"""
Generalized linear models currently supports estimation using the one-parameter
exponential families
References
----------
Gill, Jeff. 2000. Generalized Linear Models: A Unified Approach.
SAGE QASS Series.
Green, PJ. 1984. "Iteratively reweighted least squares for maximum
likelihood estimation, and some robust and resistant alternatives."
Journal of the Royal Statistical Society, Series B, 46, 149-192.
Hardin, J.W. and Hilbe, J.M. 2007. "Generalized Linear Models and
Extensions." 2nd ed. Stata Press, College Station, TX.
McCullagh, P. and Nelder, J.A. 1989. "Generalized Linear Models." 2nd ed.
Chapman & Hall, Boca Rotan.
"""
import numpy as np
from . import families
from statsmodels.tools.decorators import cache_readonly, resettable_cache
import statsmodels.base.model as base
import statsmodels.regression.linear_model as lm
import statsmodels.base.wrapper as wrap
from statsmodels.compat.numpy import np_matrix_rank
from statsmodels.tools.sm_exceptions import PerfectSeparationError
__all__ = ['GLM']
def _check_convergence(criterion, iteration, tol):
return not (np.fabs(criterion[iteration] - criterion[iteration-1]) > tol)
[docs]class GLM(base.LikelihoodModel):
__doc__ = """
Generalized Linear Models class
GLM inherits from statsmodels.base.model.LikelihoodModel
Parameters
-----------
endog : array-like
1d array of endogenous response variable. This array can be 1d or 2d.
Binomial family models accept a 2d array with two columns. If
supplied, each observation is expected to be [success, failure].
exog : array-like
A nobs x k array where `nobs` is the number of observations and `k`
is the number of regressors. An intercept is not included by default
and should be added by the user (models specified using a formula
include an intercept by default). See `statsmodels.tools.add_constant`.
family : family class instance
The default is Gaussian. To specify the binomial distribution
family = sm.family.Binomial()
Each family can take a link instance as an argument. See
statsmodels.family.family for more information.
%(extra_params)s
Attributes
-----------
df_model : float
`p` - 1, where `p` is the number of regressors including the intercept.
df_resid : float
The number of observation `n` minus the number of regressors `p`.
endog : array
See Parameters.
exog : array
See Parameters.
family : family class instance
A pointer to the distribution family of the model.
mu : array
The estimated mean response of the transformed variable.
normalized_cov_params : array
`p` x `p` normalized covariance of the design / exogenous data.
pinv_wexog : array
For GLM this is just the pseudo inverse of the original design.
scale : float
The estimate of the scale / dispersion. Available after fit is called.
scaletype : str
The scaling used for fitting the model. Available after fit is called.
weights : array
The value of the weights after the last iteration of fit.
Examples
--------
>>> import statsmodels.api as sm
>>> data = sm.datasets.scotland.load()
>>> data.exog = sm.add_constant(data.exog)
Instantiate a gamma family model with the default link function.
>>> gamma_model = sm.GLM(data.endog, data.exog,
... family=sm.families.Gamma())
>>> gamma_results = gamma_model.fit()
>>> gamma_results.params
array([-0.01776527, 0.00004962, 0.00203442, -0.00007181, 0.00011185,
-0.00000015, -0.00051868, -0.00000243])
>>> gamma_results.scale
0.0035842831734919055
>>> gamma_results.deviance
0.087388516416999198
>>> gamma_results.pearson_chi2
0.086022796163805704
>>> gamma_results.llf
-83.017202161073527
See also
--------
statsmodels.genmod.families.family
:ref:`families`
:ref:`links`
Notes
-----
Only the following combinations make sense for family and link ::
+ ident log logit probit cloglog pow opow nbinom loglog logc
Gaussian | x x x
inv Gaussian | x x x
binomial | x x x x x x x x x
Poission | x x x
neg binomial | x x x x
gamma | x x x
Not all of these link functions are currently available.
Endog and exog are references so that if the data they refer to are already
arrays and these arrays are changed, endog and exog will change.
**Attributes**
df_model : float
Model degrees of freedom is equal to p - 1, where p is the number
of regressors. Note that the intercept is not reported as a
degree of freedom.
df_resid : float
Residual degrees of freedom is equal to the number of observation n
minus the number of regressors p.
endog : array
See above. Note that endog is a reference to the data so that if
data is already an array and it is changed, then `endog` changes
as well.
exposure : array-like
Include ln(exposure) in model with coefficient constrained to 1. Can
only be used if the link is the logarithm function.
exog : array
See above. Note that endog is a reference to the data so that if
data is already an array and it is changed, then `endog` changes
as well.
iteration : int
The number of iterations that fit has run. Initialized at 0.
family : family class instance
The distribution family of the model. Can be any family in
statsmodels.families. Default is Gaussian.
mu : array
The mean response of the transformed variable. `mu` is the value of
the inverse of the link function at lin_pred, where lin_pred is the linear
predicted value of the WLS fit of the transformed variable. `mu` is
only available after fit is called. See
statsmodels.families.family.fitted of the distribution family for more
information.
normalized_cov_params : array
The p x p normalized covariance of the design / exogenous data.
This is approximately equal to (X.T X)^(-1)
offset : array-like
Include offset in model with coefficient constrained to 1.
pinv_wexog : array
The pseudoinverse of the design / exogenous data array. Note that
GLM has no whiten method, so this is just the pseudo inverse of the
design.
The pseudoinverse is approximately equal to (X.T X)^(-1)X.T
scale : float
The estimate of the scale / dispersion of the model fit. Only
available after fit is called. See GLM.fit and GLM.estimate_scale
for more information.
scaletype : str
The scaling used for fitting the model. This is only available after
fit is called. The default is None. See GLM.fit for more information.
weights : array
The value of the weights after the last iteration of fit. Only
available after fit is called. See statsmodels.families.family for
the specific distribution weighting functions.
""" % {'extra_params' : base._missing_param_doc}
[docs] def __init__(self, endog, exog, family=None, offset=None, exposure=None,
missing='none', **kwargs):
if exposure is not None:
exposure = np.log(exposure)
if offset is not None: # this should probably be done upstream
offset = np.asarray(offset)
super(GLM, self).__init__(endog, exog, missing=missing,
offset=offset, exposure=exposure,
**kwargs)
self._check_inputs(family, self.offset, self.exposure, self.endog)
if offset is None:
delattr(self, 'offset')
if exposure is None:
delattr(self, 'exposure')
#things to remove_data
self._data_attr.extend(['weights', 'pinv_wexog', 'mu', 'data_weights',
'_offset_exposure'])
# register kwds for __init__, offset and exposure are added by super
self._init_keys.append('family')
[docs] def initialize(self):
"""
Initialize a generalized linear model.
"""
#TODO: intended for public use?
self.history = {'fittedvalues' : [],
'params' : [np.inf],
'deviance' : [np.inf]}
self.pinv_wexog = np.linalg.pinv(self.exog)
self.normalized_cov_params = np.dot(self.pinv_wexog,
np.transpose(self.pinv_wexog))
self.df_model = np_matrix_rank(self.exog)-1
self.df_resid = self.exog.shape[0] - np_matrix_rank(self.exog)
def _check_inputs(self, family, offset, exposure, endog):
# Default family is Gaussian
if family is None:
family = families.Gaussian()
self.family = family
if exposure is not None:
if not isinstance(self.family.link, families.links.Log):
raise ValueError("exposure can only be used with the log "
"link function")
elif exposure.shape[0] != endog.shape[0]:
raise ValueError("exposure is not the same length as endog")
if offset is not None:
if offset.shape[0] != endog.shape[0]:
raise ValueError("offset is not the same length as endog")
[docs] def loglike(self, *args):
"""
Loglikelihood function.
Each distribution family has its own loglikelihood function.
See statsmodels.families.family
"""
return self.family.loglike(*args)
[docs] def score_obs(self, params, scale=None):
"""score first derivative of the loglikelihood for each observation.
Parameters
----------
params : ndarray
parameter at which score is evaluated
scale : None or float
If scale is None, then the default scale will be calculated.
Default scale is defined by `self.scaletype` and set in fit.
If scale is not None, then it is used as a fixed scale.
Returns
-------
score_obs : ndarray, 2d
The first derivative of the loglikelihood function evaluated at
params for each observation.
"""
score_factor = self.score_factor(params, scale=scale)
return score_factor[:, None] * self.exog
[docs] def score(self, params, scale=None):
"""score, first derivative of the loglikelihood function
Parameters
----------
params : ndarray
parameter at which score is evaluated
scale : None or float
If scale is None, then the default scale will be calculated.
Default scale is defined by `self.scaletype` and set in fit.
If scale is not None, then it is used as a fixed scale.
Returns
-------
score : ndarray_1d
The first derivative of the loglikelihood function calculated as
the sum of `score_obs`
"""
return self.score_obs(params, scale=scale).sum(0)
[docs] def score_factor(self, params, scale=None):
"""weights for score for each observation
This can be considered as score residuals.
Parameters
----------
params : ndarray
parameter at which Hessian is evaluated
scale : None or float
If scale is None, then the default scale will be calculated.
Default scale is defined by `self.scaletype` and set in fit.
If scale is not None, then it is used as a fixed scale.
Returns
-------
score_factor : ndarray_1d
A 1d weight vector used in the calculation of the score_obs.
The score_obs are obtained by `score_factor[:, None] * exog`
"""
mu = self.predict(params)
if scale is None:
scale = self.estimate_scale(mu)
score_factor = (self.endog - mu) / self.family.link.deriv(mu)
score_factor /= self.family.variance(mu)
score_factor *= self.data_weights
if not scale == 1:
score_factor /= scale
return score_factor
[docs] def hessian_factor(self, params, scale=None, observed=True):
"""Weights for calculating Hessian
Parameters
----------
params : ndarray
parameter at which Hessian is evaluated
scale : None or float
If scale is None, then the default scale will be calculated.
Default scale is defined by `self.scaletype` and set in fit.
If scale is not None, then it is used as a fixed scale.
observed : bool
If True, then the observed Hessian is returned. If false then the
expected information matrix is returned.
Returns
-------
hessian_factor : ndarray, 1d
A 1d weight vector used in the calculation of the Hessian.
The hessian is obtained by `(exog.T * hessian_factor).dot(exog)`
"""
# calculating eim_factor
mu = self.predict(params)
if scale is None:
scale = self.estimate_scale(mu)
eim_factor = 1 / (self.family.link.deriv(mu)**2 *
self.family.variance(mu))
eim_factor *= self.data_weights
if not observed:
if not scale == 1:
eim_factor /= scale
return eim_factor
# calculating oim_factor, eim_factor is with scale=1
score_factor = self.score_factor(params, scale=1.)
if eim_factor.ndim > 1 or score_factor.ndim > 1:
raise RuntimeError('something wrong')
tmp = self.family.variance(mu) * self.family.link.deriv2(mu)
tmp += self.family.variance.deriv(mu) * self.family.link.deriv(mu)
tmp = score_factor * eim_factor * tmp
# correct for duplicatee data_weights in oim_factor and score_factor
tmp /= self.data_weights
oim_factor = eim_factor * (1 + tmp)
if tmp.ndim > 1:
raise RuntimeError('something wrong')
if not scale == 1:
oim_factor /= scale
return oim_factor
[docs] def hessian(self, params, scale=None, observed=True):
"""Hessian, second derivative of loglikelihood function
Parameters
----------
params : ndarray
parameter at which Hessian is evaluated
scale : None or float
If scale is None, then the default scale will be calculated.
Default scale is defined by `self.scaletype` and set in fit.
If scale is not None, then it is used as a fixed scale.
observed : bool
If True, then the observed Hessian is returned. If false then the
expected information matrix is returned.
Returns
-------
hessian : ndarray
Hessian, i.e. observed information, or expected information matrix.
"""
factor = self.hessian_factor(params, scale=scale, observed=observed)
hess = -np.dot(self.exog.T * factor, self.exog)
return hess
[docs] def score_test(self, params_constrained, k_constraints=None,
exog_extra=None, observed=True):
"""score test for restrictions or for omitted variables
The covariance matrix for the score is based on the Hessian, i.e.
observed information matrix or optionally on the expected information
matrix..
Parameters
----------
params_constrained : array_like
estimated parameter of the restricted model. This can be the
parameter estimate for the current when testing for omitted
variables.
k_constraints : int or None
Number of constraints that were used in the estimation of params
restricted relative to the number of exog in the model.
This must be provided if no exog_extra are given. If exog_extra is
not None, then k_constraints is assumed to be zero if it is None.
exog_extra : None or array_like
Explanatory variables that are jointly tested for inclusion in the
model, i.e. omitted variables.
observed : bool
If True, then the observed Hessian is used in calculating the
covariance matrix of the score. If false then the expected
information matrix is used.
Returns
-------
chi2_stat : float
chisquare statistic for the score test
p-value : float
P-value of the score test based on the chisquare distribution.
df : int
Degrees of freedom used in the p-value calculation. This is equal
to the number of constraints.
Notes
-----
not yet verified for case with scale not equal to 1.
"""
if exog_extra is None:
if k_constraints is None:
raise ValueError('if exog_extra is None, then k_constraints'
'needs to be given')
score = self.score(params_constrained)
hessian = self.hessian(params_constrained, observed=observed)
else:
#exog_extra = np.asarray(exog_extra)
if k_constraints is None:
k_constraints = 0
ex = np.column_stack((self.exog, exog_extra))
k_constraints += ex.shape[1] - self.exog.shape[1]
score_factor = self.score_factor(params_constrained)
score = (score_factor[:, None] * ex).sum(0)
hessian_factor = self.hessian_factor(params_constrained,
observed=observed)
hessian = -np.dot(ex.T * hessian_factor, ex)
from scipy import stats
# TODO check sign, why minus?
chi2stat = -score.dot(np.linalg.solve(hessian, score[:, None]))
pval = stats.chi2.sf(chi2stat, k_constraints)
# return a stats results instance instead? Contrast?
return chi2stat, pval, k_constraints
def _update_history(self, tmp_result, mu, history):
"""
Helper method to update history during iterative fit.
"""
history['params'].append(tmp_result.params)
history['deviance'].append(self.family.deviance(self.endog, mu))
return history
[docs] def estimate_scale(self, mu):
"""
Estimates the dispersion/scale.
Type of scale can be chose in the fit method.
Parameters
----------
mu : array
mu is the mean response estimate
Returns
-------
Estimate of scale
Notes
-----
The default scale for Binomial and Poisson families is 1. The default
for the other families is Pearson's Chi-Square estimate.
See also
--------
statsmodels.glm.fit for more information
"""
if not self.scaletype:
if isinstance(self.family, (families.Binomial, families.Poisson)):
return 1.
else:
resid = self.endog - mu
return ((np.power(resid, 2) / self.family.variance(mu)).sum()
/ self.df_resid)
if isinstance(self.scaletype, float):
return np.array(self.scaletype)
if isinstance(self.scaletype, str):
if self.scaletype.lower() == 'x2':
resid = self.endog - mu
return ((np.power(resid, 2) / self.family.variance(mu)).sum()
/ self.df_resid)
elif self.scaletype.lower() == 'dev':
return self.family.deviance(self.endog, mu)/self.df_resid
else:
raise ValueError("Scale %s with type %s not understood" %
(self.scaletype, type(self.scaletype)))
else:
raise ValueError("Scale %s with type %s not understood" %
(self.scaletype, type(self.scaletype)))
[docs] def predict(self, params, exog=None, exposure=None, offset=None,
linear=False):
"""
Return predicted values for a design matrix
Parameters
----------
params : array-like
Parameters / coefficients of a GLM.
exog : array-like, optional
Design / exogenous data. Is exog is None, model exog is used.
exposure : array-like, optional
Exposure time values, only can be used with the log link
function. See notes for details.
offset : array-like, optional
Offset values. See notes for details.
linear : bool
If True, returns the linear predicted values. If False,
returns the value of the inverse of the model's link function at
the linear predicted values.
Returns
-------
An array of fitted values
Notes
-----
Any `exposure` and `offset` provided here take precedence over
the `exposure` and `offset` used in the model fit. If `exog`
is passed as an argument here, then any `exposure` and
`offset` values in the fit will be ignored.
Exposure values must be strictly positive.
"""
# Use fit offset if appropriate
if offset is None and exog is None and hasattr(self, 'offset'):
offset = getattr(self, 'offset')
elif offset is None:
offset = 0.
if exposure is not None and not isinstance(self.family.link,
families.links.Log):
raise ValueError("exposure can only be used with the log link function")
# Use fit exposure if appropriate
if exposure is None and exog is None and hasattr(self, 'exposure'):
# Already logged
exposure = getattr(self, 'exposure')
elif exposure is None:
exposure = 0.
else:
exposure = np.log(exposure)
if exog is None:
exog = self.exog
linpred = np.dot(exog, params) + offset + exposure
if linear:
return linpred
else:
return self.family.fitted(linpred)
[docs] def fit(self, start_params=None, maxiter=100, method='IRLS', tol=1e-8,
scale=None, cov_type='nonrobust', cov_kwds=None, use_t=None,
**kwargs):
"""
Fits a generalized linear model for a given family.
parameters
----------
maxiter : int, optional
Default is 100.
method : string
Default is 'IRLS' for iteratively reweighted least squares. This
is currently the only method available for GLM fit.
scale : string or float, optional
`scale` can be 'X2', 'dev', or a float
The default value is None, which uses `X2` for Gamma, Gaussian,
and Inverse Gaussian.
`X2` is Pearson's chi-square divided by `df_resid`.
The default is 1 for the Binomial and Poisson families.
`dev` is the deviance divided by df_resid
tol : float
Convergence tolerance. Default is 1e-8.
start_params : array-like, optional
Initial guess of the solution for the loglikelihood maximization.
The default is family-specific and is given by the
``family.starting_mu(endog)``. If start_params is given then the
initial mean will be calculated as ``np.dot(exog, start_params)``.
Notes
-----
This method does not take any extra undocumented ``kwargs``.
"""
endog = self.endog
if endog.ndim > 1 and endog.shape[1] == 2:
data_weights = endog.sum(1) # weights are total trials
else:
data_weights = np.ones((endog.shape[0]))
self.data_weights = data_weights
if np.shape(self.data_weights) == () and self.data_weights > 1:
self.data_weights = self.data_weights * np.ones((endog.shape[0]))
self.scaletype = scale
if isinstance(self.family, families.Binomial):
# this checks what kind of data is given for Binomial.
# family will need a reference to endog if this is to be removed from
# preprocessing
self.endog = self.family.initialize(self.endog)
# Construct a combined offset/exposure term. Note that
# exposure has already been logged if present.
offset_exposure = 0.
if hasattr(self, 'offset'):
offset_exposure = self.offset
if hasattr(self, 'exposure'):
offset_exposure = offset_exposure + self.exposure
self._offset_exposure = offset_exposure
wlsexog = self.exog
if start_params is None:
mu = self.family.starting_mu(self.endog)
lin_pred = self.family.predict(mu)
else:
lin_pred = np.dot(wlsexog, start_params) + offset_exposure
mu = self.family.fitted(lin_pred)
dev = self.family.deviance(self.endog, mu)
if np.isnan(dev):
raise ValueError("The first guess on the deviance function "
"returned a nan. This could be a boundary "
" problem and should be reported.")
# first guess on the deviance is assumed to be scaled by 1.
# params are none to start, so they line up with the deviance
history = dict(params=[None, start_params], deviance=[np.inf, dev])
converged = False
criterion = history['deviance']
# This special case is used to get the likelihood for a specific
# params vector.
if maxiter == 0:
mu = self.family.fitted(lin_pred)
self.scale = self.estimate_scale(mu)
wls_results = lm.RegressionResults(self, start_params, None)
iteration = 0
for iteration in range(maxiter):
self.weights = data_weights*self.family.weights(mu)
wlsendog = (lin_pred + self.family.link.deriv(mu) * (self.endog-mu)
- offset_exposure)
wls_results = lm.WLS(wlsendog, wlsexog, self.weights).fit()
lin_pred = np.dot(self.exog, wls_results.params) + offset_exposure
mu = self.family.fitted(lin_pred)
history = self._update_history(wls_results, mu, history)
self.scale = self.estimate_scale(mu)
if endog.squeeze().ndim == 1 and np.allclose(mu - endog, 0):
msg = "Perfect separation detected, results not available"
raise PerfectSeparationError(msg)
converged = _check_convergence(criterion, iteration, tol)
if converged:
break
self.mu = mu
glm_results = GLMResults(self, wls_results.params,
wls_results.normalized_cov_params,
self.scale,
cov_type=cov_type, cov_kwds=cov_kwds,
use_t=use_t)
history['iteration'] = iteration + 1
glm_results.fit_history = history
return GLMResultsWrapper(glm_results)
[docs] def fit_constrained(self, constraints, start_params=None, **fit_kwds):
"""fit the model subject to linear equality constraints
The constraints are of the form `R params = q`
where R is the constraint_matrix and q is the vector of
constraint_values.
The estimation creates a new model with transformed design matrix,
exog, and converts the results back to the original parameterization.
Parameters
----------
constraints : formula expression or tuple
If it is a tuple, then the constraint needs to be given by two
arrays (constraint_matrix, constraint_value), i.e. (R, q).
Otherwise, the constraints can be given as strings or list of
strings.
see t_test for details
start_params : None or array_like
starting values for the optimization. `start_params` needs to be
given in the original parameter space and are internally
transformed.
**fit_kwds : keyword arguments
fit_kwds are used in the optimization of the transformed model.
Returns
-------
results : Results instance
"""
from patsy import DesignInfo
from statsmodels.base._constraints import fit_constrained
# same pattern as in base.LikelihoodModel.t_test
lc = DesignInfo(self.exog_names).linear_constraint(constraints)
R, q = lc.coefs, lc.constants
# TODO: add start_params option, need access to tranformation
# fit_constrained needs to do the transformation
params, cov, res_constr = fit_constrained(self, R, q,
start_params=start_params,
fit_kwds=fit_kwds)
#create dummy results Instance, TODO: wire up properly
res = self.fit(start_params=params, maxiter=0) # we get a wrapper back
res._results.params = params
res._results.normalized_cov_params = cov
k_constr = len(q)
res._results.df_resid += k_constr
res._results.df_model -= k_constr
res._results.constraints = lc
res._results.k_constr = k_constr
res._results.results_constrained = res_constr
# TODO: the next is not the best. history should bin in results
res._results.model.history = res_constr.model.history
res._results.mu = res_constr.mu
return res
[docs]class GLMResults(base.LikelihoodModelResults):
"""
Class to contain GLM results.
GLMResults inherits from statsmodels.LikelihoodModelResults
Parameters
----------
See statsmodels.LikelihoodModelReesults
Returns
-------
**Attributes**
aic : float
Akaike Information Criterion
-2 * `llf` + 2*(`df_model` + 1)
bic : float
Bayes Information Criterion
`deviance` - `df_resid` * log(`nobs`)
deviance : float
See statsmodels.families.family for the distribution-specific deviance
functions.
df_model : float
See GLM.df_model
df_resid : float
See GLM.df_resid
fit_history : dict
Contains information about the iterations. Its keys are `iterations`,
`deviance` and `params`.
fittedvalues : array
Linear predicted values for the fitted model.
dot(exog, params)
llf : float
Value of the loglikelihood function evalued at params.
See statsmodels.families.family for distribution-specific
loglikelihoods.
model : class instance
Pointer to GLM model instance that called fit.
mu : array
See GLM docstring.
nobs : float
The number of observations n.
normalized_cov_params : array
See GLM docstring
null_deviance : float
The value of the deviance function for the model fit with a constant
as the only regressor.
params : array
The coefficients of the fitted model. Note that interpretation
of the coefficients often depends on the distribution family and the
data.
pearson_chi2 : array
Pearson's Chi-Squared statistic is defined as the sum of the squares
of the Pearson residuals.
pinv_wexog : array
See GLM docstring.
pvalues : array
The two-tailed p-values for the parameters.
resid_anscombe : array
Anscombe residuals. See statsmodels.families.family for distribution-
specific Anscombe residuals.
resid_deviance : array
Deviance residuals. See statsmodels.families.family for distribution-
specific deviance residuals.
resid_pearson : array
Pearson residuals. The Pearson residuals are defined as
(`endog` - `mu`)/sqrt(VAR(`mu`)) where VAR is the distribution
specific variance function. See statsmodels.families.family and
statsmodels.families.varfuncs for more information.
resid_response : array
Respnose residuals. The response residuals are defined as
`endog` - `fittedvalues`
resid_working : array
Working residuals. The working residuals are defined as
`resid_response`/link'(`mu`). See statsmodels.family.links for the
derivatives of the link functions. They are defined analytically.
scale : float
The estimate of the scale / dispersion for the model fit.
See GLM.fit and GLM.estimate_scale for more information.
stand_errors : array
The standard errors of the fitted GLM. #TODO still named bse
See Also
--------
statsmodels.base.model.LikelihoodModelResults
"""
[docs] def __init__(self, model, params, normalized_cov_params, scale,
cov_type='nonrobust', cov_kwds=None, use_t=None):
super(GLMResults, self).__init__(model, params,
normalized_cov_params=
normalized_cov_params, scale=scale)
self.family = model.family
self._endog = model.endog
self.nobs = model.endog.shape[0]
self.mu = model.mu
self._data_weights = model.data_weights
self.df_resid = model.df_resid
self.df_model = model.df_model
self.pinv_wexog = model.pinv_wexog
self._cache = resettable_cache()
# are these intermediate results needed or can we just
# call the model's attributes?
# for remove data and pickle without large arrays
self._data_attr.extend(['results_constrained'])
self.data_in_cache = getattr(self, 'data_in_cache', [])
self.data_in_cache.extend(['null'])
# robust covariance
from statsmodels.base.covtype import get_robustcov_results
if use_t is None:
self.use_t = False # TODO: class default
else:
self.use_t = use_t
if cov_type == 'nonrobust':
self.cov_type = 'nonrobust'
self.cov_kwds = {'description' : 'Standard Errors assume that the ' +
'covariance matrix of the errors is correctly ' +
'specified.'}
else:
if cov_kwds is None:
cov_kwds = {}
get_robustcov_results(self, cov_type=cov_type, use_self=True,
use_t=use_t, **cov_kwds)
@cache_readonly
[docs] def resid_response(self):
return self._data_weights * (self._endog-self.mu)
@cache_readonly
[docs] def resid_pearson(self):
return (np.sqrt(self._data_weights) * (self._endog-self.mu) /
np.sqrt(self.family.variance(self.mu)))
@cache_readonly
[docs] def resid_working(self):
val = (self.resid_response / self.family.link.deriv(self.mu))
val *= self._data_weights
return val
@cache_readonly
[docs] def resid_anscombe(self):
return self.family.resid_anscombe(self._endog, self.mu)
@cache_readonly
[docs] def resid_deviance(self):
return self.family.resid_dev(self._endog, self.mu)
@cache_readonly
[docs] def pearson_chi2(self):
chisq = (self._endog - self.mu)**2 / self.family.variance(self.mu)
chisq *= self._data_weights
chisqsum = np.sum(chisq)
return chisqsum
@cache_readonly
[docs] def fittedvalues(self):
return self.mu
@cache_readonly
[docs] def null(self):
endog = self._endog
model = self.model
exog = np.ones((len(endog), 1))
kwargs = {}
if hasattr(model, 'offset'):
kwargs['offset'] = model.offset
if hasattr(model, 'exposure'):
kwargs['exposure'] = model.exposure
if len(kwargs) > 0:
return GLM(endog, exog, family=self.family, **kwargs).fit().mu
else:
wls_model = lm.WLS(endog, exog, weights=self._data_weights)
return wls_model.fit().fittedvalues
@cache_readonly
[docs] def deviance(self):
return self.family.deviance(self._endog, self.mu)
@cache_readonly
[docs] def null_deviance(self):
return self.family.deviance(self._endog, self.null)
@cache_readonly
[docs] def llnull(self):
return self.family.loglike(self._endog, self.null, scale=self.scale)
@cache_readonly
[docs] def llf(self):
_modelfamily = self.family
if isinstance(_modelfamily, families.NegativeBinomial):
lin_pred = np.dot(self.model.exog, self.params) +\
self.model._offset_exposure
val = _modelfamily.loglike(self.model.endog,
lin_pred=lin_pred)
else:
val = _modelfamily.loglike(self._endog, self.mu, scale=self.scale)
return val
@cache_readonly
[docs] def aic(self):
return -2 * self.llf + 2*(self.df_model+1)
@cache_readonly
[docs] def bic(self):
return self.deviance - self.df_resid*np.log(self.nobs)
[docs] def remove_data(self):
#GLM has alias/reference in result instance
self._data_attr.extend([i for i in self.model._data_attr
if not '_data.' in i])
super(self.__class__, self).remove_data()
#TODO: what are these in results?
self._endog = None
self._data_weights = None
remove_data.__doc__ = base.LikelihoodModelResults.remove_data.__doc__
[docs] def summary(self, yname=None, xname=None, title=None, alpha=.05):
"""
Summarize the Regression Results
Parameters
-----------
yname : string, optional
Default is `y`
xname : list of strings, optional
Default is `var_##` for ## in p the number of regressors
title : string, optional
Title for the top table. If not None, then this replaces the
default title
alpha : float
significance level for the confidence intervals
Returns
-------
smry : Summary instance
this holds the summary tables and text, which can be printed or
converted to various output formats.
See Also
--------
statsmodels.iolib.summary.Summary : class to hold summary
results
"""
top_left = [('Dep. Variable:', None),
('Model:', None),
('Model Family:', [self.family.__class__.__name__]),
('Link Function:', [self.family.link.__class__.__name__]),
('Method:', ['IRLS']),
('Date:', None),
('Time:', None),
('No. Iterations:',
["%d" % self.fit_history['iteration']]),
]
top_right = [('No. Observations:', None),
('Df Residuals:', None),
('Df Model:', None),
('Scale:', [self.scale]),
('Log-Likelihood:', None),
('Deviance:', ["%#8.5g" % self.deviance]),
('Pearson chi2:', ["%#6.3g" % self.pearson_chi2])
]
if title is None:
title = "Generalized Linear Model Regression Results"
#create summary tables
from statsmodels.iolib.summary import Summary
smry = Summary()
smry.add_table_2cols(self, gleft=top_left, gright=top_right, # [],
yname=yname, xname=xname, title=title)
smry.add_table_params(self, yname=yname, xname=xname, alpha=alpha,
use_t=self.use_t)
if hasattr(self, 'constraints'):
smry.add_extra_txt(['Model has been estimated subject to linear '
'equality constraints.'])
#diagnostic table is not used yet:
#smry.add_table_2cols(self, gleft=diagn_left, gright=diagn_right,
# yname=yname, xname=xname,
# title="")
return smry
[docs] def summary2(self, yname=None, xname=None, title=None, alpha=.05,
float_format="%.4f"):
"""Experimental summary for regression Results
Parameters
-----------
yname : string
Name of the dependent variable (optional)
xname : List of strings of length equal to the number of parameters
Names of the independent variables (optional)
title : string, optional
Title for the top table. If not None, then this replaces the
default title
alpha : float
significance level for the confidence intervals
float_format: string
print format for floats in parameters summary
Returns
-------
smry : Summary instance
this holds the summary tables and text, which can be printed or
converted to various output formats.
See Also
--------
statsmodels.iolib.summary2.Summary : class to hold summary
results
"""
self.method = 'IRLS'
from statsmodels.iolib import summary2
smry = summary2.Summary()
smry.add_base(results=self, alpha=alpha, float_format=float_format,
xname=xname, yname=yname, title=title)
if hasattr(self, 'constraints'):
smry.add_text('Model has been estimated subject to linear '
'equality constraints.')
return smry
[docs]class GLMResultsWrapper(lm.RegressionResultsWrapper):
_attrs = {
'resid_anscombe' : 'rows',
'resid_deviance' : 'rows',
'resid_pearson' : 'rows',
'resid_response' : 'rows',
'resid_working' : 'rows'
}
_wrap_attrs = wrap.union_dicts(lm.RegressionResultsWrapper._wrap_attrs,
_attrs)
wrap.populate_wrapper(GLMResultsWrapper, GLMResults)
if __name__ == "__main__":
import statsmodels.api as sm
data = sm.datasets.longley.load()
#data.exog = add_constant(data.exog)
GLMmod = GLM(data.endog, data.exog).fit()
GLMT = GLMmod.summary(returns='tables')
## GLMT[0].extend_right(GLMT[1])
## print(GLMT[0])
## print(GLMT[2])
GLMTp = GLMmod.summary(title='Test GLM')
"""
From Stata
. webuse beetle
. glm r i.beetle ldose, family(binomial n) link(cloglog)
Iteration 0: log likelihood = -79.012269
Iteration 1: log likelihood = -76.94951
Iteration 2: log likelihood = -76.945645
Iteration 3: log likelihood = -76.945645
Generalized linear models No. of obs = 24
Optimization : ML Residual df = 20
Scale parameter = 1
Deviance = 73.76505595 (1/df) Deviance = 3.688253
Pearson = 71.8901173 (1/df) Pearson = 3.594506
Variance function: V(u) = u*(1-u/n) [Binomial]
Link function : g(u) = ln(-ln(1-u/n)) [Complementary log-log]
AIC = 6.74547
Log likelihood = -76.94564525 BIC = 10.20398
------------------------------------------------------------------------------
| OIM
r | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
beetle |
2 | -.0910396 .1076132 -0.85 0.398 -.3019576 .1198783
3 | -1.836058 .1307125 -14.05 0.000 -2.09225 -1.579867
|
ldose | 19.41558 .9954265 19.50 0.000 17.46458 21.36658
_cons | -34.84602 1.79333 -19.43 0.000 -38.36089 -31.33116
------------------------------------------------------------------------------
"""
#NOTE: wfs dataset has been removed due to a licensing issue
# example of using offset
#data = sm.datasets.wfs.load()
# get offset
#offset = np.log(data.exog[:,-1])
#exog = data.exog[:,:-1]
# convert dur to dummy
#exog = sm.tools.categorical(exog, col=0, drop=True)
# drop reference category
# convert res to dummy
#exog = sm.tools.categorical(exog, col=0, drop=True)
# convert edu to dummy
#exog = sm.tools.categorical(exog, col=0, drop=True)
# drop reference categories and add intercept
#exog = sm.add_constant(exog[:,[1,2,3,4,5,7,8,10,11,12]])
#endog = np.round(data.endog)
#mod = sm.GLM(endog, exog, family=sm.families.Poisson()).fit()
#res1 = GLM(endog, exog, family=sm.families.Poisson(),
# offset=offset).fit(tol=1e-12, maxiter=250)
#exposuremod = GLM(endog, exog, family=sm.families.Poisson(),
# exposure = data.exog[:,-1]).fit(tol=1e-12,
# maxiter=250)
#assert(np.all(res1.params == exposuremod.params))