)
vals = vals[:self._ncomp]
if cumulative:
vals = np.cumsum(vals)
if log_scale:
ax.set_yscale('log')
ax.plot(np.arange(ncomp), vals[:ncomp], 'bo')
ax.autoscale(tight=True)
xlim = np.array(ax.get_xlim())
sp = xlim[1] - xlim[0]
xlim += 0.02 * np.array([-sp, sp])
ax.set_xlim(xlim)
ylim = np.array(ax.get_ylim())
scale = 0.02
if log_scale:
sp = np.log(ylim[1] / ylim[0])
ylim = np.exp(
np.array([
np.log(ylim[0]) - scale * sp,
np.log(ylim[1]) + scale * sp
]))
else:
sp = ylim[1] - ylim[0]
ylim += scale * np.array([-sp, sp])
ax.set_ylim(ylim)
ax.set_title('Scree Plot')
ax.set_ylabel('Eigenvalue')
ax.set_xlabel('Component Number')
fig.tight_layout()
return fig
def plot_acf(x, ax=None, lags=None, alpha=.05, use_vlines=True, unbiased=False,
fft=False, title='Autocorrelation', zero=True, **kwargs):
"""Plot the autocorrelation function
Plots lags on the horizontal and the correlations on vertical axis.
Parameters
----------
x : array_like
Array of time-series values
ax : Matplotlib AxesSubplot instance, optional
If given, this subplot is used to plot in instead of a new figure being
created.
lags : int or array_like, optional
int or Array of lag values, used on horizontal axis. Uses
np.arange(lags) when lags is an int. If not provided,
``lags=np.arange(len(corr))`` is used.
alpha : scalar, optional
If a number is given, the confidence intervals for the given level are
returned. For instance if alpha=.05, 95 % confidence intervals are
returned where the standard deviation is computed according to
Bartlett's formula. If None, no confidence intervals are plotted.
use_vlines : bool, optional
If True, vertical lines and markers are plotted.
If False, only markers are plotted. The default marker is 'o'; it can
be overridden with a ``marker`` kwarg.
unbiased : bool
If True, then denominators for autocovariance are n-k, otherwise n
fft : bool, optional
If True, computes the ACF via FFT.
title : str, optional
Title to place on plot. Default is 'Autocorrelation'
zero : bool, optional
Flag indicating whether to include the 0-lag autocorrelation.
Default is True.
**kwargs : kwargs, optional
Optional keyword arguments that are directly passed on to the
Matplotlib ``plot`` and ``axhline`` functions.
Returns
-------
fig : Matplotlib figure instance
If `ax` is None, the created figure. Otherwise the figure to which
`ax` is connected.
See Also
--------
matplotlib.pyplot.xcorr
matplotlib.pyplot.acorr
mpl_examples/pylab_examples/xcorr_demo.py
Notes
-----
Adapted from matplotlib's `xcorr`.
Data are plotted as ``plot(lags, corr, **kwargs)``
"""
fig, ax = utils.create_mpl_ax(ax)
lags, nlags, irregular = _prepare_data_corr_plot(x, lags, zero)
confint = None
# acf has different return type based on alpha
if alpha is None:
acf_x = acf(x, nlags=nlags, alpha=alpha, fft=fft,
unbiased=unbiased)
else:
acf_x, confint = acf(x, nlags=nlags, alpha=alpha, fft=fft,
unbiased=unbiased)
_plot_corr(ax, title, acf_x, confint, lags, irregular, use_vlines, **kwargs)
return fig
def plot_survfunc(survfuncs, ax=None):
"""
Plot one or more survivor functions.
Parameters
----------
survfuncs : object or array-like
A single SurvfuncRight object, or a list or SurvfuncRight
objects that are plotted together.
Returns
-------
A figure instance on which the plot was drawn.
Examples
--------
Add a legend:
>>> import statsmodels.api as sm
>>> from statsmodels.duration.survfunc import plot_survfunc
>>> data = sm.datasets.get_rdataset("flchain", "survival").data
>>> df = data.loc[data.sex == "F", :]
>>> sf0 = sm.SurvfuncRight(df["futime"], df["death"])
>>> sf1 = sm.SurvfuncRight(3.0 * df["futime"], df["death"])
>>> fig = plot_survfunc([sf0, sf1])
>>> ax = fig.get_axes()[0]
>>> ax.set_position([0.1, 0.1, 0.64, 0.8])
>>> ha, lb = ax.get_legend_handles_labels()
>>> leg = fig.legend((ha[0], ha[1]), (lb[0], lb[1]), 'center right')
Change the line colors:
>>> fig = plot_survfunc([sf0, sf1])
>>> ax = fig.get_axes()[0]
>>> ax.set_position([0.1, 0.1, 0.64, 0.8])
>>> ha, lb = ax.get_legend_handles_labels()
>>> ha[0].set_color('purple')
>>> ha[1].set_color('orange')
"""
fig, ax = utils.create_mpl_ax(ax)
# If we have only a single survival function to plot, put it into
# a list.
try:
assert (type(survfuncs[0]) is SurvfuncRight)
except:
survfuncs = [survfuncs]
for gx, sf in enumerate(survfuncs):
# The estimated survival function does not include a point at
# time 0, include it here for plotting.
surv_times = np.concatenate(([0], sf.surv_times))
surv_prob = np.concatenate(([1], sf.surv_prob))
# If the final times are censoring times they are not included
# in the survival function so we add them here
mxt = max(sf.time)
if mxt > surv_times[-1]:
surv_times = np.concatenate((surv_times, [mxt]))
surv_prob = np.concatenate((surv_prob, [surv_prob[-1]]))
label = getattr(sf, "title", "Group %d" % (gx + 1))
li, = ax.step(surv_times,
surv_prob,
'-',
label=label,
lw=2,
where='post')
# Plot the censored points.
ii = np.flatnonzero(np.logical_not(sf.status))
ti = sf.time[ii]
jj = np.searchsorted(surv_times, ti) - 1
sp = surv_prob[jj]
ax.plot(ti,
sp,
'+',
ms=12,
color=li.get_color(),
label=label + " points")
ax.set_ylim(0, 1.01)
return fig
