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Source code for statsmodels.base.model

import numpy as np
from scipy import optimize, stats
from statsmodels.base.data import handle_data
from statsmodels.tools.tools import recipr, nan_dot
from statsmodels.stats.contrast import ContrastResults
from statsmodels.tools.decorators import (resettable_cache,
                                                  cache_readonly)
import statsmodels.base.wrapper as wrap
from statsmodels.tools.numdiff import approx_fprime
from statsmodels.formula import handle_formula_data


_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 interecept is not included by default
        and should be added by the user. See `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 = handle_data(endog, exog, missing, hasconst, **kwargs) self.k_constant = self.data.k_constant self.exog = self.data.exog self.endog = self.data.endog # kwargs arrays could have changed, easier to just attach here for key in kwargs: # pop so we don't start keeping all these twice or references setattr(self, key, self.data.__dict__.pop(key)) self._data_attr = [] self._data_attr.extend(['exog', 'endog', 'data.exog', 'data.endog', 'data.orig_endog', 'data.orig_exog']) @classmethod
[docs] def from_formula(cls, formula, data, subset=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` args : extra arguments These are passed to the model kwargs : extra keyword arguments These are passed to the model. Returns ------- model : 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.ix[subset] endog, exog = handle_formula_data(data, None, formula) 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): return self.data.ynames @property def exog_names(self): 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 information(self, params): """ Fisher information matrix of model Returns -Hessian of loglike evaluated at params. """ 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, **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 {'newton','nm','bfgs','powell','cg','ncg','basinhopping'} Method can be 'newton' for Newton-Raphson, 'nm' for Nelder-Mead, 'bfgs' for Broyden-Fletcher-Goldfarb-Shanno, 'powell' for modified Powell's method, 'cg' for conjugate gradient, 'ncg' for Newton- conjugate gradient or 'basinhopping' for global basin-hopping solver, if available. `method` determines which solver from scipy.optimize is used. 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 The maximum number of iterations to perform. full_output : bool 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 Set to True to print convergence messages. fargs : tuple Extra arguments passed to the likelihood function, i.e., loglike(x,*args) callback : callable callback(xk) Called after each iteration, as callback(xk), where xk is the current parameter vector. retall : bool Set to True to return list of solutions at each iteration. Available in Results object's mle_retvals attribute. Notes ----- The 'basinhopping' solver ignores `maxiter`, `retall`, `full_output` explicit arguments. Optional arguments for the solvers (available in 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. '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` """ # Extract kwargs specific to fit_regularized calling fit extra_fit_funcs = kwargs.setdefault('extra_fit_funcs', dict()) cov_params_func = kwargs.setdefault('cov_params_func', None) Hinv = None # JP error if full_output=0, Hinv not defined methods = ['newton', 'nm', 'bfgs', 'powell', 'cg', 'ncg', 'basinhopping'] methods += extra_fit_funcs.keys() 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") if method.lower() not in methods: message = "Unknown fit method %s" % method raise ValueError(message) method = method.lower() # 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 score = lambda params: -self.score(params) / nobs try: hess = lambda params: -self.hessian(params) / nobs except: hess = None fit_funcs = { 'newton': _fit_mle_newton, 'nm': _fit_mle_nm, # Nelder-Mead 'bfgs': _fit_mle_bfgs, 'cg': _fit_mle_cg, 'ncg': _fit_mle_ncg, 'powell': _fit_mle_powell, 'basinhopping': _fit_mle_basinhopping, } if extra_fit_funcs: fit_funcs.update(extra_fit_funcs) if method == 'newton': score = lambda params: self.score(params) / nobs hess = lambda params: self.hessian(params) / nobs #TODO: why are score and hess positive? func = fit_funcs[method] xopt, retvals = func(f, score, start_params, fargs, kwargs, disp=disp, maxiter=maxiter, callback=callback, retall=retall, full_output=full_output, hess=hess) if not full_output: # xopt should be None and retvals is argmin xopt = retvals elif cov_params_func: Hinv = cov_params_func(self, xopt, retvals) elif method == 'newton' and full_output: Hinv = np.linalg.inv(-retvals['Hessian']) / nobs else: try: Hinv = np.linalg.inv(-1 * self.hessian(xopt)) except: #might want custom warning ResultsWarning? NumericalWarning? from warnings import warn warndoc = ('Inverting hessian failed, no bse or ' 'cov_params available') warn(warndoc, Warning) Hinv = None #TODO: add Hessian approximation and change the above if needed mlefit = LikelihoodModelResults(self, xopt, Hinv, scale=1.) #TODO: hardcode scale? if isinstance(retvals, dict): mlefit.mle_retvals = retvals optim_settings = {'optimizer': method, 'start_params': start_params, 'maxiter': maxiter, 'full_output': full_output, 'disp': disp, 'fargs': fargs, 'callback': callback, 'retall': retall} optim_settings.update(kwargs) mlefit.mle_settings = optim_settings return mlefit
def _fit_mle_newton(f, score, start_params, fargs, kwargs, disp=True, maxiter=100, callback=None, retall=False, full_output=True, hess=None): tol = kwargs.setdefault('tol', 1e-8) iterations = 0 oldparams = np.inf newparams = np.asarray(start_params) if retall: history = [oldparams, newparams] while (iterations < maxiter and np.any(np.abs(newparams - oldparams) > tol)): H = hess(newparams) oldparams = newparams newparams = oldparams - np.dot(np.linalg.inv(H), score(oldparams)) if retall: history.append(newparams) if callback is not None: callback(newparams) iterations += 1 fval = f(newparams, *fargs) # this is the negative likelihood if iterations == maxiter: warnflag = 1 if disp: print ("Warning: Maximum number of iterations has been " "exceeded.") print " Current function value: %f" % fval print " Iterations: %d" % iterations else: warnflag = 0 if disp: print "Optimization terminated successfully." print " Current function value: %f" % fval print " Iterations %d" % iterations if full_output: (xopt, fopt, niter, gopt, hopt) = (newparams, f(newparams, *fargs), iterations, score(newparams), hess(newparams)) converged = not warnflag retvals = {'fopt': fopt, 'iterations': niter, 'score': gopt, 'Hessian': hopt, 'warnflag': warnflag, 'converged': converged} if retall: retvals.update({'allvecs': history}) else: retvals = newparams xopt = None return xopt, retvals def _fit_mle_bfgs(f, score, start_params, fargs, kwargs, disp=True, maxiter=100, callback=None, retall=False, full_output=True, hess=None): gtol = kwargs.setdefault('gtol', 1.0000000000000001e-05) norm = kwargs.setdefault('norm', np.Inf) epsilon = kwargs.setdefault('epsilon', 1.4901161193847656e-08) retvals = optimize.fmin_bfgs(f, start_params, score, args=fargs, gtol=gtol, norm=norm, epsilon=epsilon, maxiter=maxiter, full_output=full_output, disp=disp, retall=retall, callback=callback) if full_output: if not retall: xopt, fopt, gopt, Hinv, fcalls, gcalls, warnflag = retvals else: (xopt, fopt, gopt, Hinv, fcalls, gcalls, warnflag, allvecs) = retvals converged = not warnflag retvals = {'fopt': fopt, 'gopt': gopt, 'Hinv': Hinv, 'fcalls': fcalls, 'gcalls': gcalls, 'warnflag': warnflag, 'converged': converged} if retall: retvals.update({'allvecs': allvecs}) else: xopt = None return xopt, retvals def _fit_mle_nm(f, score, start_params, fargs, kwargs, disp=True, maxiter=100, callback=None, retall=False, full_output=True, hess=None): xtol = kwargs.setdefault('xtol', 0.0001) ftol = kwargs.setdefault('ftol', 0.0001) maxfun = kwargs.setdefault('maxfun', None) retvals = optimize.fmin(f, start_params, args=fargs, xtol=xtol, ftol=ftol, maxiter=maxiter, maxfun=maxfun, full_output=full_output, disp=disp, retall=retall, callback=callback) if full_output: if not retall: xopt, fopt, niter, fcalls, warnflag = retvals else: xopt, fopt, niter, fcalls, warnflag, allvecs = retvals converged = not warnflag retvals = {'fopt': fopt, 'iterations': niter, 'fcalls': fcalls, 'warnflag': warnflag, 'converged': converged} if retall: retvals.update({'allvecs': allvecs}) else: xopt = None return xopt, retvals def _fit_mle_cg(f, score, start_params, fargs, kwargs, disp=True, maxiter=100, callback=None, retall=False, full_output=True, hess=None): gtol = kwargs.setdefault('gtol', 1.0000000000000001e-05) norm = kwargs.setdefault('norm', np.Inf) epsilon = kwargs.setdefault('epsilon', 1.4901161193847656e-08) retvals = optimize.fmin_cg(f, start_params, score, gtol=gtol, norm=norm, epsilon=epsilon, maxiter=maxiter, full_output=full_output, disp=disp, retall=retall, callback=callback) if full_output: if not retall: xopt, fopt, fcalls, gcalls, warnflag = retvals else: xopt, fopt, fcalls, gcalls, warnflag, allvecs = retvals converged = not warnflag retvals = {'fopt': fopt, 'fcalls': fcalls, 'gcalls': gcalls, 'warnflag': warnflag, 'converged': converged} if retall: retvals.update({'allvecs': allvecs}) else: xopt = None return xopt, retvals def _fit_mle_ncg(f, score, start_params, fargs, kwargs, disp=True, maxiter=100, callback=None, retall=False, full_output=True, hess=None): fhess_p = kwargs.setdefault('fhess_p', None) avextol = kwargs.setdefault('avextol', 1.0000000000000001e-05) epsilon = kwargs.setdefault('epsilon', 1.4901161193847656e-08) retvals = optimize.fmin_ncg(f, start_params, score, fhess_p=fhess_p, fhess=hess, args=fargs, avextol=avextol, epsilon=epsilon, maxiter=maxiter, full_output=full_output, disp=disp, retall=retall, callback=callback) if full_output: if not retall: xopt, fopt, fcalls, gcalls, hcalls, warnflag = retvals else: xopt, fopt, fcalls, gcalls, hcalls, warnflag, allvecs =\ retvals converged = not warnflag retvals = {'fopt': fopt, 'fcalls': fcalls, 'gcalls': gcalls, 'hcalls': hcalls, 'warnflag': warnflag, 'converged': converged} if retall: retvals.update({'allvecs': allvecs}) else: xopt = None return xopt, retvals def _fit_mle_powell(f, score, start_params, fargs, kwargs, disp=True, maxiter=100, callback=None, retall=False, full_output=True, hess=None): xtol = kwargs.setdefault('xtol', 0.0001) ftol = kwargs.setdefault('ftol', 0.0001) maxfun = kwargs.setdefault('maxfun', None) start_direc = kwargs.setdefault('start_direc', None) retvals = optimize.fmin_powell(f, start_params, args=fargs, xtol=xtol, ftol=ftol, maxiter=maxiter, maxfun=maxfun, full_output=full_output, disp=disp, retall=retall, callback=callback, direc=start_direc) if full_output: if not retall: xopt, fopt, direc, niter, fcalls, warnflag = retvals else: xopt, fopt, direc, niter, fcalls, warnflag, allvecs =\ retvals converged = not warnflag retvals = {'fopt': fopt, 'direc': direc, 'iterations': niter, 'fcalls': fcalls, 'warnflag': warnflag, 'converged': converged} if retall: retvals.update({'allvecs': allvecs}) else: xopt = None return xopt, retvals def _fit_mle_basinhopping(f, score, start_params, fargs, kwargs, disp=True, maxiter=100, callback=None, retall=False, full_output=True, hess=None): if not 'basinhopping' in vars(optimize): msg = 'basinhopping solver is not available, use e.g. bfgs instead!' raise ValueError(msg) from copy import copy kwargs = copy(kwargs) niter = kwargs.setdefault('niter', 100) niter_success = kwargs.setdefault('niter_success', None) T = kwargs.setdefault('T', 1.0) stepsize = kwargs.setdefault('stepsize', 0.5) interval = kwargs.setdefault('interval', 50) minimizer_kwargs = kwargs.get('minimizer', {}) minimizer_kwargs['args'] = fargs minimizer_kwargs['jac'] = score minimizer_kwargs['hess'] = hess res = optimize.basinhopping(f, start_params, minimizer_kwargs=minimizer_kwargs, niter=niter, niter_success=niter_success, T=T, stepsize=stepsize, disp=disp, callback=callback, interval=interval) if full_output: xopt, fopt, niter, fcalls = res.x, res.fun, res.nit, res.nfev converged = 'completed successfully' in res.message[0] retvals = {'fopt': fopt, 'iterations': niter, 'fcalls': fcalls, 'converged': converged} else: xopt = None return xopt, retvals #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 not loglike is None: self.loglike = loglike if not score is None: self.score = score if not hessian is None: self.hessian = hessian self.confint_dist = stats.norm self.__dict__.update(kwds) # TODO: data structures? #TODO temporary solution, force approx normal #self.df_model = 9999 #somewhere: CacheWriteWarning: The attribute '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: #try: 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. from statsmodels.tools import tools if self.exog is not None: self.df_model = float(tools.rank(self.exog) - 1) # assumes constant self.df_resid = float(self.exog.shape[0] - tools.rank(self.exog)) 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 jac(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 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', UserWarning) 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. 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. Returns ------- See self.model.predict """ if transform and hasattr(self.model, 'formula') and exog is not None: from patsy import dmatrix exog = dmatrix(self.model.data.orig_exog.design_info.builder, exog) return self.model.predict(self.params, exog, *args, **kwargs) #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_ouput 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. '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. """ def __init__(self, model, params, normalized_cov_params=None, scale=1.): super(LikelihoodModelResults, self).__init__(model, params) self.normalized_cov_params = normalized_cov_params self.scale = scale
[docs] def normalized_cov_params(self): raise NotImplementedError
@cache_readonly
[docs] def llf(self): return self.model.loglike(self.params)
@cache_readonly
[docs] def bse(self): return np.sqrt(np.diag(self.cov_params()))
@cache_readonly
[docs] def tvalues(self): """ Return the t-statistic for a given parameter estimate. """ return self.params / self.bse
@cache_readonly
[docs] def pvalues(self): 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 ------- (The below are assumed to be in matrix notation.) cov : ndarray 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: 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 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][:, column] 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, q_matrix=None, cov_p=None, scale=None): """ Compute a t-test for a joint 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. - 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), since q_matrix is deprecated. q_matrix : array-like or scalar, optional This is deprecated. See `r_matrix` and the examples for more information on new usage. Can be either a scalar or a length p row vector. If omitted and r_matrix is an array, `q_matrix` is assumed to be a conformable array of zeros. 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. 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 <T contrast: effect=-1829.2025687192481, sd=455.39079425193762, t=-4.0167754636411717, p=0.0015163772380899498, df_denom=9> >>> 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 >>> 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 See also --------- tvalues : individual t statistics f_test : for F tests patsy.DesignInfo.linear_constraint """ from patsy import DesignInfo if q_matrix is not None: from warnings import warn warn("The `q_matrix` keyword is deprecated and will be removed " "in 0.6.0. See the documentation for the new API", FutureWarning) r_matrix = (r_matrix, q_matrix) LC = DesignInfo(self.model.exog_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: 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") _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) return ContrastResults(effect=_effect, t=_t, sd=_sd, df_denom=self.model.df_resid) #TODO: untested for GLMs?
[docs] def f_test(self, r_matrix, q_matrix=None, cov_p=None, scale=1.0, invcov=None): """ Compute an F-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. - 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), since q_matrix is deprecated. q_matrix : array-like This is deprecated. See `r_matrix` and the examples for more information on new usage. Can be either a scalar or a length p row vector. If omitted and r_matrix is an array, `q_matrix` is assumed to be a conformable array of zeros. 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. 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 contrast: F=330.28533923463488, p=4.98403052872e-10, df_denom=9, df_num=6> Compare this to >>> results.F 330.2853392346658 >>> results.F_p 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 contrast: F=9.740461873303655, p=0.00560528853174, 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 See also -------- statsmodels.contrasts statsmodels.model.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. """ from patsy import DesignInfo if q_matrix is not None: from warnings import warn warn("The `q_matrix` keyword is deprecated and will be removed " "in 0.6.0. See the documentation for the new API", FutureWarning) r_matrix = (r_matrix, q_matrix) LC = DesignInfo(self.model.exog_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): 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.inv(cov_p) if (hasattr(self, 'mle_settings') and self.mle_settings['optimizer'] in ['l1', 'l1_cvxopt_cp']): F = nan_dot(nan_dot(Rbq.T, invcov), Rbq) / J else: F = np.dot(np.dot(Rbq.T, invcov), Rbq) / J return ContrastResults(F=F, df_denom=self.model.df_resid, df_num=invcov.shape[0])
[docs] def conf_int(self, alpha=.05, cols=None, method='default'): """ Returns the confidence interval of the fitted parameters. Parameters ---------- alpha : float, optional The `alpha` 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 "jhj" : "jac" : "boot-bse" "boot_quant" "profile" Returns -------- conf_int : array Each row contains [lower, upper] confidence interval 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 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(zip(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)
@classmethod
[docs] 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 list of arrays to delete is maintained as an attribute of the result and model instance, except for cached values. These lists could be changed before calling remove_data. ''' def wipe(obj, att): #get to last element in attribute path p = att.split('.') att_ = p.pop(-1) try: obj_ = reduce(getattr, [obj] + p) #print repr(obj), repr(att) #print hasattr(obj_, att_) if hasattr(obj_, att_): #print 'removing3', att_ setattr(obj_, att_, None) except AttributeError: pass model_attr = ['model.'+ i for i in self.model._data_attr] for att in self._data_attr + model_attr: #print 'removing', att 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, LikelihoodModelResults)
[docs]class ResultMixin(object): @cache_readonly
[docs] 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
@cache_readonly
[docs] def aic(self): return -2 * self.llf + 2 * (self.df_modelwc)
@cache_readonly
[docs] def bic(self): return -2 * self.llf + np.log(self.nobs) * (self.df_modelwc)
@cache_readonly
[docs] def jacv(self): '''cached Jacobian of log-likelihood ''' return self.model.jac(self.params)
@cache_readonly
[docs] def hessv(self): '''cached Hessian of log-likelihood ''' return self.model.hessian(self.params)
@cache_readonly
[docs] 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.jacv return np.linalg.inv(np.dot(jacv.T, jacv))
@cache_readonly
[docs] def covjhj(self): '''covariance of parameters based on HJJH dot product of Hessian, Jacobian, Jacobian, Hessian of likelihood name should be covhjh ''' jacv = self.jacv ## hessv = self.hessv ## hessinv = np.linalg.inv(hessv) ## self.hessinv = hessinv hessinv = self.cov_params() return np.dot(hessinv, np.dot(np.dot(jacv.T, jacv), hessinv))
@cache_readonly
[docs] def bsejhj(self): '''standard deviation of parameter estimates based on covHJH ''' return np.sqrt(np.diag(self.covjhj))
@cache_readonly
[docs] 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 xrange(nrep): rvsind = np.random.randint(self.nobs - 1, 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): # super(DiscreteResults, self).__init__(model, params, # np.linalg.inv(-hessian), scale=1.) 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]), #TODO: spelling ('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