from __future__ import print_function
from statsmodels.compat.python import lzip, range, reduce
import numpy as np
from scipy import stats
from statsmodels.base.data import handle_data
from statsmodels.tools.data import _is_using_pandas
from statsmodels.tools.tools import recipr, nan_dot
from statsmodels.stats.contrast import (ContrastResults, WaldTestResults,
t_test_pairwise)
from statsmodels.tools.decorators import resettable_cache, cache_readonly
import statsmodels.base.wrapper as wrap
from statsmodels.tools.numdiff import approx_fprime
from statsmodels.tools.sm_exceptions import ValueWarning, \
HessianInversionWarning
from statsmodels.formula import handle_formula_data
from statsmodels.compat.numpy import np_matrix_rank
from statsmodels.base.optimizer import Optimizer
_model_params_doc = """
Parameters
----------
endog : array-like
1-d endogenous response variable. The dependent variable.
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. See
:func:`statsmodels.tools.add_constant`."""
_missing_param_doc = """\
missing : str
Available options are 'none', 'drop', and 'raise'. If 'none', no nan
checking is done. If 'drop', any observations with nans are dropped.
If 'raise', an error is raised. Default is 'none.'"""
_extra_param_doc = """
hasconst : None or bool
Indicates whether the RHS includes a user-supplied constant. If True,
a constant is not checked for and k_constant is set to 1 and all
result statistics are calculated as if a constant is present. If
False, a constant is not checked for and k_constant is set to 0.
"""
[docs]class Model(object):
__doc__ = """
A (predictive) statistical model. Intended to be subclassed not used.
%(params_doc)s
%(extra_params_doc)s
Notes
-----
`endog` and `exog` are references to any data provided. So if the data is
already stored in numpy arrays and it is changed then `endog` and `exog`
will change as well.
""" % {'params_doc': _model_params_doc,
'extra_params_doc': _missing_param_doc + _extra_param_doc}
def __init__(self, endog, exog=None, **kwargs):
missing = kwargs.pop('missing', 'none')
hasconst = kwargs.pop('hasconst', None)
self.data = self._handle_data(endog, exog, missing, hasconst,
**kwargs)
self.k_constant = self.data.k_constant
self.exog = self.data.exog
self.endog = self.data.endog
self._data_attr = []
self._data_attr.extend(['exog', 'endog', 'data.exog', 'data.endog'])
if 'formula' not in kwargs: # won't be able to unpickle without these
self._data_attr.extend(['data.orig_endog', 'data.orig_exog'])
# store keys for extras if we need to recreate model instance
# we don't need 'missing', maybe we need 'hasconst'
self._init_keys = list(kwargs.keys())
if hasconst is not None:
self._init_keys.append('hasconst')
def _get_init_kwds(self):
"""return dictionary with extra keys used in model.__init__
"""
kwds = dict(((key, getattr(self, key, None))
for key in self._init_keys))
return kwds
def _handle_data(self, endog, exog, missing, hasconst, **kwargs):
data = handle_data(endog, exog, missing, hasconst, **kwargs)
# kwargs arrays could have changed, easier to just attach here
for key in kwargs:
if key in ['design_info', 'formula']: # leave attached to data
continue
# pop so we don't start keeping all these twice or references
try:
setattr(self, key, data.__dict__.pop(key))
except KeyError: # panel already pops keys in data handling
pass
return data
@property
def endog_names(self):
"""Names of endogenous variables"""
return self.data.ynames
@property
def exog_names(self):
"""Names of exogenous variables"""
return self.data.xnames
[docs] def fit(self):
"""
Fit a model to data.
"""
raise NotImplementedError
[docs] def predict(self, params, exog=None, *args, **kwargs):
"""
After a model has been fit predict returns the fitted values.
This is a placeholder intended to be overwritten by individual models.
"""
raise NotImplementedError
[docs]class LikelihoodModel(Model):
"""
Likelihood model is a subclass of Model.
"""
def __init__(self, endog, exog=None, **kwargs):
super(LikelihoodModel, self).__init__(endog, exog, **kwargs)
self.initialize()
[docs] def initialize(self):
"""
Initialize (possibly re-initialize) a Model instance. For
instance, the design matrix of a linear model may change
and some things must be recomputed.
"""
pass
# TODO: if the intent is to re-initialize the model with new data then this
# method needs to take inputs...
[docs] def loglike(self, params):
"""
Log-likelihood of model.
"""
raise NotImplementedError
[docs] def score(self, params):
"""
Score vector of model.
The gradient of logL with respect to each parameter.
"""
raise NotImplementedError
[docs] def hessian(self, params):
"""
The Hessian matrix of the model
"""
raise NotImplementedError
[docs] def fit(self, start_params=None, method='newton', maxiter=100,
full_output=True, disp=True, fargs=(), callback=None, retall=False,
skip_hessian=False, **kwargs):
"""
Fit method for likelihood based models
Parameters
----------
start_params : array-like, optional
Initial guess of the solution for the loglikelihood maximization.
The default is an array of zeros.
method : str, optional
The `method` determines which solver from `scipy.optimize`
is used, and it can be chosen from among the following strings:
- 'newton' for Newton-Raphson, 'nm' for Nelder-Mead
- 'bfgs' for Broyden-Fletcher-Goldfarb-Shanno (BFGS)
- 'lbfgs' for limited-memory BFGS with optional box constraints
- 'powell' for modified Powell's method
- 'cg' for conjugate gradient
- 'ncg' for Newton-conjugate gradient
- 'basinhopping' for global basin-hopping solver
- 'minimize' for generic wrapper of scipy minimize (BFGS by default)
The explicit arguments in `fit` are passed to the solver,
with the exception of the basin-hopping solver. Each
solver has several optional arguments that are not the same across
solvers. See the notes section below (or scipy.optimize) for the
available arguments and for the list of explicit arguments that the
basin-hopping solver supports.
maxiter : int, optional
The maximum number of iterations to perform.
full_output : bool, optional
Set to True to have all available output in the Results object's
mle_retvals attribute. The output is dependent on the solver.
See LikelihoodModelResults notes section for more information.
disp : bool, optional
Set to True to print convergence messages.
fargs : tuple, optional
Extra arguments passed to the likelihood function, i.e.,
loglike(x,*args)
callback : callable callback(xk), optional
Called after each iteration, as callback(xk), where xk is the
current parameter vector.
retall : bool, optional
Set to True to return list of solutions at each iteration.
Available in Results object's mle_retvals attribute.
skip_hessian : bool, optional
If False (default), then the negative inverse hessian is calculated
after the optimization. If True, then the hessian will not be
calculated. However, it will be available in methods that use the
hessian in the optimization (currently only with `"newton"`).
kwargs : keywords
All kwargs are passed to the chosen solver with one exception. The
following keyword controls what happens after the fit::
warn_convergence : bool, optional
If True, checks the model for the converged flag. If the
converged flag is False, a ConvergenceWarning is issued.
Notes
-----
The 'basinhopping' solver ignores `maxiter`, `retall`, `full_output`
explicit arguments.
Optional arguments for solvers (see returned Results.mle_settings)::
'newton'
tol : float
Relative error in params acceptable for convergence.
'nm' -- Nelder Mead
xtol : float
Relative error in params acceptable for convergence
ftol : float
Relative error in loglike(params) acceptable for
convergence
maxfun : int
Maximum number of function evaluations to make.
'bfgs'
gtol : float
Stop when norm of gradient is less than gtol.
norm : float
Order of norm (np.Inf is max, -np.Inf is min)
epsilon
If fprime is approximated, use this value for the step
size. Only relevant if LikelihoodModel.score is None.
'lbfgs'
m : int
This many terms are used for the Hessian approximation.
factr : float
A stop condition that is a variant of relative error.
pgtol : float
A stop condition that uses the projected gradient.
epsilon
If fprime is approximated, use this value for the step
size. Only relevant if LikelihoodModel.score is None.
maxfun : int
Maximum number of function evaluations to make.
bounds : sequence
(min, max) pairs for each element in x,
defining the bounds on that parameter.
Use None for one of min or max when there is no bound
in that direction.
'cg'
gtol : float
Stop when norm of gradient is less than gtol.
norm : float
Order of norm (np.Inf is max, -np.Inf is min)
epsilon : float
If fprime is approximated, use this value for the step
size. Can be scalar or vector. Only relevant if
Likelihoodmodel.score is None.
'ncg'
fhess_p : callable f'(x,*args)
Function which computes the Hessian of f times an arbitrary
vector, p. Should only be supplied if
LikelihoodModel.hessian is None.
avextol : float
Stop when the average relative error in the minimizer
falls below this amount.
epsilon : float or ndarray
If fhess is approximated, use this value for the step size.
Only relevant if Likelihoodmodel.hessian is None.
'powell'
xtol : float
Line-search error tolerance
ftol : float
Relative error in loglike(params) for acceptable for
convergence.
maxfun : int
Maximum number of function evaluations to make.
start_direc : ndarray
Initial direction set.
'basinhopping'
niter : integer
The number of basin hopping iterations.
niter_success : integer
Stop the run if the global minimum candidate remains the
same for this number of iterations.
T : float
The "temperature" parameter for the accept or reject
criterion. Higher "temperatures" mean that larger jumps
in function value will be accepted. For best results
`T` should be comparable to the separation (in function
value) between local minima.
stepsize : float
Initial step size for use in the random displacement.
interval : integer
The interval for how often to update the `stepsize`.
minimizer : dict
Extra keyword arguments to be passed to the minimizer
`scipy.optimize.minimize()`, for example 'method' - the
minimization method (e.g. 'L-BFGS-B'), or 'tol' - the
tolerance for termination. Other arguments are mapped from
explicit argument of `fit`:
- `args` <- `fargs`
- `jac` <- `score`
- `hess` <- `hess`
'minimize'
min_method : str, optional
Name of minimization method to use.
Any method specific arguments can be passed directly.
For a list of methods and their arguments, see
documentation of `scipy.optimize.minimize`.
If no method is specified, then BFGS is used.
"""
Hinv = None # JP error if full_output=0, Hinv not defined
if start_params is None:
if hasattr(self, 'start_params'):
start_params = self.start_params
elif self.exog is not None:
# fails for shape (K,)?
start_params = [0] * self.exog.shape[1]
else:
raise ValueError("If exog is None, then start_params should "
"be specified")
# TODO: separate args from nonarg taking score and hessian, ie.,
# user-supplied and numerically evaluated estimate frprime doesn't take
# args in most (any?) of the optimize function
nobs = self.endog.shape[0]
# f = lambda params, *args: -self.loglike(params, *args) / nobs
def f(params, *args):
return -self.loglike(params, *args) / nobs
if method == 'newton':
# TODO: why are score and hess positive?
def score(params, *args):
return self.score(params, *args) / nobs
def hess(params, *args):
return self.hessian(params, *args) / nobs
else:
def score(params, *args):
return -self.score(params, *args) / nobs
def hess(params, *args):
return -self.hessian(params, *args) / nobs
warn_convergence = kwargs.pop('warn_convergence', True)
optimizer = Optimizer()
xopt, retvals, optim_settings = optimizer._fit(f, score, start_params,
fargs, kwargs,
hessian=hess,
method=method,
disp=disp,
maxiter=maxiter,
callback=callback,
retall=retall,
full_output=full_output)
# NOTE: this is for fit_regularized and should be generalized
cov_params_func = kwargs.setdefault('cov_params_func', None)
if cov_params_func:
Hinv = cov_params_func(self, xopt, retvals)
elif method == 'newton' and full_output:
Hinv = np.linalg.inv(-retvals['Hessian']) / nobs
elif not skip_hessian:
H = -1 * self.hessian(xopt)
invertible = False
if np.all(np.isfinite(H)):
eigvals, eigvecs = np.linalg.eigh(H)
if np.min(eigvals) > 0:
invertible = True
if invertible:
Hinv = eigvecs.dot(np.diag(1.0 / eigvals)).dot(eigvecs.T)
Hinv = np.asfortranarray((Hinv + Hinv.T) / 2.0)
else:
from warnings import warn
warn('Inverting hessian failed, no bse or cov_params '
'available', HessianInversionWarning)
Hinv = None
if 'cov_type' in kwargs:
cov_kwds = kwargs.get('cov_kwds', {})
kwds = {'cov_type': kwargs['cov_type'], 'cov_kwds': cov_kwds}
else:
kwds = {}
if 'use_t' in kwargs:
kwds['use_t'] = kwargs['use_t']
# TODO: add Hessian approximation and change the above if needed
mlefit = LikelihoodModelResults(self, xopt, Hinv, scale=1., **kwds)
# TODO: hardcode scale?
if isinstance(retvals, dict):
mlefit.mle_retvals = retvals
if warn_convergence and not retvals['converged']:
from warnings import warn
from statsmodels.tools.sm_exceptions import ConvergenceWarning
warn("Maximum Likelihood optimization failed to converge. "
"Check mle_retvals", ConvergenceWarning)
mlefit.mle_settings = optim_settings
return mlefit
# TODO: the below is unfinished
[docs]class GenericLikelihoodModel(LikelihoodModel):
"""
Allows the fitting of any likelihood function via maximum likelihood.
A subclass needs to specify at least the log-likelihood
If the log-likelihood is specified for each observation, then results that
require the Jacobian will be available. (The other case is not tested yet.)
Notes
-----
Optimization methods that require only a likelihood function are 'nm' and
'powell'
Optimization methods that require a likelihood function and a
score/gradient are 'bfgs', 'cg', and 'ncg'. A function to compute the
Hessian is optional for 'ncg'.
Optimization method that require a likelihood function, a score/gradient,
and a Hessian is 'newton'
If they are not overwritten by a subclass, then numerical gradient,
Jacobian and Hessian of the log-likelihood are caclulated by numerical
forward differentiation. This might results in some cases in precision
problems, and the Hessian might not be positive definite. Even if the
Hessian is not positive definite the covariance matrix of the parameter
estimates based on the outer product of the Jacobian might still be valid.
Examples
--------
see also subclasses in directory miscmodels
import statsmodels.api as sm
data = sm.datasets.spector.load()
data.exog = sm.add_constant(data.exog)
# in this dir
from model import GenericLikelihoodModel
probit_mod = sm.Probit(data.endog, data.exog)
probit_res = probit_mod.fit()
loglike = probit_mod.loglike
score = probit_mod.score
mod = GenericLikelihoodModel(data.endog, data.exog, loglike, score)
res = mod.fit(method="nm", maxiter = 500)
import numpy as np
np.allclose(res.params, probit_res.params)
"""
def __init__(self, endog, exog=None, loglike=None, score=None,
hessian=None, missing='none', extra_params_names=None,
**kwds):
# let them be none in case user wants to use inheritance
if loglike is not None:
self.loglike = loglike
if score is not None:
self.score = score
if hessian is not None:
self.hessian = hessian
self.__dict__.update(kwds)
# TODO: data structures?
# TODO temporary solution, force approx normal
# self.df_model = 9999
# somewhere: CacheWriteWarning: 'df_model' cannot be overwritten
super(GenericLikelihoodModel, self).__init__(endog, exog,
missing=missing)
# this won't work for ru2nmnl, maybe np.ndim of a dict?
if exog is not None:
self.nparams = (exog.shape[1] if np.ndim(exog) == 2 else 1)
if extra_params_names is not None:
self._set_extra_params_names(extra_params_names)
def _set_extra_params_names(self, extra_params_names):
# check param_names
if extra_params_names is not None:
if self.exog is not None:
self.exog_names.extend(extra_params_names)
else:
self.data.xnames = extra_params_names
self.nparams = len(self.exog_names)
# this is redundant and not used when subclassing
[docs] def initialize(self):
if not self.score: # right now score is not optional
self.score = approx_fprime
if not self.hessian:
pass
else: # can use approx_hess_p if we have a gradient
if not self.hessian:
pass
# Initialize is called by
# statsmodels.model.LikelihoodModel.__init__
# and should contain any preprocessing that needs to be done for a model
if self.exog is not None:
# assume constant
er = np_matrix_rank(self.exog)
self.df_model = float(er - 1)
self.df_resid = float(self.exog.shape[0] - er)
else:
self.df_model = np.nan
self.df_resid = np.nan
super(GenericLikelihoodModel, self).initialize()
[docs] def expandparams(self, params):
"""
expand to full parameter array when some parameters are fixed
Parameters
----------
params : array
reduced parameter array
Returns
-------
paramsfull : array
expanded parameter array where fixed parameters are included
Notes
-----
Calling this requires that self.fixed_params and self.fixed_paramsmask
are defined.
*developer notes:*
This can be used in the log-likelihood to ...
this could also be replaced by a more general parameter
transformation.
"""
paramsfull = self.fixed_params.copy()
paramsfull[self.fixed_paramsmask] = params
return paramsfull
[docs] def reduceparams(self, params):
return params[self.fixed_paramsmask]
[docs] def loglike(self, params):
return self.loglikeobs(params).sum(0)
[docs] def nloglike(self, params):
return -self.loglikeobs(params).sum(0)
[docs] def loglikeobs(self, params):
return -self.nloglikeobs(params)
[docs] def score(self, params):
"""
Gradient of log-likelihood evaluated at params
"""
kwds = {}
kwds.setdefault('centered', True)
return approx_fprime(params, self.loglike, **kwds).ravel()
[docs] def score_obs(self, params, **kwds):
"""
Jacobian/Gradient of log-likelihood evaluated at params for each
observation.
"""
# kwds.setdefault('epsilon', 1e-4)
kwds.setdefault('centered', True)
return approx_fprime(params, self.loglikeobs, **kwds)
[docs] def hessian(self, params):
"""
Hessian of log-likelihood evaluated at params
"""
from statsmodels.tools.numdiff import approx_hess
# need options for hess (epsilon)
return approx_hess(params, self.loglike)
[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)`
"""
raise NotImplementedError
[docs] def fit(self, start_params=None, method='nm', maxiter=500, full_output=1,
disp=1, callback=None, retall=0, **kwargs):
"""
Fit the model using maximum likelihood.
The rest of the docstring is from
statsmodels.LikelihoodModel.fit
"""
if start_params is None:
if hasattr(self, 'start_params'):
start_params = self.start_params
else:
start_params = 0.1 * np.ones(self.nparams)
fit_method = super(GenericLikelihoodModel, self).fit
mlefit = fit_method(start_params=start_params,
method=method, maxiter=maxiter,
full_output=full_output,
disp=disp, callback=callback, **kwargs)
genericmlefit = GenericLikelihoodModelResults(self, mlefit)
# amend param names
exog_names = [] if (self.exog_names is None) else self.exog_names
k_miss = len(exog_names) - len(mlefit.params)
if not k_miss == 0:
if k_miss < 0:
self._set_extra_params_names(['par%d' % i
for i in range(-k_miss)])
else:
# I don't want to raise after we have already fit()
import warnings
warnings.warn('more exog_names than parameters', ValueWarning)
return genericmlefit
# fit.__doc__ += LikelihoodModel.fit.__doc__
[docs]class Results(object):
"""
Class to contain model results
Parameters
----------
model : class instance
the previously specified model instance
params : array
parameter estimates from the fit model
"""
def __init__(self, model, params, **kwd):
self.__dict__.update(kwd)
self.initialize(model, params, **kwd)
self._data_attr = []
[docs] def initialize(self, model, params, **kwd):
self.params = params
self.model = model
if hasattr(model, 'k_constant'):
self.k_constant = model.k_constant
[docs] def predict(self, exog=None, transform=True, *args, **kwargs):
"""
Call self.model.predict with self.params as the first argument.
Parameters
----------
exog : array-like, optional
The values for which you want to predict. see Notes below.
transform : bool, optional
If the model was fit via a formula, do you want to pass
exog through the formula. Default is True. E.g., if you fit
a model y ~ log(x1) + log(x2), and transform is True, then
you can pass a data structure that contains x1 and x2 in
their original form. Otherwise, you'd need to log the data
first.
args, kwargs :
Some models can take additional arguments or keywords, see the
predict method of the model for the details.
Returns
-------
prediction : ndarray, pandas.Series or pandas.DataFrame
See self.model.predict
Notes
-----
The types of exog that are supported depends on whether a formula
was used in the specification of the model.
If a formula was used, then exog is processed in the same way as
the original data. This transformation needs to have key access to the
same variable names, and can be a pandas DataFrame or a dict like
object.
If no formula was used, then the provided exog needs to have the
same number of columns as the original exog in the model. No
transformation of the data is performed except converting it to
a numpy array.
Row indices as in pandas data frames are supported, and added to the
returned prediction.
"""
import pandas as pd
is_pandas = _is_using_pandas(exog, None)
exog_index = exog.index if is_pandas else None
if transform and hasattr(self.model, 'formula') and (exog is not None):
design_info = self.model.data.design_info
from patsy import dmatrix
if isinstance(exog, pd.Series):
# we are guessing whether it should be column or row
if (hasattr(exog, 'name') and
isinstance(exog.name, str) and
exog.name in design_info.describe()):
# assume we need one column
exog = pd.DataFrame(exog)
else:
# assume we need a row
exog = pd.DataFrame(exog).T
orig_exog_len = len(exog)
is_dict = isinstance(exog, dict)
exog = dmatrix(design_info, exog, return_type="dataframe")
if orig_exog_len > len(exog) and not is_dict:
import warnings
if exog_index is None:
warnings.warn('nan values have been dropped', ValueWarning)
else:
exog = exog.reindex(exog_index)
exog_index = exog.index
if exog is not None:
exog = np.asarray(exog)
if exog.ndim == 1 and (self.model.exog.ndim == 1 or
self.model.exog.shape[1] == 1):
exog = exog[:, None]
exog = np.atleast_2d(exog) # needed in count model shape[1]
predict_results = self.model.predict(self.params, exog, *args,
**kwargs)
if exog_index is not None and not hasattr(predict_results,
'predicted_values'):
if predict_results.ndim == 1:
return pd.Series(predict_results, index=exog_index)
else:
return pd.DataFrame(predict_results, index=exog_index)
else:
return predict_results
[docs] def summary(self):
pass
# TODO: public method?
[docs]class LikelihoodModelResults(Results):
"""
Class to contain results from likelihood models
Parameters
-----------
model : LikelihoodModel instance or subclass instance
LikelihoodModelResults holds a reference to the model that is fit.
params : 1d array_like
parameter estimates from estimated model
normalized_cov_params : 2d array
Normalized (before scaling) covariance of params. (dot(X.T,X))**-1
scale : float
For (some subset of models) scale will typically be the
mean square error from the estimated model (sigma^2)
Returns
-------
**Attributes**
mle_retvals : dict
Contains the values returned from the chosen optimization method if
full_output is True during the fit. Available only if the model
is fit by maximum likelihood. See notes below for the output from
the different methods.
mle_settings : dict
Contains the arguments passed to the chosen optimization method.
Available if the model is fit by maximum likelihood. See
LikelihoodModel.fit for more information.
model : model instance
LikelihoodResults contains a reference to the model that is fit.
params : ndarray
The parameters estimated for the model.
scale : float
The scaling factor of the model given during instantiation.
tvalues : array
The t-values of the standard errors.
Notes
-----
The covariance of params is given by scale times normalized_cov_params.
Return values by solver if full_output is True during fit:
'newton'
fopt : float
The value of the (negative) loglikelihood at its
minimum.
iterations : int
Number of iterations performed.
score : ndarray
The score vector at the optimum.
Hessian : ndarray
The Hessian at the optimum.
warnflag : int
1 if maxiter is exceeded. 0 if successful convergence.
converged : bool
True: converged. False: did not converge.
allvecs : list
List of solutions at each iteration.
'nm'
fopt : float
The value of the (negative) loglikelihood at its
minimum.
iterations : int
Number of iterations performed.
warnflag : int
1: Maximum number of function evaluations made.
2: Maximum number of iterations reached.
converged : bool
True: converged. False: did not converge.
allvecs : list
List of solutions at each iteration.
'bfgs'
fopt : float
Value of the (negative) loglikelihood at its minimum.
gopt : float
Value of gradient at minimum, which should be near 0.
Hinv : ndarray
value of the inverse Hessian matrix at minimum. Note
that this is just an approximation and will often be
different from the value of the analytic Hessian.
fcalls : int
Number of calls to loglike.
gcalls : int
Number of calls to gradient/score.
warnflag : int
1: Maximum number of iterations exceeded. 2: Gradient
and/or function calls are not changing.
converged : bool
True: converged. False: did not converge.
allvecs : list
Results at each iteration.
'lbfgs'
fopt : float
Value of the (negative) loglikelihood at its minimum.
gopt : float
Value of gradient at minimum, which should be near 0.
fcalls : int
Number of calls to loglike.
warnflag : int
Warning flag:
- 0 if converged
- 1 if too many function evaluations or too many iterations
- 2 if stopped for another reason
converged : bool
True: converged. False: did not converge.
'powell'
fopt : float
Value of the (negative) loglikelihood at its minimum.
direc : ndarray
Current direction set.
iterations : int
Number of iterations performed.
fcalls : int
Number of calls to loglike.
warnflag : int
1: Maximum number of function evaluations. 2: Maximum number
of iterations.
converged : bool
True : converged. False: did not converge.
allvecs : list
Results at each iteration.
'cg'
fopt : float
Value of the (negative) loglikelihood at its minimum.
fcalls : int
Number of calls to loglike.
gcalls : int
Number of calls to gradient/score.
warnflag : int
1: Maximum number of iterations exceeded. 2: Gradient and/
or function calls not changing.
converged : bool
True: converged. False: did not converge.
allvecs : list
Results at each iteration.
'ncg'
fopt : float
Value of the (negative) loglikelihood at its minimum.
fcalls : int
Number of calls to loglike.
gcalls : int
Number of calls to gradient/score.
hcalls : int
Number of calls to hessian.
warnflag : int
1: Maximum number of iterations exceeded.
converged : bool
True: converged. False: did not converge.
allvecs : list
Results at each iteration.
"""
# by default we use normal distribution
# can be overwritten by instances or subclasses
use_t = False
def __init__(self, model, params, normalized_cov_params=None, scale=1.,
**kwargs):
super(LikelihoodModelResults, self).__init__(model, params)
self.normalized_cov_params = normalized_cov_params
self.scale = scale
# robust covariance
# We put cov_type in kwargs so subclasses can decide in fit whether to
# use this generic implementation
if 'use_t' in kwargs:
use_t = kwargs['use_t']
if use_t is not None:
self.use_t = use_t
if 'cov_type' in kwargs:
cov_type = kwargs.get('cov_type', 'nonrobust')
cov_kwds = kwargs.get('cov_kwds', {})
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:
from statsmodels.base.covtype import get_robustcov_results
if cov_kwds is None:
cov_kwds = {}
use_t = self.use_t
# TODO: we shouldn't need use_t in get_robustcov_results
get_robustcov_results(self, cov_type=cov_type, use_self=True,
use_t=use_t, **cov_kwds)
[docs] def normalized_cov_params(self):
raise NotImplementedError
def _get_robustcov_results(self, cov_type='nonrobust', use_self=True,
use_t=None, **cov_kwds):
from statsmodels.base.covtype import get_robustcov_results
if cov_kwds is None:
cov_kwds = {}
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:
# TODO: we shouldn't need use_t in get_robustcov_results
get_robustcov_results(self, cov_type=cov_type, use_self=True,
use_t=use_t, **cov_kwds)
[docs] @cache_readonly
def llf(self):
return self.model.loglike(self.params)
[docs] @cache_readonly
def bse(self):
# Issue 3299
if ((not hasattr(self, 'cov_params_default')) and
(self.normalized_cov_params is None)):
bse_ = np.empty(len(self.params))
bse_[:] = np.nan
else:
bse_ = np.sqrt(np.diag(self.cov_params()))
return bse_
[docs] @cache_readonly
def tvalues(self):
"""
Return the t-statistic for a given parameter estimate.
"""
return self.params / self.bse
[docs] @cache_readonly
def pvalues(self):
if self.use_t:
df_resid = getattr(self, 'df_resid_inference', self.df_resid)
return stats.t.sf(np.abs(self.tvalues), df_resid) * 2
else:
return stats.norm.sf(np.abs(self.tvalues)) * 2
[docs] def cov_params(self, r_matrix=None, column=None, scale=None, cov_p=None,
other=None):
"""
Returns the variance/covariance matrix.
The variance/covariance matrix can be of a linear contrast
of the estimates of params or all params multiplied by scale which
will usually be an estimate of sigma^2. Scale is assumed to be
a scalar.
Parameters
----------
r_matrix : array-like
Can be 1d, or 2d. Can be used alone or with other.
column : array-like, optional
Must be used on its own. Can be 0d or 1d see below.
scale : float, optional
Can be specified or not. Default is None, which means that
the scale argument is taken from the model.
other : array-like, optional
Can be used when r_matrix is specified.
Returns
-------
cov : ndarray
covariance matrix of the parameter estimates or of linear
combination of parameter estimates. See Notes.
Notes
-----
(The below are assumed to be in matrix notation.)
If no argument is specified returns the covariance matrix of a model
``(scale)*(X.T X)^(-1)``
If contrast is specified it pre and post-multiplies as follows
``(scale) * r_matrix (X.T X)^(-1) r_matrix.T``
If contrast and other are specified returns
``(scale) * r_matrix (X.T X)^(-1) other.T``
If column is specified returns
``(scale) * (X.T X)^(-1)[column,column]`` if column is 0d
OR
``(scale) * (X.T X)^(-1)[column][:,column]`` if column is 1d
"""
if (hasattr(self, 'mle_settings') and
self.mle_settings['optimizer'] in ['l1', 'l1_cvxopt_cp']):
dot_fun = nan_dot
else:
dot_fun = np.dot
if (cov_p is None and self.normalized_cov_params is None and
not hasattr(self, 'cov_params_default')):
raise ValueError('need covariance of parameters for computing '
'(unnormalized) covariances')
if column is not None and (r_matrix is not None or other is not None):
raise ValueError('Column should be specified without other '
'arguments.')
if other is not None and r_matrix is None:
raise ValueError('other can only be specified with r_matrix')
if cov_p is None:
if hasattr(self, 'cov_params_default'):
cov_p = self.cov_params_default
else:
if scale is None:
scale = self.scale
cov_p = self.normalized_cov_params * scale
if column is not None:
column = np.asarray(column)
if column.shape == ():
return cov_p[column, column]
else:
return cov_p[column[:, None], column]
elif r_matrix is not None:
r_matrix = np.asarray(r_matrix)
if r_matrix.shape == ():
raise ValueError("r_matrix should be 1d or 2d")
if other is None:
other = r_matrix
else:
other = np.asarray(other)
tmp = dot_fun(r_matrix, dot_fun(cov_p, np.transpose(other)))
return tmp
else: # if r_matrix is None and column is None:
return cov_p
# TODO: make sure this works as needed for GLMs
[docs] def t_test(self, r_matrix, cov_p=None, scale=None, use_t=None):
"""
Compute a t-test for a each linear hypothesis of the form Rb = q
Parameters
----------
r_matrix : array-like, str, tuple
- array : If an array is given, a p x k 2d array or length k 1d
array specifying the linear restrictions. It is assumed
that the linear combination is equal to zero.
- str : The full hypotheses to test can be given as a string.
See the examples.
- tuple : A tuple of arrays in the form (R, q). If q is given,
can be either a scalar or a length p row vector.
cov_p : array-like, optional
An alternative estimate for the parameter covariance matrix.
If None is given, self.normalized_cov_params is used.
scale : float, optional
An optional `scale` to use. Default is the scale specified
by the model fit.
use_t : bool, optional
If use_t is None, then the default of the model is used.
If use_t is True, then the p-values are based on the t
distribution.
If use_t is False, then the p-values are based on the normal
distribution.
Returns
-------
res : ContrastResults instance
The results for the test are attributes of this results instance.
The available results have the same elements as the parameter table
in `summary()`.
Examples
--------
>>> import numpy as np
>>> import statsmodels.api as sm
>>> data = sm.datasets.longley.load()
>>> data.exog = sm.add_constant(data.exog)
>>> results = sm.OLS(data.endog, data.exog).fit()
>>> r = np.zeros_like(results.params)
>>> r[5:] = [1,-1]
>>> print(r)
[ 0. 0. 0. 0. 0. 1. -1.]
r tests that the coefficients on the 5th and 6th independent
variable are the same.
>>> T_test = results.t_test(r)
>>> print(T_test)
Test for Constraints
==============================================================================
coef std err t P>|t| [0.025 0.975]
------------------------------------------------------------------------------
c0 -1829.2026 455.391 -4.017 0.003 -2859.368 -799.037
==============================================================================
>>> T_test.effect
-1829.2025687192481
>>> T_test.sd
455.39079425193762
>>> T_test.tvalue
-4.0167754636411717
>>> T_test.pvalue
0.0015163772380899498
Alternatively, you can specify the hypothesis tests using a string
>>> from statsmodels.formula.api import ols
>>> dta = sm.datasets.longley.load_pandas().data
>>> formula = 'TOTEMP ~ GNPDEFL + GNP + UNEMP + ARMED + POP + YEAR'
>>> results = ols(formula, dta).fit()
>>> hypotheses = 'GNPDEFL = GNP, UNEMP = 2, YEAR/1829 = 1'
>>> t_test = results.t_test(hypotheses)
>>> print(t_test)
Test for Constraints
==============================================================================
coef std err t P>|t| [0.025 0.975]
------------------------------------------------------------------------------
c0 15.0977 84.937 0.178 0.863 -177.042 207.238
c1 -2.0202 0.488 -8.231 0.000 -3.125 -0.915
c2 1.0001 0.249 0.000 1.000 0.437 1.563
==============================================================================
See Also
---------
tvalues : individual t statistics
f_test : for F tests
patsy.DesignInfo.linear_constraint
"""
from patsy import DesignInfo
names = self.model.data.param_names
LC = DesignInfo(names).linear_constraint(r_matrix)
r_matrix, q_matrix = LC.coefs, LC.constants
num_ttests = r_matrix.shape[0]
num_params = r_matrix.shape[1]
if (cov_p is None and self.normalized_cov_params is None and
not hasattr(self, 'cov_params_default')):
raise ValueError('Need covariance of parameters for computing '
'T statistics')
if num_params != self.params.shape[0]:
raise ValueError('r_matrix and params are not aligned')
if q_matrix is None:
q_matrix = np.zeros(num_ttests)
else:
q_matrix = np.asarray(q_matrix)
q_matrix = q_matrix.squeeze()
if q_matrix.size > 1:
if q_matrix.shape[0] != num_ttests:
raise ValueError("r_matrix and q_matrix must have the same "
"number of rows")
if use_t is None:
# switch to use_t false if undefined
use_t = (hasattr(self, 'use_t') and self.use_t)
_t = _sd = None
_effect = np.dot(r_matrix, self.params)
# nan_dot multiplies with the convention nan * 0 = 0
# Perform the test
if num_ttests > 1:
_sd = np.sqrt(np.diag(self.cov_params(
r_matrix=r_matrix, cov_p=cov_p)))
else:
_sd = np.sqrt(self.cov_params(r_matrix=r_matrix, cov_p=cov_p))
_t = (_effect - q_matrix) * recipr(_sd)
df_resid = getattr(self, 'df_resid_inference', self.df_resid)
if use_t:
return ContrastResults(effect=_effect, t=_t, sd=_sd,
df_denom=df_resid)
else:
return ContrastResults(effect=_effect, statistic=_t, sd=_sd,
df_denom=df_resid,
distribution='norm')
[docs] def f_test(self, r_matrix, cov_p=None, scale=1.0, invcov=None):
"""
Compute the F-test for a joint linear hypothesis.
This is a special case of `wald_test` that always uses the F
distribution.
Parameters
----------
r_matrix : array-like, str, or tuple
- array : An r x k array where r is the number of restrictions to
test and k is the number of regressors. It is assumed
that the linear combination is equal to zero.
- str : The full hypotheses to test can be given as a string.
See the examples.
- tuple : A tuple of arrays in the form (R, q), ``q`` can be
either a scalar or a length k row vector.
cov_p : array-like, optional
An alternative estimate for the parameter covariance matrix.
If None is given, self.normalized_cov_params is used.
scale : float, optional
Default is 1.0 for no scaling.
invcov : array-like, optional
A q x q array to specify an inverse covariance matrix based on a
restrictions matrix.
Returns
-------
res : ContrastResults instance
The results for the test are attributes of this results instance.
Examples
--------
>>> import numpy as np
>>> import statsmodels.api as sm
>>> data = sm.datasets.longley.load()
>>> data.exog = sm.add_constant(data.exog)
>>> results = sm.OLS(data.endog, data.exog).fit()
>>> A = np.identity(len(results.params))
>>> A = A[1:,:]
This tests that each coefficient is jointly statistically
significantly different from zero.
>>> print(results.f_test(A))
<F test: F=array([[ 330.28533923]]), p=4.984030528700946e-10, df_denom=9, df_num=6>
Compare this to
>>> results.fvalue
330.2853392346658
>>> results.f_pvalue
4.98403096572e-10
>>> B = np.array(([0,0,1,-1,0,0,0],[0,0,0,0,0,1,-1]))
This tests that the coefficient on the 2nd and 3rd regressors are
equal and jointly that the coefficient on the 5th and 6th regressors
are equal.
>>> print(results.f_test(B))
<F test: F=array([[ 9.74046187]]), p=0.005605288531708235, df_denom=9, df_num=2>
Alternatively, you can specify the hypothesis tests using a string
>>> from statsmodels.datasets import longley
>>> from statsmodels.formula.api import ols
>>> dta = longley.load_pandas().data
>>> formula = 'TOTEMP ~ GNPDEFL + GNP + UNEMP + ARMED + POP + YEAR'
>>> results = ols(formula, dta).fit()
>>> hypotheses = '(GNPDEFL = GNP), (UNEMP = 2), (YEAR/1829 = 1)'
>>> f_test = results.f_test(hypotheses)
>>> print(f_test)
<F test: F=array([[ 144.17976065]]), p=6.322026217355609e-08, df_denom=9, df_num=3>
See Also
--------
statsmodels.stats.contrast.ContrastResults
wald_test
t_test
patsy.DesignInfo.linear_constraint
Notes
-----
The matrix `r_matrix` is assumed to be non-singular. More precisely,
r_matrix (pX pX.T) r_matrix.T
is assumed invertible. Here, pX is the generalized inverse of the
design matrix of the model. There can be problems in non-OLS models
where the rank of the covariance of the noise is not full.
"""
res = self.wald_test(r_matrix, cov_p=cov_p, scale=scale,
invcov=invcov, use_f=True)
return res
# TODO: untested for GLMs?
[docs] def wald_test(self, r_matrix, cov_p=None, scale=1.0, invcov=None,
use_f=None):
"""
Compute a Wald-test for a joint linear hypothesis.
Parameters
----------
r_matrix : array-like, str, or tuple
- array : An r x k array where r is the number of restrictions to
test and k is the number of regressors. It is assumed that the
linear combination is equal to zero.
- str : The full hypotheses to test can be given as a string.
See the examples.
- tuple : A tuple of arrays in the form (R, q), ``q`` can be
either a scalar or a length p row vector.
cov_p : array-like, optional
An alternative estimate for the parameter covariance matrix.
If None is given, self.normalized_cov_params is used.
scale : float, optional
Default is 1.0 for no scaling.
invcov : array-like, optional
A q x q array to specify an inverse covariance matrix based on a
restrictions matrix.
use_f : bool
If True, then the F-distribution is used. If False, then the
asymptotic distribution, chisquare is used. If use_f is None, then
the F distribution is used if the model specifies that use_t is True.
The test statistic is proportionally adjusted for the distribution
by the number of constraints in the hypothesis.
Returns
-------
res : ContrastResults instance
The results for the test are attributes of this results instance.
See also
--------
statsmodels.stats.contrast.ContrastResults
f_test
t_test
patsy.DesignInfo.linear_constraint
Notes
-----
The matrix `r_matrix` is assumed to be non-singular. More precisely,
r_matrix (pX pX.T) r_matrix.T
is assumed invertible. Here, pX is the generalized inverse of the
design matrix of the model. There can be problems in non-OLS models
where the rank of the covariance of the noise is not full.
"""
if use_f is None:
# switch to use_t false if undefined
use_f = (hasattr(self, 'use_t') and self.use_t)
from patsy import DesignInfo
names = self.model.data.param_names
LC = DesignInfo(names).linear_constraint(r_matrix)
r_matrix, q_matrix = LC.coefs, LC.constants
if (self.normalized_cov_params is None and cov_p is None and
invcov is None and not hasattr(self, 'cov_params_default')):
raise ValueError('need covariance of parameters for computing '
'F statistics')
cparams = np.dot(r_matrix, self.params[:, None])
J = float(r_matrix.shape[0]) # number of restrictions
if q_matrix is None:
q_matrix = np.zeros(J)
else:
q_matrix = np.asarray(q_matrix)
if q_matrix.ndim == 1:
q_matrix = q_matrix[:, None]
if q_matrix.shape[0] != J:
raise ValueError("r_matrix and q_matrix must have the same "
"number of rows")
Rbq = cparams - q_matrix
if invcov is None:
cov_p = self.cov_params(r_matrix=r_matrix, cov_p=cov_p)
if np.isnan(cov_p).max():
raise ValueError("r_matrix performs f_test for using "
"dimensions that are asymptotically "
"non-normal")
invcov = np.linalg.pinv(cov_p)
J_ = np.linalg.matrix_rank(cov_p)
if J_ < J:
import warnings
from statsmodels.tools.sm_exceptions import ValueWarning
warnings.warn('covariance of constraints does not have full '
'rank. The number of constraints is %d, but '
'rank is %d' % (J, J_), ValueWarning)
J = J_
if (hasattr(self, 'mle_settings') and
self.mle_settings['optimizer'] in ['l1', 'l1_cvxopt_cp']):
F = nan_dot(nan_dot(Rbq.T, invcov), Rbq)
else:
F = np.dot(np.dot(Rbq.T, invcov), Rbq)
df_resid = getattr(self, 'df_resid_inference', self.df_resid)
if use_f:
F /= J
return ContrastResults(F=F, df_denom=df_resid,
df_num=J) #invcov.shape[0])
else:
return ContrastResults(chi2=F, df_denom=J, statistic=F,
distribution='chi2', distargs=(J,))
[docs] def wald_test_terms(self, skip_single=False, extra_constraints=None,
combine_terms=None):
"""
Compute a sequence of Wald tests for terms over multiple columns
This computes joined Wald tests for the hypothesis that all
coefficients corresponding to a `term` are zero.
`Terms` are defined by the underlying formula or by string matching.
Parameters
----------
skip_single : boolean
If true, then terms that consist only of a single column and,
therefore, refers only to a single parameter is skipped.
If false, then all terms are included.
extra_constraints : ndarray
not tested yet
combine_terms : None or list of strings
Each string in this list is matched to the name of the terms or
the name of the exogenous variables. All columns whose name
includes that string are combined in one joint test.
Returns
-------
test_result : result instance
The result instance contains `table` which is a pandas DataFrame
with the test results: test statistic, degrees of freedom and
pvalues.
Examples
--------
>>> res_ols = ols("np.log(Days+1) ~ C(Duration, Sum)*C(Weight, Sum)", data).fit()
>>> res_ols.wald_test_terms()
<class 'statsmodels.stats.contrast.WaldTestResults'>
F P>F df constraint df denom
Intercept 279.754525 2.37985521351e-22 1 51
C(Duration, Sum) 5.367071 0.0245738436636 1 51
C(Weight, Sum) 12.432445 3.99943118767e-05 2 51
C(Duration, Sum):C(Weight, Sum) 0.176002 0.83912310946 2 51
>>> res_poi = Poisson.from_formula("Days ~ C(Weight) * C(Duration)", \
data).fit(cov_type='HC0')
>>> wt = res_poi.wald_test_terms(skip_single=False, \
combine_terms=['Duration', 'Weight'])
>>> print(wt)
chi2 P>chi2 df constraint
Intercept 15.695625 7.43960374424e-05 1
C(Weight) 16.132616 0.000313940174705 2
C(Duration) 1.009147 0.315107378931 1
C(Weight):C(Duration) 0.216694 0.897315972824 2
Duration 11.187849 0.010752286833 3
Weight 30.263368 4.32586407145e-06 4
"""
# lazy import
from collections import defaultdict
result = self
if extra_constraints is None:
extra_constraints = []
if combine_terms is None:
combine_terms = []
design_info = getattr(result.model.data, 'design_info', None)
if design_info is None and extra_constraints is None:
raise ValueError('no constraints, nothing to do')
identity = np.eye(len(result.params))
constraints = []
combined = defaultdict(list)
if design_info is not None:
for term in design_info.terms:
cols = design_info.slice(term)
name = term.name()
constraint_matrix = identity[cols]
# check if in combined
for cname in combine_terms:
if cname in name:
combined[cname].append(constraint_matrix)
k_constraint = constraint_matrix.shape[0]
if skip_single:
if k_constraint == 1:
continue
constraints.append((name, constraint_matrix))
combined_constraints = []
for cname in combine_terms:
combined_constraints.append((cname, np.vstack(combined[cname])))
else:
# check by exog/params names if there is no formula info
for col, name in enumerate(result.model.exog_names):
constraint_matrix = identity[col]
# check if in combined
for cname in combine_terms:
if cname in name:
combined[cname].append(constraint_matrix)
if skip_single:
continue
constraints.append((name, constraint_matrix))
combined_constraints = []
for cname in combine_terms:
combined_constraints.append((cname, np.vstack(combined[cname])))
use_t = result.use_t
distribution = ['chi2', 'F'][use_t]
res_wald = []
index = []
for name, constraint in constraints + combined_constraints + extra_constraints:
wt = result.wald_test(constraint)
row = [wt.statistic.item(), wt.pvalue, constraint.shape[0]]
if use_t:
row.append(wt.df_denom)
res_wald.append(row)
index.append(name)
# distribution nerutral names
col_names = ['statistic', 'pvalue', 'df_constraint']
if use_t:
col_names.append('df_denom')
# TODO: maybe move DataFrame creation to results class
from pandas import DataFrame
table = DataFrame(res_wald, index=index, columns=col_names)
res = WaldTestResults(None, distribution, None, table=table)
# TODO: remove temp again, added for testing
res.temp = constraints + combined_constraints + extra_constraints
return res
[docs] def t_test_pairwise(self, term_name, method='hs', alpha=0.05,
factor_labels=None):
"""perform pairwise t_test with multiple testing corrected p-values
This uses the formula design_info encoding contrast matrix and should
work for all encodings of a main effect.
Parameters
----------
result : result instance
The results of an estimated model with a categorical main effect.
term_name : str
name of the term for which pairwise comparisons are computed.
Term names for categorical effects are created by patsy and
correspond to the main part of the exog names.
method : str or list of strings
multiple testing p-value correction, default is 'hs',
see stats.multipletesting
alpha : float
significance level for multiple testing reject decision.
factor_labels : None, list of str
Labels for the factor levels used for pairwise labels. If not
provided, then the labels from the formula design_info are used.
Returns
-------
results : instance of a simple Results class
The results are stored as attributes, the main attributes are the
following two. Other attributes are added for debugging purposes
or as background information.
- result_frame : pandas DataFrame with t_test results and multiple
testing corrected p-values.
- contrasts : matrix of constraints of the null hypothesis in the
t_test.
Notes
-----
Status: experimental. Currently only checked for treatment coding with
and without specified reference level.
Currently there are no multiple testing corrected confidence intervals
available.
Examples
--------
>>> res = ols("np.log(Days+1) ~ C(Weight) + C(Duration)", data).fit()
>>> pw = res.t_test_pairwise("C(Weight)")
>>> pw.result_frame
coef std err t P>|t| Conf. Int. Low
2-1 0.632315 0.230003 2.749157 8.028083e-03 0.171563
3-1 1.302555 0.230003 5.663201 5.331513e-07 0.841803
3-2 0.670240 0.230003 2.914044 5.119126e-03 0.209488
Conf. Int. Upp. pvalue-hs reject-hs
2-1 1.093067 0.010212 True
3-1 1.763307 0.000002 True
3-2 1.130992 0.010212 True
"""
res = t_test_pairwise(self, term_name, method=method, alpha=alpha,
factor_labels=factor_labels)
return res
[docs] def conf_int(self, alpha=.05, cols=None, method='default'):
"""
Returns the confidence interval of the fitted parameters.
Parameters
----------
alpha : float, optional
The significance level for the confidence interval.
ie., The default `alpha` = .05 returns a 95% confidence interval.
cols : array-like, optional
`cols` specifies which confidence intervals to return
method : string
Not Implemented Yet
Method to estimate the confidence_interval.
"Default" : uses self.bse which is based on inverse Hessian for MLE
"hjjh" :
"jac" :
"boot-bse"
"boot_quant"
"profile"
Returns
--------
conf_int : array
Each row contains [lower, upper] limits of the confidence interval
for the corresponding parameter. The first column contains all
lower, the second column contains all upper limits.
Examples
--------
>>> import statsmodels.api as sm
>>> data = sm.datasets.longley.load()
>>> data.exog = sm.add_constant(data.exog)
>>> results = sm.OLS(data.endog, data.exog).fit()
>>> results.conf_int()
array([[-5496529.48322745, -1467987.78596704],
[ -177.02903529, 207.15277984],
[ -0.1115811 , 0.03994274],
[ -3.12506664, -0.91539297],
[ -1.5179487 , -0.54850503],
[ -0.56251721, 0.460309 ],
[ 798.7875153 , 2859.51541392]])
>>> results.conf_int(cols=(2,3))
array([[-0.1115811 , 0.03994274],
[-3.12506664, -0.91539297]])
Notes
-----
The confidence interval is based on the standard normal distribution.
Models wish to use a different distribution should overwrite this
method.
"""
bse = self.bse
if self.use_t:
dist = stats.t
df_resid = getattr(self, 'df_resid_inference', self.df_resid)
q = dist.ppf(1 - alpha / 2, df_resid)
else:
dist = stats.norm
q = dist.ppf(1 - alpha / 2)
if cols is None:
lower = self.params - q * bse
upper = self.params + q * bse
else:
cols = np.asarray(cols)
lower = self.params[cols] - q * bse[cols]
upper = self.params[cols] + q * bse[cols]
return np.asarray(lzip(lower, upper))
[docs] def save(self, fname, remove_data=False):
"""
save a pickle of this instance
Parameters
----------
fname : string or filehandle
fname can be a string to a file path or filename, or a filehandle.
remove_data : bool
If False (default), then the instance is pickled without changes.
If True, then all arrays with length nobs are set to None before
pickling. See the remove_data method.
In some cases not all arrays will be set to None.
Notes
-----
If remove_data is true and the model result does not implement a
remove_data method then this will raise an exception.
"""
from statsmodels.iolib.smpickle import save_pickle
if remove_data:
self.remove_data()
save_pickle(self, fname)
[docs] @classmethod
def load(cls, fname):
"""
load a pickle, (class method)
Parameters
----------
fname : string or filehandle
fname can be a string to a file path or filename, or a filehandle.
Returns
-------
unpickled instance
"""
from statsmodels.iolib.smpickle import load_pickle
return load_pickle(fname)
[docs] def remove_data(self):
"""remove data arrays, all nobs arrays from result and model
This reduces the size of the instance, so it can be pickled with less
memory. Currently tested for use with predict from an unpickled
results and model instance.
.. warning:: Since data and some intermediate results have been removed
calculating new statistics that require them will raise exceptions.
The exception will occur the first time an attribute is accessed
that has been set to None.
Not fully tested for time series models, tsa, and might delete too much
for prediction or not all that would be possible.
The lists of arrays to delete are maintained as attributes of
the result and model instance, except for cached values. These
lists could be changed before calling remove_data.
The attributes to remove are named in:
model._data_attr : arrays attached to both the model instance
and the results instance with the same attribute name.
result.data_in_cache : arrays that may exist as values in
result._cache (TODO : should privatize name)
result._data_attr_model : arrays attached to the model
instance but not to the results instance
"""
def wipe(obj, att):
# get to last element in attribute path
p = att.split('.')
att_ = p.pop(-1)
try:
obj_ = reduce(getattr, [obj] + p)
if hasattr(obj_, att_):
setattr(obj_, att_, None)
except AttributeError:
pass
model_only = ['model.' + i for i in getattr(self, "_data_attr_model", [])]
model_attr = ['model.' + i for i in self.model._data_attr]
for att in self._data_attr + model_attr + model_only:
wipe(self, att)
data_in_cache = getattr(self, 'data_in_cache', [])
data_in_cache += ['fittedvalues', 'resid', 'wresid']
for key in data_in_cache:
try:
self._cache[key] = None
except (AttributeError, KeyError):
pass
class LikelihoodResultsWrapper(wrap.ResultsWrapper):
_attrs = {
'params': 'columns',
'bse': 'columns',
'pvalues': 'columns',
'tvalues': 'columns',
'resid': 'rows',
'fittedvalues': 'rows',
'normalized_cov_params': 'cov',
}
_wrap_attrs = _attrs
_wrap_methods = {
'cov_params': 'cov',
'conf_int': 'columns'
}
wrap.populate_wrapper(LikelihoodResultsWrapper, # noqa:E305
LikelihoodModelResults)
[docs]class ResultMixin(object):
[docs] @cache_readonly
def df_modelwc(self):
# collect different ways of defining the number of parameters, used for
# aic, bic
if hasattr(self, 'df_model'):
if hasattr(self, 'hasconst'):
hasconst = self.hasconst
else:
# default assumption
hasconst = 1
return self.df_model + hasconst
else:
return self.params.size
[docs] @cache_readonly
def aic(self):
return -2 * self.llf + 2 * (self.df_modelwc)
[docs] @cache_readonly
def bic(self):
return -2 * self.llf + np.log(self.nobs) * (self.df_modelwc)
[docs] @cache_readonly
def score_obsv(self):
"""cached Jacobian of log-likelihood
"""
return self.model.score_obs(self.params)
[docs] @cache_readonly
def hessv(self):
"""cached Hessian of log-likelihood
"""
return self.model.hessian(self.params)
[docs] @cache_readonly
def covjac(self):
"""
covariance of parameters based on outer product of jacobian of
log-likelihood
"""
# if not hasattr(self, '_results'):
# raise ValueError('need to call fit first')
# #self.fit()
# self.jacv = jacv = self.jac(self._results.params)
jacv = self.score_obsv
return np.linalg.inv(np.dot(jacv.T, jacv))
[docs] @cache_readonly
def covjhj(self):
"""covariance of parameters based on HJJH
dot product of Hessian, Jacobian, Jacobian, Hessian of likelihood
name should be covhjh
"""
jacv = self.score_obsv
hessv = self.hessv
hessinv = np.linalg.inv(hessv)
# self.hessinv = hessin = self.cov_params()
return np.dot(hessinv, np.dot(np.dot(jacv.T, jacv), hessinv))
[docs] @cache_readonly
def bsejhj(self):
"""standard deviation of parameter estimates based on covHJH
"""
return np.sqrt(np.diag(self.covjhj))
[docs] @cache_readonly
def bsejac(self):
"""standard deviation of parameter estimates based on covjac
"""
return np.sqrt(np.diag(self.covjac))
[docs] def bootstrap(self, nrep=100, method='nm', disp=0, store=1):
"""simple bootstrap to get mean and variance of estimator
see notes
Parameters
----------
nrep : int
number of bootstrap replications
method : str
optimization method to use
disp : bool
If true, then optimization prints results
store : bool
If true, then parameter estimates for all bootstrap iterations
are attached in self.bootstrap_results
Returns
-------
mean : array
mean of parameter estimates over bootstrap replications
std : array
standard deviation of parameter estimates over bootstrap
replications
Notes
-----
This was mainly written to compare estimators of the standard errors of
the parameter estimates. It uses independent random sampling from the
original endog and exog, and therefore is only correct if observations
are independently distributed.
This will be moved to apply only to models with independently
distributed observations.
"""
results = []
print(self.model.__class__)
hascloneattr = True if hasattr(self, 'cloneattr') else False
for i in range(nrep):
rvsind = np.random.randint(self.nobs, size=self.nobs)
# this needs to set startparam and get other defining attributes
# need a clone method on model
fitmod = self.model.__class__(self.endog[rvsind],
self.exog[rvsind, :])
if hascloneattr:
for attr in self.model.cloneattr:
setattr(fitmod, attr, getattr(self.model, attr))
fitres = fitmod.fit(method=method, disp=disp)
results.append(fitres.params)
results = np.array(results)
if store:
self.bootstrap_results = results
return results.mean(0), results.std(0), results
[docs] def get_nlfun(self, fun):
# I think this is supposed to get the delta method that is currently
# in miscmodels count (as part of Poisson example)
pass
[docs]class GenericLikelihoodModelResults(LikelihoodModelResults, ResultMixin):
"""
A results class for the discrete dependent variable models.
..Warning :
The following description has not been updated to this version/class.
Where are AIC, BIC, ....? docstring looks like copy from discretemod
Parameters
----------
model : A DiscreteModel instance
mlefit : instance of LikelihoodResults
This contains the numerical optimization results as returned by
LikelihoodModel.fit(), in a superclass of GnericLikelihoodModels
Returns
-------
*Attributes*
Warning most of these are not available yet
aic : float
Akaike information criterion. -2*(`llf` - p) where p is the number
of regressors including the intercept.
bic : float
Bayesian information criterion. -2*`llf` + ln(`nobs`)*p where p is the
number of regressors including the intercept.
bse : array
The standard errors of the coefficients.
df_resid : float
See model definition.
df_model : float
See model definition.
fitted_values : array
Linear predictor XB.
llf : float
Value of the loglikelihood
llnull : float
Value of the constant-only loglikelihood
llr : float
Likelihood ratio chi-squared statistic; -2*(`llnull` - `llf`)
llr_pvalue : float
The chi-squared probability of getting a log-likelihood ratio
statistic greater than llr. llr has a chi-squared distribution
with degrees of freedom `df_model`.
prsquared : float
McFadden's pseudo-R-squared. 1 - (`llf`/`llnull`)
"""
def __init__(self, model, mlefit):
self.model = model
self.endog = model.endog
self.exog = model.exog
self.nobs = model.endog.shape[0]
# TODO: possibly move to model.fit()
# and outsource together with patching names
if hasattr(model, 'df_model'):
self.df_model = model.df_model
else:
self.df_model = len(mlefit.params)
# retrofitting the model, used in t_test TODO: check design
self.model.df_model = self.df_model
if hasattr(model, 'df_resid'):
self.df_resid = model.df_resid
else:
self.df_resid = self.endog.shape[0] - self.df_model
# retrofitting the model, used in t_test TODO: check design
self.model.df_resid = self.df_resid
self._cache = resettable_cache()
self.__dict__.update(mlefit.__dict__)
[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),
('Method:', ['Maximum Likelihood']),
('Date:', None),
('Time:', None),
('No. Observations:', None),
('Df Residuals:', None), # [self.df_resid]),
('Df Model:', None), # [self.df_model])
]
top_right = [ # ('R-squared:', ["%#8.3f" % self.rsquared]),
# ('Adj. R-squared:', ["%#8.3f" % self.rsquared_adj]),
# ('F-statistic:', ["%#8.4g" % self.fvalue] ),
# ('Prob (F-statistic):', ["%#6.3g" % self.f_pvalue]),
('Log-Likelihood:', None), # ["%#6.4g" % self.llf]),
('AIC:', ["%#8.4g" % self.aic]),
('BIC:', ["%#8.4g" % self.bic])
]
if title is None:
title = self.model.__class__.__name__ + ' ' + "Results"
# create summary table instance
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=False)
return smry
