Source code for statsmodels.base.model

from statsmodels.compat.python import lzip

from functools import reduce
import warnings

import numpy as np
from scipy import stats

from statsmodels.base.data import handle_data
from statsmodels.base.optimizer import Optimizer
import statsmodels.base.wrapper as wrap
from statsmodels.formula import handle_formula_data
from statsmodels.stats.contrast import (
    ContrastResults,
    WaldTestResults,
    t_test_pairwise,
)
from statsmodels.tools.data import _is_using_pandas
from statsmodels.tools.decorators import (
    cache_readonly,
    cached_data,
    cached_value,
)
from statsmodels.tools.numdiff import approx_fprime
from statsmodels.tools.sm_exceptions import (
    HessianInversionWarning,
    ValueWarning,
)
from statsmodels.tools.tools import nan_dot, recipr
from statsmodels.tools.validation import bool_like

_model_params_doc = """Parameters
    ----------
    endog : array_like
        A 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.
    **kwargs
        Extra arguments that are used to set model properties when using the
        formula interface."""


[docs]class Model(object): __doc__ = """ A (predictive) statistical model. Intended to be subclassed not used. %(params_doc)s %(extra_params_doc)s Attributes ---------- exog_names endog_names 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} # Maximum number of endogenous variables when using a formula # Default is 1, which is more common. Override in models when needed # Set to None to skip check _formula_max_endog = 1 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: # will not 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 do not 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 do not 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
[docs] @classmethod def from_formula(cls, formula, data, subset=None, drop_cols=None, *args, **kwargs): """ Create a Model from a formula and dataframe. Parameters ---------- formula : str or generic Formula object The formula specifying the model. data : array_like The data for the model. See Notes. subset : array_like An array-like object of booleans, integers, or index values that indicate the subset of df to use in the model. Assumes df is a `pandas.DataFrame`. drop_cols : array_like Columns to drop from the design matrix. Cannot be used to drop terms involving categoricals. *args Additional positional argument that are passed to the model. **kwargs These are passed to the model with one exception. The ``eval_env`` keyword is passed to patsy. It can be either a :class:`patsy:patsy.EvalEnvironment` object or an integer indicating the depth of the namespace to use. For example, the default ``eval_env=0`` uses the calling namespace. If you wish to use a "clean" environment set ``eval_env=-1``. Returns ------- model The model instance. Notes ----- data must define __getitem__ with the keys in the formula terms args and kwargs are passed on to the model instantiation. E.g., a numpy structured or rec array, a dictionary, or a pandas DataFrame. """ # TODO: provide a docs template for args/kwargs from child models # TODO: subset could use syntax. issue #469. if subset is not None: data = data.loc[subset] eval_env = kwargs.pop('eval_env', None) if eval_env is None: eval_env = 2 elif eval_env == -1: from patsy import EvalEnvironment eval_env = EvalEnvironment({}) elif isinstance(eval_env, int): eval_env += 1 # we're going down the stack again missing = kwargs.get('missing', 'drop') if missing == 'none': # with patsy it's drop or raise. let's raise. missing = 'raise' tmp = handle_formula_data(data, None, formula, depth=eval_env, missing=missing) ((endog, exog), missing_idx, design_info) = tmp max_endog = cls._formula_max_endog if (max_endog is not None and endog.ndim > 1 and endog.shape[1] > max_endog): raise ValueError('endog has evaluated to an array with multiple ' 'columns that has shape {0}. This occurs when ' 'the variable converted to endog is non-numeric' ' (e.g., bool or str).'.format(endog.shape)) if drop_cols is not None and len(drop_cols) > 0: cols = [x for x in exog.columns if x not in drop_cols] if len(cols) < len(exog.columns): exog = exog[cols] cols = list(design_info.term_names) for col in drop_cols: try: cols.remove(col) except ValueError: pass # OK if not present design_info = design_info.subset(cols) kwargs.update({'missing_idx': missing_idx, 'missing': missing, 'formula': formula, # attach formula for unpckling 'design_info': design_info}) mod = cls(endog, exog, *args, **kwargs) mod.formula = formula # since we got a dataframe, attach the original mod.data.frame = data return mod
@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().__init__(endog, exog, **kwargs) self.initialize()
[docs] def initialize(self): """ Initialize (possibly re-initialize) a Model instance. For example, if the the design matrix of a linear model changes then initialized can be used to recompute values using the modified design matrix. """ 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. Parameters ---------- params : ndarray The model parameters used to compute the log-likelihood. Notes ----- Must be overridden by subclasses. """ raise NotImplementedError
[docs] def score(self, params): """ Score vector of model. The gradient of logL with respect to each parameter. Parameters ---------- params : ndarray The parameters to use when evaluating the Hessian. Returns ------- ndarray The score vector evaluated at the parameters. """ raise NotImplementedError
[docs] def information(self, params): """ Fisher information matrix of model. Returns -1 * Hessian of the log-likelihood evaluated at params. Parameters ---------- params : ndarray The model parameters. """ raise NotImplementedError
[docs] def hessian(self, params): """ The Hessian matrix of the model. Parameters ---------- params : ndarray The parameters to use when evaluating the Hessian. Returns ------- ndarray The hessian evaluated at the parameters. """ 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 : int The number of basin hopping iterations. niter_success : int 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 : int 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 does not 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) # Remove covariance args before calling fir to allow strict checking if 'cov_type' in kwargs: cov_kwds = kwargs.get('cov_kwds', {}) kwds = {'cov_type': kwargs['cov_type'], 'cov_kwds': cov_kwds} if cov_kwds: del kwargs["cov_kwds"] del kwargs["cov_type"] else: kwds = {} if 'use_t' in kwargs: kwds['use_t'] = kwargs['use_t'] del kwargs["use_t"] 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) # Restore cov_type, cov_kwds and use_t optim_settings.update(kwds) # 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: warnings.warn('Inverting hessian failed, no bse or cov_params ' 'available', HessianInversionWarning) Hinv = None # TODO: add Hessian approximation and change the above if needed mlefit = LikelihoodModelResults(self, xopt, Hinv, scale=1., **kwds) # TODO: hardcode scale? mlefit.mle_retvals = retvals if isinstance(retvals, dict): if warn_convergence and not retvals['converged']: from statsmodels.tools.sm_exceptions import ConvergenceWarning warnings.warn("Maximum Likelihood optimization failed to " "converge. Check mle_retvals", ConvergenceWarning) mlefit.mle_settings = optim_settings return mlefit
def _fit_zeros(self, keep_index=None, start_params=None, return_auxiliary=False, k_params=None, **fit_kwds): """experimental, fit the model subject to zero constraints Intended for internal use cases until we know what we need. API will need to change to handle models with two exog. This is not yet supported by all model subclasses. This is essentially a simplified version of `fit_constrained`, and does not need to use `offset`. The estimation creates a new model with transformed design matrix, exog, and converts the results back to the original parameterization. Some subclasses could use a more efficient calculation than using a new model. Parameters ---------- keep_index : array_like (int or bool) or slice variables that should be dropped. 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. k_params : int or None If None, then we try to infer from start_params or model. **fit_kwds : keyword arguments fit_kwds are used in the optimization of the transformed model. Returns ------- results : Results instance """ # we need to append index of extra params to keep_index as in # NegativeBinomial if hasattr(self, 'k_extra') and self.k_extra > 0: # we cannot change the original, TODO: should we add keep_index_params? keep_index = np.array(keep_index, copy=True) k = self.exog.shape[1] extra_index = np.arange(k, k + self.k_extra) keep_index_p = np.concatenate((keep_index, extra_index)) else: keep_index_p = keep_index # not all models support start_params, drop if None, hide them in fit_kwds if start_params is not None: fit_kwds['start_params'] = start_params[keep_index_p] k_params = len(start_params) # ignore k_params in this case, or verify consisteny? # build auxiliary model and fit init_kwds = self._get_init_kwds() mod_constr = self.__class__(self.endog, self.exog[:, keep_index], **init_kwds) res_constr = mod_constr.fit(**fit_kwds) # switch name, only need keep_index for params below keep_index = keep_index_p if k_params is None: k_params = self.exog.shape[1] k_params += getattr(self, 'k_extra', 0) params_full = np.zeros(k_params) params_full[keep_index] = res_constr.params # create dummy results Instance, TODO: wire up properly # TODO: this could be moved into separate private method if needed # discrete L1 fit_regularized doens't reestimate AFAICS # RLM does not have method, disp nor warn_convergence keywords # OLS, WLS swallows extra kwds with **kwargs, but does not have method='nm' try: # Note: addding full_output=False causes exceptions res = self.fit(maxiter=0, disp=0, method='nm', skip_hessian=True, warn_convergence=False, start_params=params_full) # we get a wrapper back except (TypeError, ValueError): res = self.fit() # Warning: make sure we are not just changing the wrapper instead of # results #2400 # TODO: do we need to change res._results.scale in some models? if hasattr(res_constr.model, 'scale'): # Note: res.model is self # GLM problem, see #2399, # TODO: remove from model if not needed anymore res.model.scale = res._results.scale = res_constr.model.scale if hasattr(res_constr, 'mle_retvals'): res._results.mle_retvals = res_constr.mle_retvals # not available for not scipy optimization, e.g. glm irls # TODO: what retvals should be required? # res.mle_retvals['fcall'] = res_constr.mle_retvals.get('fcall', np.nan) # res.mle_retvals['iterations'] = res_constr.mle_retvals.get( # 'iterations', np.nan) # res.mle_retvals['converged'] = res_constr.mle_retvals['converged'] # overwrite all mle_settings if hasattr(res_constr, 'mle_settings'): res._results.mle_settings = res_constr.mle_settings res._results.params = params_full if (not hasattr(res._results, 'normalized_cov_params') or res._results.normalized_cov_params is None): res._results.normalized_cov_params = np.zeros((k_params, k_params)) else: res._results.normalized_cov_params[...] = 0 # fancy indexing requires integer array keep_index = np.array(keep_index) res._results.normalized_cov_params[keep_index[:, None], keep_index] = \ res_constr.normalized_cov_params k_constr = res_constr.df_resid - res._results.df_resid if hasattr(res_constr, 'cov_params_default'): res._results.cov_params_default = np.zeros((k_params, k_params)) res._results.cov_params_default[keep_index[:, None], keep_index] = \ res_constr.cov_params_default if hasattr(res_constr, 'cov_type'): res._results.cov_type = res_constr.cov_type res._results.cov_kwds = res_constr.cov_kwds res._results.keep_index = keep_index res._results.df_resid = res_constr.df_resid res._results.df_model = res_constr.df_model res._results.k_constr = k_constr res._results.results_constrained = res_constr # special temporary workaround for RLM # need to be able to override robust covariances if hasattr(res.model, 'M'): del res._results._cache['resid'] del res._results._cache['fittedvalues'] del res._results._cache['sresid'] cov = res._results._cache['bcov_scaled'] # inplace adjustment cov[...] = 0 cov[keep_index[:, None], keep_index] = res_constr.bcov_scaled res._results.cov_params_default = cov return res def _fit_collinear(self, atol=1e-14, rtol=1e-13, **kwds): """experimental, fit of the model without collinear variables This currently uses QR to drop variables based on the given sequence. Options will be added in future, when the supporting functions to identify collinear variables become available. """ # ------ copied from PR #2380 remove when merged x = self.exog tol = atol + rtol * x.var(0) r = np.linalg.qr(x, mode='r') mask = np.abs(r.diagonal()) < np.sqrt(tol) # TODO add to results instance # idx_collinear = np.where(mask)[0] idx_keep = np.where(~mask)[0] return self._fit_zeros(keep_index=idx_keep, **kwds)
# 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 calculated 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 hasconst = kwds.pop("hasconst", None) 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, hasconst=hasconst, **kwds ) # this will not 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): """ Initialize (possibly re-initialize) a Model instance. For instance, the design matrix of a linear model may change and some things must be recomputed. """ if not self.score: # right now score is not optional self.score = lambda x: approx_fprime(x, self.loglike) 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.linalg.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 : ndarray reduced parameter array Returns ------- paramsfull : ndarray 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): """Reduce parameters""" return params[self.fixed_paramsmask]
[docs] def loglike(self, params): """Log-likelihood of model at params""" return self.loglikeobs(params).sum(0)
[docs] def nloglike(self, params): """Negative log-likelihood of model at params""" return -self.loglikeobs(params).sum(0)
[docs] def loglikeobs(self, params): """Log-likelihood of individual observations at 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): 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) results_class = getattr(self, 'results_class', GenericLikelihoodModelResults) genericmlefit = results_class(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 do not want to raise after we have already fit() warnings.warn('more exog_names than parameters', ValueWarning) return genericmlefit
[docs]class Results(object): """ Class to contain model results Parameters ---------- model : class instance the previously specified model instance params : ndarray parameter estimates from the fit model """ def __init__(self, model, params, **kwd): self.__dict__.update(kwd) self.initialize(model, params, **kwd) self._data_attr = [] # Variables to clear from cache self._data_in_cache = ['fittedvalues', 'resid', 'wresid']
[docs] def initialize(self, model, params, **kwargs): """ Initialize (possibly re-initialize) a Results instance. Parameters ---------- model : Model The model instance. params : ndarray The model parameters. **kwargs Any additional keyword arguments required to initialize the model. """ 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 Additional arguments to pass to the model, see the predict method of the model for the details. **kwargs Additional keywords arguments to pass to the model, see the predict method of the model for the details. Returns ------- array_like 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 that contains numpy arrays. 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 = None if is_pandas: if exog.ndim == 2 or self.params.size == 1: exog_index = exog.index else: exog_index = [exog.index.name] if transform and hasattr(self.model, 'formula') and (exog is not None): # allow both location of design_info, see #7043 design_info = (getattr(self.model, "design_info", None) or 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) try: exog = dmatrix(design_info, exog, return_type="dataframe") except Exception as exc: msg = ('predict requires that you use a DataFrame when ' 'predicting from a model\nthat was created using the ' 'formula api.' '\n\nThe original error message returned by patsy is:\n' '{0}'.format(str(str(exc)))) raise exc.__class__(msg) if orig_exog_len > len(exog) and not is_dict: 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): """ Summary Not implemented """ raise NotImplementedError
# 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) 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 : ndarray 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 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 self._use_t = False # 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'] self.use_t = use_t if use_t is not None else False 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 should not 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): """See specific model class docstring""" raise NotImplementedError
def _get_robustcov_results(self, cov_type='nonrobust', use_self=True, use_t=None, **cov_kwds): if use_self is False: raise ValueError("use_self should have been removed long ago. " "See GH#4401") 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 should not need use_t in get_robustcov_results get_robustcov_results(self, cov_type=cov_type, use_self=True, use_t=use_t, **cov_kwds) @property def use_t(self): """Flag indicating to use the Student's distribution in inference.""" return self._use_t @use_t.setter def use_t(self, value): self._use_t = bool(value) @cached_value def llf(self): """Log-likelihood of model""" return self.model.loglike(self.params) @cached_value def bse(self): """The standard errors of the parameter estimates.""" # 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: with warnings.catch_warnings(): warnings.simplefilter("ignore", RuntimeWarning) bse_ = np.sqrt(np.diag(self.cov_params())) return bse_ @cached_value def tvalues(self): """ Return the t-statistic for a given parameter estimate. """ with warnings.catch_warnings(): warnings.simplefilter("ignore", RuntimeWarning) return self.params / self.bse @cached_value def pvalues(self): """The two-tailed p values for the t-stats of the params.""" with warnings.catch_warnings(): warnings.simplefilter("ignore", RuntimeWarning) 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): """ Compute the variance/covariance matrix. The variance/covariance matrix can be of a linear contrast of the estimated parameters 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. cov_p : ndarray, optional The covariance of the parameters. If not provided, this value is read from `self.normalized_cov_params` or `self.cov_params_default`. other : array_like, optional Can be used when r_matrix is specified. Returns ------- ndarray The 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, use_t=None): """ Compute a t-test for a each linear hypothesis of the form Rb = q. Parameters ---------- r_matrix : {array_like, str, tuple} One of: - 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. 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 ------- ContrastResults The results for the test are attributes of this results instance. The available results have the same elements as the parameter table in `summary()`. See Also -------- tvalues : Individual t statistics for the estimated parameters. f_test : Perform an F tests on model parameters. patsy.DesignInfo.linear_constraint : Specify a linear constraint. 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 ============================================================================== """ from patsy import DesignInfo use_t = bool_like(use_t, "use_t", strict=True, optional=True) names = self.model.data.cov_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') params = self.params.ravel() if num_params != 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) _effect = np.dot(r_matrix, params) # 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, 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, tuple} One of: - 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. invcov : array_like, optional A q x q array to specify an inverse covariance matrix based on a restrictions matrix. Returns ------- ContrastResults The results for the test are attributes of this results instance. See Also -------- t_test : Perform a single hypothesis test. wald_test : Perform a Wald-test using a quadratic form. statsmodels.stats.contrast.ContrastResults : Test results. patsy.DesignInfo.linear_constraint : Specify a 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. 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> """ res = self.wald_test(r_matrix, cov_p=cov_p, invcov=invcov, use_f=True) return res
# TODO: untested for GLMs?
[docs] def wald_test(self, r_matrix, cov_p=None, invcov=None, use_f=None, df_constraints=None): """ Compute a Wald-test for a joint linear hypothesis. Parameters ---------- r_matrix : {array_like, str, tuple} One of: - 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. 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. df_constraints : int, optional The number of constraints. If not provided the number of constraints is determined from r_matrix. Returns ------- ContrastResults The results for the test are attributes of this results instance. See Also -------- f_test : Perform an F tests on model parameters. t_test : Perform a single hypothesis test. statsmodels.stats.contrast.ContrastResults : Test results. patsy.DesignInfo.linear_constraint : Specify a 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. """ use_f = bool_like(use_f, "use_f", strict=True, optional=True) 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.cov_names params = self.params.ravel() 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, 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: 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_ # TODO streamline computation, we do not need to compute J if given if df_constraints is not None: # let caller override J by df_constraint J = df_constraints 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 : bool 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 Additional constraints to test. Note that this input has not been tested. combine_terms : {list[str], None} 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 ------- WaldTestResults 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 = np.atleast_2d(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.item(), 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 ---------- term_name : str The 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, list[str]} The multiple testing p-value correction to apply. The default is 'hs'. See stats.multipletesting. alpha : float The significance level for multiple testing reject decision. factor_labels : {list[str], None} Labels for the factor levels used for pairwise labels. If not provided, then the labels from the formula design_info are used. Returns ------- MultiCompResult 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): """ Construct confidence interval for the fitted parameters. Parameters ---------- alpha : float, optional The significance level for the confidence interval. The default `alpha` = .05 returns a 95% confidence interval. cols : array_like, optional Specifies which confidence intervals to return. Returns ------- array_like 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. Notes ----- The confidence interval is based on the standard normal distribution if self.use_t is False. If self.use_t is True, then uses a Student's t with self.df_resid_inference (or self.df_resid if df_resid_inference is not defined) degrees of freedom. 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]]) """ 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) params = self.params lower = params - q * bse upper = params + q * bse if cols is not None: cols = np.asarray(cols) lower = lower[cols] upper = upper[cols] return np.asarray(lzip(lower, upper))
[docs] def save(self, fname, remove_data=False): """ Save a pickle of this instance. Parameters ---------- fname : {str, handle} A string filename or a file handle. 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 pickled results instance .. warning:: Loading pickled models is not secure against erroneous or maliciously constructed data. Never unpickle data received from an untrusted or unauthenticated source. Parameters ---------- fname : {str, handle, pathlib.Path} A string filename or a file handle. Returns ------- Results The unpickled results 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 result._data_attr_model : arrays attached to the model instance but not to the results instance """ cls = self.__class__ # Note: we cannot just use `getattr(cls, x)` or `getattr(self, x)` # because of redirection involved with property-like accessors cls_attrs = {} for name in dir(cls): try: attr = object.__getattribute__(cls, name) except AttributeError: pass else: cls_attrs[name] = attr data_attrs = [x for x in cls_attrs if isinstance(cls_attrs[x], cached_data)] for name in data_attrs: self._cache[name] = None 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: if att in data_attrs: # these have been handled above, and trying to call wipe # would raise an Exception anyway, so skip these continue wipe(self, att) for key in self._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): @cache_readonly def df_modelwc(self): """Model WC""" # collect different ways of defining the number of parameters, used for # aic, bic if hasattr(self, 'df_model'): if hasattr(self, 'k_constant'): hasconst = self.k_constant elif hasattr(self, 'hasconst'): hasconst = self.hasconst else: # default assumption hasconst = 1 return self.df_model + hasconst else: return self.params.size @cache_readonly def aic(self): """Akaike information criterion""" return -2 * self.llf + 2 * (self.df_modelwc) @cache_readonly def bic(self): """Bayesian information criterion""" return -2 * self.llf + np.log(self.nobs) * (self.df_modelwc) @cache_readonly def score_obsv(self): """cached Jacobian of log-likelihood """ return self.model.score_obs(self.params) @cache_readonly def hessv(self): """cached Hessian of log-likelihood """ return self.model.hessian(self.params) @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)) @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)) @cache_readonly def bsejhj(self): """standard deviation of parameter estimates based on covHJH """ return np.sqrt(np.diag(self.covjhj)) @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 : ndarray mean of parameter estimates over bootstrap replications std : ndarray 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 = [] hascloneattr = True if hasattr(self.model, '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 if self.exog is not None: exog_resamp = self.exog[rvsind, :] else: exog_resamp = None # build auxiliary model and fit init_kwds = self.model._get_init_kwds() fitmod = self.model.__class__(self.endog[rvsind], exog=exog_resamp, **init_kwds) 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): """ get_nlfun This is not Implemented """ # I think this is supposed to get the delta method that is currently # in miscmodels count (as part of Poisson example) raise NotImplementedError
class _LLRMixin(): """Mixin class for Null model and likelihood ratio """ # methods copied from DiscreteResults, adjusted pseudo R2 def pseudo_rsquared(self, kind="mcf"): """ McFadden's pseudo-R-squared. `1 - (llf / llnull)` """ kind = kind.lower() if kind.startswith("mcf"): prsq = 1 - self.llf / self.llnull elif kind.startswith("cox") or kind in ["cs", "lr"]: prsq = 1 - np.exp((self.llnull - self.llf) * (2 / self.nobs)) else: raise ValueError("only McFadden and Cox-Snell are available") return prsq @cache_readonly def llr(self): """ Likelihood ratio chi-squared statistic; `-2*(llnull - llf)` """ return -2*(self.llnull - self.llf) @cache_readonly def llr_pvalue(self): """ 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`. """ # see also RegressionModel compare_lr_test llr = self.llr df_full = self.df_resid df_restr = self.df_resid_null lrdf = (df_restr - df_full) self.df_lr_null = lrdf return stats.distributions.chi2.sf(llr, lrdf) def set_null_options(self, llnull=None, attach_results=True, **kwargs): """ Set the fit options for the Null (constant-only) model. This resets the cache for related attributes which is potentially fragile. This only sets the option, the null model is estimated when llnull is accessed, if llnull is not yet in cache. Parameters ---------- llnull : {None, float} If llnull is not None, then the value will be directly assigned to the cached attribute "llnull". attach_results : bool Sets an internal flag whether the results instance of the null model should be attached. By default without calling this method, thenull model results are not attached and only the loglikelihood value llnull is stored. **kwargs Additional keyword arguments used as fit keyword arguments for the null model. The override and model default values. Notes ----- Modifies attributes of this instance, and so has no return. """ # reset cache, note we need to add here anything that depends on # llnullor the null model. If something is missing, then the attribute # might be incorrect. self._cache.pop('llnull', None) self._cache.pop('llr', None) self._cache.pop('llr_pvalue', None) self._cache.pop('prsquared', None) if hasattr(self, 'res_null'): del self.res_null if llnull is not None: self._cache['llnull'] = llnull self._attach_nullmodel = attach_results self._optim_kwds_null = kwargs @cache_readonly def llnull(self): """ Value of the constant-only loglikelihood """ model = self.model kwds = model._get_init_kwds().copy() for key in getattr(model, '_null_drop_keys', []): del kwds[key] # TODO: what parameters to pass to fit? mod_null = model.__class__(model.endog, np.ones(self.nobs), **kwds) # TODO: consider catching and warning on convergence failure? # in the meantime, try hard to converge. see # TestPoissonConstrained1a.test_smoke optim_kwds = getattr(self, '_optim_kwds_null', {}).copy() if 'start_params' in optim_kwds: # user provided sp_null = optim_kwds.pop('start_params') elif hasattr(model, '_get_start_params_null'): # get moment estimates if available sp_null = model._get_start_params_null() else: sp_null = None opt_kwds = dict(method='bfgs', warn_convergence=False, maxiter=10000, disp=0) opt_kwds.update(optim_kwds) if optim_kwds: res_null = mod_null.fit(start_params=sp_null, **opt_kwds) else: # this should be a reasonably method case across versions res_null = mod_null.fit(start_params=sp_null, method='nm', warn_convergence=False, maxiter=10000, disp=0) res_null = mod_null.fit(start_params=res_null.params, method='bfgs', warn_convergence=False, maxiter=10000, disp=0) if getattr(self, '_attach_nullmodel', False) is not False: self.res_null = res_null self.k_null = len(res_null.params) self.df_resid_null = res_null.df_resid return res_null.llf
[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 Attributes ---------- 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 : ndarray The standard errors of the coefficients. df_resid : float See model definition. df_model : float See model definition. fitted_values : ndarray 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 = {} self.__dict__.update(mlefit.__dict__) k_params = len(mlefit.params) # checks mainly for adding new models or subclassing if self.df_model + self.model.k_constant != k_params: warnings.warn("df_model + k_constant differs from nparams") if self.df_resid != self.nobs - k_params: warnings.warn("df_resid differs from nobs - nparams")
[docs] def summary(self, yname=None, xname=None, title=None, alpha=.05): """Summarize the Regression Results Parameters ---------- yname : str, optional Default is `y` xname : list[str], optional Names for the exogenous variables, default is "var_xx". Must match the number of parameters in the model title : str, 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), ('Df Model:', None), ] top_right = [('Log-Likelihood:', None), ('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=self.use_t) return smry