M/Ph&'8dZddlZddlmZGddZdS)z( Author: Josef Perktold License: BSD-3 N)statscXeZdZdZddZddZdZdZdZdZ d Z dd Z dd Z dS)NonlinearDeltaCovaAsymptotic covariance by Deltamethod The function is designed for 2d array, with rows equal to the number of equations or constraints and columns equal to the number of parameters. 1d params work by chance ? fun: R^{m*k) -> R^{m} where m is number of equations and k is the number of parameters. equations follow Greene This class does not use any caching. The intended usage is as a helper function. Extra methods have been added for convenience but might move to calling functions. The naming in this class uses params for the original random variable, and cov_params for it's covariance matrix. However, this class is independent of the use cases in support of the models. Parameters ---------- func : callable, f(params) Nonlinear function of the estimation parameters. The return of the function can be vector valued, i.e. a 1-D array. params : ndarray Parameters at which function `func` is evaluated. cov_params : ndarray Covariance matrix of the parameters `params`. deriv : function or None First derivative or Jacobian of func. If deriv is None, then a numerical derivative will be used. If func returns a 1-D array, then the `deriv` should have rows corresponding to the elements of the return of func. func_args : None Not yet implemented. Ncv||_||_||_||_||nd|_|t ddS)Nzfunc_args not yet implemented)funparams cov_params_grad func_argsNotImplementedError)selffuncr r derivr s _/var/www/html/test/jupyter/venv/lib/python3.11/site-packages/statsmodels/stats/_delta_method.py__init__zNonlinearDeltaCov.__init__2sK $ &/&;  %&EFF F ! c ||j}|j||S ddlm}|||jfi|}n%#t $rddlm}|||jfi|}YnwxYw|S)aiFirst derivative, jacobian of func evaluated at params. Parameters ---------- params : None or ndarray Values at which gradient is evaluated. If params is None, then the attached params are used. TODO: should we drop this kwds : keyword arguments This keyword arguments are used without changes in the calulation of numerical derivatives. These are only used if a `deriv` function was not provided. Returns ------- grad : ndarray gradient or jacobian of the function Nr)approx_fprime_cs) approx_fprime)r r statsmodels.tools.numdiffrr TypeErrorr)rr kwdsrjacrs rgradzNonlinearDeltaCov.grad;s& >[F : !::f%% % >FFFFFF&&vtx@@4@@ > > >CCCCCC#mFDH==== >Js=AAc|}tjtj||j|j}|S)z>Covariance matrix of the transformed random variable. )rnpdotr T)rgcovars rcovzNonlinearDeltaCov.cov]s7 IIKKrva111377 rcx||j}|jdkr|}|S)a=Value of the function evaluated at the attached params. Note: This is not equal to the expected value if the transformation is nonlinear. If params is the maximum likelihood estimate, then `predicted` is the maximum likelihood estimate of the value of the nonlinear function. )rr ndimsqueeze)r predicteds rr'zNonlinearDeltaCov.predictedds=HHT[))  >A  !))++Irc\|}|}tj|}||z }tjtj|jtj||}|tj ||fS)aJoint hypothesis tests that H0: f(params) = value. The alternative hypothesis is two-sided H1: f(params) != value. Warning: this might be replaced with more general version that returns ContrastResults. currently uses chisquare distribution, use_f option not yet implemented Parameters ---------- value : float or ndarray value of f(params) under the Null Hypothesis Returns ------- statistic : float Value of the test statistic. pvalue : float The p-value for the hypothesis test, based and chisquare distribution and implies a two-sided hypothesis test ) r'r"rsizerrlinalginvrchi2sf)rvaluemvdf_constraintsdifflmstats r wald_testzNonlinearDeltaCov.wald_testts~. NN   HHJJ5ytvry}}Q'7'788$??uz}}V^<<<>>7DI  ((I :##%%B  Q*++B DHQ^ 0i 0 0 0AF"AF" _eU^ , , 8A;!  BCC C rcnddlm}|}|}t j|}|jdkr|}t j|}||z } |r|} ||| || } n||| |dd} | |||S) aSummarize the Results of the nonlinear transformation. This provides a parameter table equivalent to `t_test` and reuses `ContrastResults`. Parameters ----------- xname : list of strings, optional Default is `c_##` for ## in p the number of regressors alpha : float Significance level for the confidence intervals. Default is alpha = 0.05 which implies a confidence level of 95%. title : string, optional Title for the params table. If not None, then this replaces the default title use_t : boolean If use_t is False (default), then the normal distribution is used for the confidence interval, otherwise the t distribution with `df` degrees of freedom is used. df : int or float degrees of freedom for t distribution. Only used and required if use_t is True. Returns ------- smry : string or Summary instance This contains a parameter results table in the case of t or z test in the same form as the parameter results table in the model results summary. For F or Wald test, the return is a string. r)ContrastResultsr$)effectrBsddf_denomNr@)rU statisticrVrW distribution)xnamerGtitle) statsmodels.stats.contrastrTr'r=r atleast_1dr%r&summary) rrZrGr[rHrIrTr'rKrXdf_residcrs rr^zNonlinearDeltaCov.summarysD ?>>>>>NN$$    ! !M),, >A  !))++I ]2  N  EH  Y2*2444BB! Y2*.VEEEBzzU%z@@@r)NN)N)r>FNNNN)Nr>NFN) __name__ __module__ __qualname____doc__rrr"r'r4r:r=rRr^rrrrr s%%LGGGG    D ===<   DH$(<<<<|AF4A4A4A4A4A4Arr)rdnumpyrscipyrrrrrrgsu KAKAKAKAKAKAKAKAKAKAr