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Source code for scikits.statsmodels.base.model

import numpy as np
from scipy.stats import t, norm
from scipy import optimize
from scikits.statsmodels.tools.tools import recipr
from scikits.statsmodels.stats.contrast import ContrastResults
from scikits.statsmodels.tools.decorators import (resettable_cache,
                                                        cache_readonly)

[docs]class Model(object): """ A (predictive) statistical model. The class Model itself is not to be used. Model lays out the methods expected of any subclass. Parameters ---------- endog : array-like Endogenous response variable. exog : array-like Exogenous design. 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. """ _results = None def __init__(self, endog, exog=None): endog = np.asarray(endog) endog = np.squeeze(endog) # for consistent outputs if endog is (n,1) ## # not sure if we want type conversion, needs tests with integers ## if np.issubdtype(endog.dtype, int): ## endog = endog.astype(float) ## if np.issubdtype(exog.dtype, int): ## endog = exog.astype(float) if not exog is None: exog = np.asarray(exog) if exog.ndim == 1: exog = exog[:,None] if exog.ndim != 2: raise ValueError("exog is not 1d or 2d") if endog.shape[0] != exog.shape[0]: raise ValueError("endog and exog matrices are not aligned.") if np.any(exog.var(0) == 0): # assumes one constant in first or last position # avoid exception if more than one constant const_idx = np.where(exog.var(0) == 0)[0][0].item() if const_idx == exog.shape[1] - 1: exog_names = ['x%d' % i for i in range(1,exog.shape[1])] exog_names += ['const'] else: exog_names = ['x%d' % i for i in range(exog.shape[1])] exog_names[const_idx] = 'const' self.exog_names = exog_names else: self.exog_names = ['x%d' % i for i in range(exog.shape[1])] if endog.ndim == 1 or endog.shape[1] == 1: self.endog_names = ['y'] else: # for VAR self.endog_names = ['y%d' % (i+1) for i in range(endog.shape[1])] self.endog = endog self.exog = exog
[docs] def fit(self): """ Fit a model to data. """ raise NotImplementedError
[docs] def predict(self, exog, params=None): """ After a model has been fit predict returns the fitted values. If the model has not been fit, then fit is called. """ raise NotImplementedError
[docs]class LikelihoodModel(Model): """ Likelihood model is a subclass of Model. """ def __init__(self, endog, exog=None): super(LikelihoodModel, self).__init__(endog, exog) 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=1,disp=1, fargs=(), callback=None, retall=0, **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', or 'ncg'} 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, or 'ncg' for Newton- conjugate gradient. `method` determines which solver from scipy.optimize is used. The explicit arguments in `fit` are passed to the 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. 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 ----- 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. """ Hinv = None #JP error if full_output=0, Hinv not defined methods = ['newton', 'nm', 'bfgs', 'powell', 'cg', 'ncg'] if start_params is None: if hasattr(self, 'start_params'): start_params = self.start_params elif self.exog is not None: start_params = [0]*self.exog.shape[1] # fails for shape (K,)? else: raise ValueError("If exog is None, then start_params should be " "specified") #print 'repr(start_params)', repr(start_params) if method.lower() not in methods: raise ValueError, "Unknown fit method %s" % method 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 f = lambda params, *args: -self.loglike(params, *args) score = lambda params: -self.score(params) try: hess = lambda params: -self.hessian(params) except: hess = None if method == 'newton': tol = kwargs.setdefault('tol', 1e-8) score = lambda params: self.score(params) #JP: redundant ? hess = lambda params: self.hessian(params) #JP: redundant ? iterations = 0 oldparams = np.inf newparams = np.asarray(start_params) if retall: history = [oldparams, newparams] while (iterations < maxiter and np.all(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 elif method == 'nm': # Nelder-Mead 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}) elif method == 'bfgs': 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}) elif method == 'ncg': 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}) elif method == 'cg': 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}) elif method == 'powell': 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}) if not full_output: xopt = retvals #NOTE: better just to use the Analytic Hessian here, as approximation isn't # great # if method == 'bfgs' and full_output: # Hinv = retvals.setdefault('Hinv', 0) elif method == 'newton' and full_output: Hinv = np.linalg.inv(-hopt) 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 self._results = mlefit return mlefit #TODO: the below is unfinished
[docs]class GenericLikelihoodModel(LikelihoodModel): """ Allows the fitting of any likelihood function via maximum likelihood. A subclass needs to specify at least the log-likelihood If the log-likelihood is specified for each observation, then results that require the Jacobian will be available. (The other case is not tested yet.) Notes ----- Optimization methods that require only a likelihood function are 'nm' and 'powell' Optimization methods that require a likelihood function and a score/gradient are 'bfgs', 'cg', and 'ncg'. A function to compute the Hessian is optional for 'ncg'. Optimization method that require a likelihood function, a score/gradient, and a Hessian is 'newton' If they are not overwritten by a subclass, then numerical gradient, Jacobian and Hessian of the log-likelihood are caclulated by numerical forward differentiation. This might results in some cases in precision problems, and the Hessian might not be positive definite. Even if the Hessian is not positive definite the covariance matrix of the parameter estimates based on the outer product of the Jacobian might still be valid. Examples -------- see also subclasses in directory miscmodels import scikits.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): # let them be none in case user wants to use inheritance if loglike: self.loglike = loglike if score: self.score = score if hessian: self.hessian = hessian self.confint_dist = norm if not exog is None: #this won't work for ru2nmnl, maybe np.ndim of a dict? #try: self.nparams = self.df_model = exog.shape[1] if np.ndim(exog)==2 else 1 super(GenericLikelihoodModel, self).__init__(endog, exog) #this is redundant and not used when subclassing
[docs] def initialize(self): if not self.score: # right now score is not optional from scikits.statsmodels.sandbox.regression.numdiff import approx_fprime1 self.score = approx_fprime1 if not self.hessian: pass else: # can use approx_hess_p if we have a gradient if not self.hessian: pass
[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 ''' from scikits.statsmodels.sandbox.regression.numdiff import approx_fprime1 return approx_fprime1(params, self.loglike, epsilon=1e-4).ravel()
[docs] def jac(self, params, **kwds): ''' Jacobian/Gradient of log-likelihood evaluated at params for each observation. ''' kwds.setdefault('epsilon', 1e-4) from scikits.statsmodels.sandbox.regression.numdiff import approx_fprime1 return approx_fprime1(params, self.loglikeobs, **kwds)
[docs] def hessian(self, params): ''' Hessian of log-likelihood evaluated at params ''' from scikits.statsmodels.sandbox.regression.numdiff import approx_hess return approx_hess(params, self.loglike)[0] #need options for hess (epsilon)
[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 scikits.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) mlefit = super(GenericLikelihoodModel, self).fit(start_params=start_params, method=method, maxiter=maxiter, full_output=full_output, disp=disp, callback=callback, **kwargs) genericmlefit = GenericLikelihoodModelResults(self, mlefit) return genericmlefit #fit.__doc__ += LikelihoodModel.fit.__doc__ #------------------------------ #TODO: the following have been moved to the result mixin class # check if anything is still using them from here
@cache_readonly def jacv(self): if not hasattr(self, '_results'): raise ValueError('need to call fit first') return self.jac(self._results.params) @cache_readonly def hessv(self): if not hasattr(self, '_results'): raise ValueError('need to call fit first') return self.hessian(self._results.params) # the following could be moved to results @cache_readonly def covjac(self): ''' covariance of parameters based on loglike outer product of jacobian ''' ## 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 def covjhj(self): jacv = self.jacv ## hessv = self.hessv ## hessinv = np.linalg.inv(hessv) ## self.hessinv = hessinv hessinv = self._results.cov_params() return np.dot(hessinv, np.dot(np.dot(jacv.T, jacv), hessinv)) @cache_readonly def bsejhj(self): return np.sqrt(np.diag(self.covjhj)) @cache_readonly def bsejac(self): return np.sqrt(np.diag(self.covjac))
[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)
[docs] def initialize(self, model, params, **kwd): self.params = params self.model = model #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 #JP: add methods that are valid generically higher up in class hierarchy
@cache_readonly def llf(self): return self.model.loglike(self.params) @cache_readonly def bse(self): return np.sqrt(np.diag(self.cov_params()))
[docs] def t(self, column=None): """ deprecated: Return the t-statistic for a given parameter estimate. FutureWarning: use attribute tvalues instead, t will be removed in the next release Parameters ---------- column : array-like The columns for which you would like the t-value. Note that this uses Python's indexing conventions. See also --------- Use t_test for more complicated t-statistics. Examples -------- >>> import scikits.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.tvalues array([ 0.17737603, -1.06951632, -4.13642736, -4.82198531, -0.22605114, 4.01588981, -3.91080292]) >>> results.tvalues[[1,2,4]] array([-1.06951632, -4.13642736, -0.22605114]) >>> import numpy as np >>> results.tvalues[np.array([1,2,4]] array([-1.06951632, -4.13642736, -0.22605114]) """ import warnings warnings.warn("`t` will be removed in the next release, use attribute" "`tvalues` instead", FutureWarning) if self.normalized_cov_params is None: raise ValueError('need covariance of parameters for computing T ' 'statistics') if column is None: column = range(self.params.shape[0]) column = np.asarray(column) _params = self.params[column] _cov = self.cov_params(column=column) if _cov.ndim == 2: _cov = np.diag(_cov) _t = _params * recipr(np.sqrt(_cov)) # repicr drops precision for MNLogit? _t = _params / np.sqrt(_cov) return _t
@cache_readonly def tvalues(self): """ Return the t-statistic for a given parameter estimate. """ return self.params / self.bse
[docs] def cov_params(self, r_matrix=None, column=None, scale=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 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 scale is None: scale = self.scale if column is not None: column = np.asarray(column) if column.shape == (): return self.normalized_cov_params[column, column] * scale else: return self.normalized_cov_params[column][:,column] * scale 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 = np.dot(r_matrix, np.dot(self.normalized_cov_params, np.transpose(other))) return tmp * scale if r_matrix is None and column is None: return self.normalized_cov_params * scale #TODO: make sure this works as needed for GLMs
[docs] def t_test(self, r_matrix, q_matrix=None, scale=None): """ Compute a tcontrast/t-test for a row vector array of the form Rb = q where R is r_matrix, b = the parameter vector, and q is q_matrix. Parameters ---------- r_matrix : array-like A length p row vector specifying the linear restrictions. q_matrix : array-like or scalar, optional Either a scalar or a length p row vector. scale : float, optional An optional `scale` to use. Default is the scale specified by the model fit. Examples -------- >>> import numpy as np >>> import scikits.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[4:6] = [1,-1] >>> print r [ 0. 0. 0. 0. 1. -1. 0.] 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.t -4.0167754636411717 >>> T_test.p 0.0015163772380899498 See also --------- t : method to get simpler t values f_test : for f tests """ r_matrix = np.atleast_2d(np.asarray(r_matrix)) num_ttests = r_matrix.shape[0] num_params = r_matrix.shape[1] if 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) 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) if num_ttests > 1: _sd = np.sqrt(np.diag(self.cov_params(r_matrix=r_matrix))) else: _sd = np.sqrt(self.cov_params(r_matrix=r_matrix)) _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, scale=1.0, invcov=None): """ Compute an Fcontrast/F-test for a contrast matrix. Here, 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. Parameters ---------- r_matrix : array-like q x p array where q is the number of restrictions to test and p is the number of regressors in the full model fit. If q is 1 then f_test(r_matrix).fvalue is equivalent to the square of t_test(r_matrix).t q_matrix : array-like q x 1 array, that represents the sum of each linear restriction. Default is all zeros for each restriction. scale : float, optional Default is 1.0 for no scaling. invcov : array-like, optional A qxq matrix to specify an inverse covariance matrix based on a restrictions matrix. Examples -------- >>> import numpy as np >>> import scikits.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(([0,1,-1,0,0,0,0],[0,0,0,0,1,-1,0])) 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> See also -------- scikits.statsmodels.contrasts scikits.statsmodels.model.t_test """ r_matrix = np.asarray(r_matrix) r_matrix = np.atleast_2d(r_matrix) if self.normalized_cov_params 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: invcov = np.linalg.inv(self.cov_params(r_matrix=r_matrix)) 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 scikits.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([[ -1.77029035e+02, 2.07152780e+02], [ -1.11581102e-01, 3.99427438e-02], [ -3.12506664e+00, -9.15392966e-01], [ -1.51794870e+00, -5.48505034e-01], [ -5.62517214e-01, 4.60309003e-01], [ 7.98787515e+02, 2.85951541e+03], [ -5.49652948e+06, -1.46798779e+06]]) >>> results.conf_int(cols=(1,2)) array([[-0.1115811 , 0.03994274], [-3.12506664, -0.91539297]]) Notes ----- The confidence interval is based on Student's t distribution for all models except RLM and GLM, which uses the standard normal distribution. """ bse = self.bse #TODO: simplify structure, DRY if hasattr(self.model, 'confint_dist'): dist = self.model.confint_dist elif self.__class__.__name__ in ['RLMResults','GLMResults','DiscreteResults']: dist = norm else: dist = t if cols is None and dist == t: lower = self.params - dist.ppf(1-alpha/2,self.model.df_resid) *\ bse upper = self.params + dist.ppf(1-alpha/2,self.model.df_resid) *\ bse elif cols is None and dist == norm: lower = self.params - dist.ppf(1-alpha/2) * bse upper = self.params + dist.ppf(1-alpha/2) * bse elif cols is not None and dist == t: cols = np.asarray(cols) lower = self.params[cols] - dist.ppf(1-\ alpha/2,self.model.df_resid) * bse[cols] upper = self.params[cols] + dist.ppf(1-\ alpha/2,self.model.df_resid) * bse[cols] elif cols is not None and dist == norm: cols = np.asarray(cols) lower = self.params[cols] - dist.ppf(1-alpha/2) * bse[cols] upper = self.params[cols] + dist.ppf(1-alpha/2) * bse[cols] return np.asarray(zip(lower,upper))
[docs]class ResultMixin(object): @cache_readonly def df_modelwc(self): #collect different ways of defining the number of parameters, used for aic, bic if hasattr(self, 'df_model'): if hasattr(self, 'hasconst'): hasconst = self.hasconst else: hasconst = 1 #default assumption return self.df_model + hasconst else: return self.params.size @cache_readonly def aic(self): return -2 * self.llf + 2 * (self.df_modelwc) @cache_readonly def bic(self): return -2 * self.llf + np.log(self.nobs) * (self.df_modelwc) @cache_readonly def jacv(self): '''cached Jacobian of log-likelihood ''' return self.model.jac(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.jacv 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.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 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 : 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.df_model = model.df_model #self.df_resid = model.df_resid self.endog = model.endog self.exog = model.exog self.nobs = model.endog.shape[0] self._cache = resettable_cache() self.__dict__.update(mlefit.__dict__)