M/Ph"ddlmZddlmZddlmZddlZddlZddl Z ddl m Z ddl mZddlmZddlmcmZddlmZdd lmZmZmZdd lmZdd lmZmZm Z dd l!m"Z"dd l#m$Z$m%Z%ddl&m'Z'm(Z(ddl)m*Z*dZ+dZ,dZ-dZ.GddZ/Gdde/Z0Gdde0Z1GddZ2Gdde2Z3Gddej4Z5ej6e5e3Gd d!Z7Gd"d#Z8Gd$d%e3e7Z9dS)&) annotations)lzip)reduceN)stats) handle_data) Optimizer)handle_formula_data)ContrastResultsWaldTestResultst_test_pairwise)_is_using_pandas)cache_readonly cached_data cached_value) approx_fprime)HessianInversionWarning ValueWarning)nan_dotrecipr) bool_likeFaParameters ---------- endog : array_like A 1-d endogenous response variable. The dependent variable. exog : array_like A nobs x k array where `nobs` is the number of observations and `k` is the number of regressors. An intercept is not included by default and should be added by the user. See :func:`statsmodels.tools.add_constant`.zmissing : str Available options are 'none', 'drop', and 'raise'. If 'none', no nan checking is done. If 'drop', any observations with nans are dropped. If 'raise', an error is raised. Default is 'none'.a hasconst : None or bool Indicates whether the RHS includes a user-supplied constant. If True, a constant is not checked for and k_constant is set to 1 and all result statistics are calculated as if a constant is present. If False, a constant is not checked for and k_constant is set to 0. **kwargs Extra arguments that are used to set model properties when using the formula interface.ceZdZdeeezZdZgdZ ddZ dZ de fdZ d Zedd Zed ZeddZdZddZdS)Modela A (predictive) statistical model. Intended to be subclassed not used. {params_doc} {extra_params_doc} Attributes ---------- exog_names endog_names Notes ----- `endog` and `exog` are references to any data provided. So if the data is already stored in numpy arrays and it is changed then `endog` and `exog` will change as well. ) params_docextra_params_docmissing missing_idxformula design_infohasconstNc |dd}|dd}|j||||fi||_|jj|_|jj|_|jj|_g|_|jgdd|vr|jddgt| |_ ||j ddSdS)Nrnoner!)exogendogz data.exogz data.endogrzdata.orig_endogzdata.orig_exog) pop _handle_datadata k_constantr$r% _data_attrextendlistkeys _init_keysappend)selfr%r$kwargsrr!s V/var/www/html/test/jupyter/venv/lib/python3.11/site-packages/statsmodels/base/model.py__init__zModel.__init__\s**Y//::j$//%D%eT7H00(.00 ).IN Y_  KKKLLL F " " O " "$57G#H I I Iv{{}}--   O " ": . . . . . c.fdjD}|S)zAreturn dictionary with extra keys used in model.__init__ c4i|]}|t|dSN)getattr).0keyr0s r2 z(Model._get_init_kwds..qs7111WT3--111r4)r.)r0kwdss` r2_get_init_kwdszModel._get_init_kwdsns41111 $111 r4cgd|r|fd|D}|rAdt|z}|durtj|tdSt |dS)Nrcg|]}|v| Sr@)r9ikwargs_alloweds r2 z'Model._check_kwargs..~s#GGGq/F/F!/F/F/Fr4zunknown kwargs F)r+reprwarningswarnr ValueError)r0r1 keys_extraerrorkwargs_invalidmsgrBs @r2 _check_kwargszModel._check_kwargsvs  .  ! !* - - -GGGGVGGG  &#d>&:&::C~~ c<00000 oo%  & &r4c t||||fi|}|D]A}|dvr t|||j|2#t$rY>wxYw|S)N)r r)rsetattr__dict__r&KeyError)r0r%r$rr!r1r(r:s r2r'zModel._handle_datas5$DDVDD  C000 c4=#4#4S#9#9::::     s)A AAc| |j|}|dd}|d}n2|dkrddlm}|i}nt |t r|dz }|dd } | d krd } t|d||| } | \\} } } }|j}|C| j dkr8| j d|kr'td | j tdkrfd| jD}t|t| jkr\| |} t|j}D](} ||#t$rY%wxYw||}|| | ||d|| | g|Ri|}||_||j_|S)a Create a Model from a formula and dataframe. Parameters ---------- formula : str or generic Formula object The formula specifying the model. data : array_like The data for the model. See Notes. subset : array_like An array-like object of booleans, integers, or index values that indicate the subset of df to use in the model. Assumes df is a `pandas.DataFrame`. drop_cols : array_like Columns to drop from the design matrix. Cannot be used to drop terms involving categoricals. *args Additional positional argument that are passed to the model. **kwargs These are passed to the model with one exception. The ``eval_env`` keyword is passed to patsy. It can be either a :class:`patsy:patsy.EvalEnvironment` object or an integer indicating the depth of the namespace to use. For example, the default ``eval_env=0`` uses the calling namespace. If you wish to use a "clean" environment set ``eval_env=-1``. Returns ------- model The model instance. Notes ----- data must define __getitem__ with the keys in the formula terms args and kwargs are passed on to the model instantiation. E.g., a numpy structured or rec array, a dictionary, or a pandas DataFrame. Neval_envr)EvalEnvironmentrrdropr#raise)depthrzendog has evaluated to an array with multiple columns that has shape {}. This occurs when the variable converted to endog is non-numeric (e.g., bool or str).cg|]}|v| Sr@r@)r9x drop_colss r2rCz&Model.from_formula..s#BBB!q /A/AA/A/A/Ar4)rrrr )locr&patsyrU isinstanceintgetr _formula_max_endogndimshaperGformatlencolumnsr, term_namesremovesubsetupdaterr(frame)clsrr(rir[argsr1rRrUrtmpr%r$rr max_endogcolscolmods ` r2 from_formulazModel.from_formulasKT  8F#D::j$//  HH ^^ - - - - - -&r**HH # & &  MH**Y// f  G!$gX*1333471% [*  ! Q5;q>I#=#=56.fs% DL/$////$6 6r4rc&j|g|Rz Sr7rrs r2rz"LikelihoodModel.fit..scores"!tz&04000477r4c&j|g|Rz Sr7rrs r2hessz!LikelihoodModel.fit..hesss"#t|F2T222T99r4c(j|g|R z Sr7rrs r2rz"LikelihoodModel.fit..score s%" 61D1111D88r4c(j|g|R z Sr7rrs r2rz!LikelihoodModel.fit..hess#s%$ V3d3333d::r4warn_convergenceTcov_typecov_kwds)rruse_t)rmethoddispmaxitercallbackretall full_outputcov_params_funcHessianrTF?g@z8Inverting hessian failed, no bse or cov_params availablescale converged)ConvergenceWarningzEMaximum Likelihood optimization failed to converge. Check mle_retvals)"hasattrrr$rcrGr%r&r`r_fitrj setdefaultnplinalginvrallisfiniteeighmindotdiagTasfortranarrayrErFrLikelihoodModelResults mle_retvalsr^dictstatsmodels.tools.sm_exceptionsr mle_settings)r0rrrrrfargsrr skip_hessianr1Hinvrrrrrr< optimizerxoptretvalsoptim_settingsrH invertibleeigvalseigvecsmlefitrrs` @r2rzLikelihoodModel.fit\sL  t^,, 1#0 & #utyq'99  "0111z" 7 7 7 7 7 7 X   8 8 8 8 8 8 : : : : : : : 9 9 9 9 9 9 ; ; ; ; ; ;"::&8$??   zz*b11H &z 2IID ':&z""D f  "7ODMwKK (1q%7D<@?F@H>DCN)7)P)P%g~ d### ++,=tDD  "?4w77DD x  K 9==')"4!455>!#4#4 6'??Q&&!%J {{273=#9#9::>>wyII($-3)>?? *+BDDD(dDKKKdKK% gt $ $ 2 2 (< 2NNNNNN <0222- r4c t|drg|jdkr\tj|d}|jjd}tj|||jz}tj||f}n|}||||d<t|}| } |j |j |jdd|ffi| } | j di|} |}|&|jjd}|t|ddz }tj|} | j| |< | ddddd | } n+#t t"f$r| } YnwxYwt| jd r"| jjx| j_| j_t| d r| j| j_t| d r| j| j_| | j_t| jdr | jj!tj||f| j_nd| jjd<tj|}| j| jj|dddf|f<| j| jjz }t| dr@tj||f| j_| j| jj|dddf|f<t| dr"| j| j_| j| j_|| j_| j| j_| j| j_|| j_| | j_t| jdr`| jj d=| jj d=| jj d=| jj d}d|d<| j!||dddf|f<|| j_| S)aexperimental, fit the model subject to zero constraints Intended for internal use cases until we know what we need. API will need to change to handle models with two exog. This is not yet supported by all model subclasses. This is essentially a simplified version of `fit_constrained`, and does not need to use `offset`. The estimation creates a new model with transformed design matrix, exog, and converts the results back to the original parameterization. Some subclasses could use a more efficient calculation than using a new model. Parameters ---------- keep_index : array_like (int or bool) or slice variables that should be dropped. start_params : None or array_like starting values for the optimization. `start_params` needs to be given in the original parameter space and are internally transformed. k_params : int or None If None, then we try to infer from start_params or model. **fit_kwds : keyword arguments fit_kwds are used in the optimization of the transformed model. Returns ------- results : Results instance k_extrarT)copyrNrnmF)rrrrrrrrrnormalized_cov_params.cov_params_defaultrMresid fittedvaluessresid bcov_scaledr@)"rrrarrayr$rcarange concatenaterer=rr%rr8zerosr TypeErrorrGmodelr_resultsrrrdf_residrrr keep_indexdf_modelk_constrresults_constrained_cacher)r0rrreturn_auxiliaryk_paramsfit_kwdsk extra_index keep_index_p init_kwds mod_constr res_constr params_fullresrcovs r2 _fit_zeroszLikelihoodModel._fit_zerosfsH 4 # # & q(8(8*4888J "A)Aq4<'788K>:{*CDDLL%L  #'3L'AH^ $<((H'')) #T^DJ !!!Z-0H11&/11 #Z^//h// !  yq)H i33 3Hhx(( ","3 J ((11T,1 MMCC:&   ((**CCC  :#W - - J4>3C3I ICIOcl0 :} - - >'1'=CL $ :~ . . @(2(?CL %)  &=>> 8 2:138X:N1O1OCL . .67CL .s 3Xj))  , *:aaag+> +JK&)>> :3 4 4 ..0h(7K.L.LCL +- L +Jqqq$w,?,K L :z * * 8$.$7CL !$.$7CL !",  * 3  * 3  ( +5 ( 39c " " 2 #G, #N3 #H-,%m4CCH3=3IC 111d7#Z/ 0.1CL + s#D??%E'&E'+=vIh%<=c T|j}|||dzz}tj|d}tj|tj|k}tj|d}|j dd|i|S)aexperimental, fit of the model without collinear variables This currently uses QR to drop variables based on the given sequence. Options will be added in future, when the supporting functions to identify collinear variables become available. rr)moderr@) r$varrrqrabsdiagonalsqrtwherer) r0atolrtolr<rZtolrmaskidx_keeps r2_fit_collinearzLikelihoodModel._fit_collinears ITAEE!HH_$ ILLL % %vajjll##bgcll28TE??1%t;;(;d;;;r4r7) NrrTTr@NFF)NNFN)rr)rrrrr3rrrrrrrr __classcell__rs@r2rrs    " " """"$ " " """" ?BINHHHHT8<48KKKKZ<<<<<<<z3GenericLikelihoodModel.initialize..js=DL#A#Ar4Nrr) rrr$rr matrix_rankfloatrrcrnanrr)r0errs` r2rz!GenericLikelihoodModel.initializecs z AAAADJ< <  9 &&ty11B!"q&MMDM!$)/!"4r"9::DMMFDMFDM r4cL|j}|||j<|S)ag expand to full parameter array when some parameters are fixed Parameters ---------- params : ndarray reduced parameter array Returns ------- paramsfull : ndarray expanded parameter array where fixed parameters are included Notes ----- Calling this requires that self.fixed_params and self.fixed_paramsmask are defined. *developer notes:* This can be used in the log-likelihood to ... this could also be replaced by a more general parameter transformation. ) fixed_paramsrfixed_paramsmask)r0r paramsfulls r2 expandparamsz#GenericLikelihoodModel.expandparams}s+4&++-- ,2 4()r4c||jS)zReduce parameters)r(rs r2 reduceparamsz#GenericLikelihoodModel.reduceparamssd+,,r4cR||dS)z!Log-likelihood of model at paramsr loglikeobssumrs r2rzGenericLikelihoodModel.loglikes"v&&**1---r4cT||d S)z*Negative log-likelihood of model at paramsrr.rs r2nloglikezGenericLikelihoodModel.nloglikes%''++A....r4c.|| S)a: Log-likelihood of the model for all observations at params. Parameters ---------- params : array_like The parameters of the model. Returns ------- loglike : array_like The log likelihood of the model evaluated at `params`. ) nloglikeobsrs r2r/z!GenericLikelihoodModel.loglikeobss  ((((r4c|i}|ddt||jfi|S)z@ Gradient of log-likelihood evaluated at params centeredT)rrrravelr0rr<s r2rzGenericLikelihoodModel.scoresC  D)))VT\::T::@@BBBr4c T|ddt||jfi|S)zg Jacobian/Gradient of log-likelihood evaluated at params for each observation. r6T)rrr/r8s r2 score_obsz GenericLikelihoodModel.score_obss2  D)))VT_=====r4c0ddlm}|||jS)z? Hessian of log-likelihood evaluated at params r) approx_hess)statsmodels.tools.numdiffr<r)r0rr<s r2rzGenericLikelihoodModel.hessians, :99999{64<000r4Tct)aWeights for calculating Hessian Parameters ---------- params : ndarray parameter at which Hessian is evaluated scale : None or float If scale is None, then the default scale will be calculated. Default scale is defined by `self.scaletype` and set in fit. If scale is not None, then it is used as a fixed scale. observed : bool If True, then the observed Hessian is returned. If false then the expected information matrix is returned. Returns ------- hessian_factor : ndarray, 1d A 1d weight vector used in the calculation of the Hessian. The hessian is obtained by `(exog.T * hessian_factor).dot(exog)` r)r0rrobserveds r2hessian_factorz%GenericLikelihoodModel.hessian_factors ,"!r4rrrc |4t|dr|j}ndtj|jz}d|vrd|d<t j} | d ||||||d|} t|dt} | || } |j gn|j } t| t| j z }|dksN|dkr.| dt| Dntjd t | S) Nrg?r nonrobust)rrrrrr results_classrcg|]}d|zS)zpar%dr@r9rAs r2rCz.GenericLikelihoodModel.fit..s2.G.G.G23/6k.G.G.Gr4zmore exog_names than parametersr@)rrronesrrrr8GenericLikelihoodModelResultsr}rerrrangerErFr)r0rrrrrrrr1 fit_methodrrD genericmlefitr}k_missrs r2rzGenericLikelihoodModel.fitse  t^,, ;#0 "RWT\%:%:: V # #!,F: WW[ D#)7(3!%DD=CDD  o =?? % dF33 !O3RR$/ Z3v}#5#55{{zz,,.G.G7BBF======< , , ,4<---...///))) CCC>>>111""""0LM*+""""""""""r4rc4eZdZdZdZdZd dZd dZdZdS) Resultsz Class to contain model results Parameters ---------- model : class instance the previously specified model instance params : ndarray parameter estimates from the fit model c x|j||j||fi|g|_gd|_dS)N)rrwresid)rOrjrr*_data_in_cache)r0rrkwds r2r3zResults.__init__sO S!!!v-----AAAr4c ^||_||_t|dr|j|_dSdS)aA Initialize (possibly re-initialize) a Results instance. Parameters ---------- model : Model The model instance. params : ndarray The model parameters. **kwargs Any additional keyword arguments required to initialize the model. r)N)rrrr))r0rrr1s r2rzResults.initialize s<  5, ' ' /#.DOOO / /r4Tct|d}d}|r0|jdks|jjdkr|j}n |jjg}|rt |jdr|t|jddp|jj j }ddl m }t|tjrzt |drJt|jt r0|j|vrtj|}ntj|j}|j}t)|}t|t*} |||d }nV#t,$rI} d t!t!| } | | d} ~ wwxYw|t)|kr4|s2|t3jd t6n||}|j}|ot;j|}|jdkr<|jjjdks|jjj ddkr |dddf}t;j!|}||fS) NrSrrr r)dmatrixname dataframe) return_typezpredict requires that you use a DataFrame when predicting from a model that was created using the formula api. The original error message returned by patsy is: {}znan values have been dropped)"r rbrsizeindexrWrrr8r(r r]rVr^pdSeriesstrdescribe DataFramerrer ExceptionrdrrErFrreindexrasarrayr$rc atleast_2d) r0r$ transform is_pandas exog_indexr rV orig_exog_lenis_dictexcrKs r2_transform_predict_exogzResults._transform_predict_exog2sp$T400   /yA~~!1Q!6!6!Z "jo.  $Y77 $T=M"4:}dCC7:?6  % % % % % %$ ** (D&))0jC.H.H0 [%9%9%;%;;;<--DD<--/D!Z IIM t,,G )w{DkJJJ ) ) )#F3s3xx==11  mmC(((  )s4yy(((%M"@,OOOO<< 33DJ  :d##DyA~~4:?#71#<#<#':?#8#;q#@#@AAAtG}=&&DZsE F) AF$$F)Nc|||\}}|jj|j|g|Ri|}|Gt |ds7|jdkrt j||St j||S|S)a Call self.model.predict with self.params as the first argument. Parameters ---------- exog : array_like, optional The values for which you want to predict. see Notes below. transform : bool, optional If the model was fit via a formula, do you want to pass exog through the formula. Default is True. E.g., if you fit a model y ~ log(x1) + log(x2), and transform is True, then you can pass a data structure that contains x1 and x2 in their original form. Otherwise, you'd need to log the data first. *args Additional arguments to pass to the model, see the predict method of the model for the details. **kwargs Additional keywords arguments to pass to the model, see the predict method of the model for the details. Returns ------- array_like See self.model.predict. Notes ----- The types of exog that are supported depends on whether a formula was used in the specification of the model. If a formula was used, then exog is processed in the same way as the original data. This transformation needs to have key access to the same variable names, and can be a pandas DataFrame or a dict like object that contains numpy arrays. If no formula was used, then the provided exog needs to have the same number of columns as the original exog in the model. No transformation of the data is performed except converting it to a numpy array. Row indices as in pandas data frames are supported, and added to the returned prediction. )reNpredicted_valuesr)r[) rkrrrrrbr\r]r`)r0r$rermr1rgpredict_resultss r2rzResults.predictfsZ 77BK8MMj-$*,T[$7777/577  !'/2D+F+F !#q((y CCCC|O:FFFF" "r4ct)z2 Summary Not implemented rrvs r2summaryzResults.summaryrr4)TrM) rrrrr3rrkrrpr@r4r2rOrOsx  BBB///$2 2 2 2 h:#:#:#:#x"""""r4rOc8eZdZdZdfd ZdZ ddZed Zej d Ze d Z e d Z e d Z e dZ ddZd dZd dZ ddZ d!dZ d"dZd#dZd$dZd%dZedZdZxZS)&ra$ Class to contain results from likelihood models Parameters ---------- model : LikelihoodModel instance or subclass instance LikelihoodModelResults holds a reference to the model that is fit. params : 1d array_like parameter estimates from estimated model normalized_cov_params : 2d array Normalized (before scaling) covariance of params. (dot(X.T,X))**-1 scale : float For (some subset of models) scale will typically be the mean square error from the estimated model (sigma^2) Attributes ---------- mle_retvals : dict Contains the values returned from the chosen optimization method if full_output is True during the fit. Available only if the model is fit by maximum likelihood. See notes below for the output from the different methods. mle_settings : dict Contains the arguments passed to the chosen optimization method. Available if the model is fit by maximum likelihood. See LikelihoodModel.fit for more information. model : model instance LikelihoodResults contains a reference to the model that is fit. params : ndarray The parameters estimated for the model. scale : float The scaling factor of the model given during instantiation. tvalues : ndarray The t-values of the standard errors. Notes ----- The covariance of params is given by scale times normalized_cov_params. Return values by solver if full_output is True during fit: 'newton' fopt : float The value of the (negative) loglikelihood at its minimum. iterations : int Number of iterations performed. score : ndarray The score vector at the optimum. Hessian : ndarray The Hessian at the optimum. warnflag : int 1 if maxiter is exceeded. 0 if successful convergence. converged : bool True: converged. False: did not converge. allvecs : list List of solutions at each iteration. 'nm' fopt : float The value of the (negative) loglikelihood at its minimum. iterations : int Number of iterations performed. warnflag : int 1: Maximum number of function evaluations made. 2: Maximum number of iterations reached. converged : bool True: converged. False: did not converge. allvecs : list List of solutions at each iteration. 'bfgs' fopt : float Value of the (negative) loglikelihood at its minimum. gopt : float Value of gradient at minimum, which should be near 0. Hinv : ndarray value of the inverse Hessian matrix at minimum. Note that this is just an approximation and will often be different from the value of the analytic Hessian. fcalls : int Number of calls to loglike. gcalls : int Number of calls to gradient/score. warnflag : int 1: Maximum number of iterations exceeded. 2: Gradient and/or function calls are not changing. converged : bool True: converged. False: did not converge. allvecs : list Results at each iteration. 'lbfgs' fopt : float Value of the (negative) loglikelihood at its minimum. gopt : float Value of gradient at minimum, which should be near 0. fcalls : int Number of calls to loglike. warnflag : int Warning flag: - 0 if converged - 1 if too many function evaluations or too many iterations - 2 if stopped for another reason converged : bool True: converged. False: did not converge. 'powell' fopt : float Value of the (negative) loglikelihood at its minimum. direc : ndarray Current direction set. iterations : int Number of iterations performed. fcalls : int Number of calls to loglike. warnflag : int 1: Maximum number of function evaluations. 2: Maximum number of iterations. converged : bool True : converged. False: did not converge. allvecs : list Results at each iteration. 'cg' fopt : float Value of the (negative) loglikelihood at its minimum. fcalls : int Number of calls to loglike. gcalls : int Number of calls to gradient/score. warnflag : int 1: Maximum number of iterations exceeded. 2: Gradient and/ or function calls not changing. converged : bool True: converged. False: did not converge. allvecs : list Results at each iteration. 'ncg' fopt : float Value of the (negative) loglikelihood at its minimum. fcalls : int Number of calls to loglike. gcalls : int Number of calls to gradient/score. hcalls : int Number of calls to hessian. warnflag : int 1: Maximum number of iterations exceeded. converged : bool True: converged. False: did not converge. allvecs : list Results at each iteration. Nrc tt||||_||_d|_d|vr|d}||nd|_d|vrd|dd}|di}|dkrd|_ddi|_dSdd l m } |i}|j}| |f|d |d |dSdS) NFrrrCr descriptionWStandard Errors assume that the covariance matrix of the errors is correctly specified.rget_robustcov_resultsTruse_selfr) rr3rr_use_trr`rrstatsmodels.base.covtyperv) r0rrrrr1rrrrvrs r2r3zLikelihoodModelResults.__init__Js '''%:"   f  7OE"'"3DJ   zz*k::Hzz*b11H;&& + !.1.!/ KJJJJJ#!H %%d?X,1??5=????? r4ct)z"See specific model class docstringrrvs r2rz,LikelihoodModelResults.normalized_cov_paramshs!!r4rCTc |durtdddlm}|i}|dkrd|_ddi|_dS||f|d|d |dS) NFz8use_self should have been removed long ago. See GH#4401rrurCrsrtTrw)rGrzrvrr)r0rrxrrrvs r2_get_robustcov_resultsz-LikelihoodModelResults._get_robustcov_resultsls u  +,, ,BBBBBB  H { " "'DM*-*+DMMM " !$ ;D(- ; ;19 ; ; ; ; ;r4c|jS)z?Flag indicating to use the Student's distribution in inference.)ryrvs r2rzLikelihoodModelResults.use_t~s {r4c.t||_dSr7)boolry)r0values r2rzLikelihoodModelResults.use_ts5kk r4c@|j|jS)zLog-likelihood of model)rrrrvs r2llfzLikelihoodModelResults.llfsz!!$+...r4ct|ds?|j8tjt |j}tj|dd<n}tj5tj dttj tj | }dddn #1swxYwY|S)z/The standard errors of the parameter estimates.rNignore)rrremptyrerr$rEcatch_warnings simplefilterRuntimeWarningrr cov_params)r0bse_s r2bsezLikelihoodModelResults.bses344 ;+38C ,,--DfDGG(** ; ;%h???wrwt'8'899:: ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; s#ACC Cctj5tjdt|j|jz cdddS#1swxYwYdS)zH Return the t-statistic for a given parameter estimate. rN)rErrrrrrvs r2tvalueszLikelihoodModelResults.tvaluess  $ & & * *  !(N ; ; ;;) * * * * * * * * * * * * * * * * * *s)A  AActj5tjdt|jr\t |d|j}tj tj |j |dzcdddStj tj |j dzcdddS#1swxYwYdS)z6The two-tailed p values for the t-stats of the params.rdf_resid_inferencerSN)rErrrrr8rrtsfrr rnorm)r0rs r2pvalueszLikelihoodModelResults.pvaluess $ & & ? ?  !(N ; ; ;z ?"4)=t}MMwzz"&"6"6AAAE  ? ? ? ? ? ? ? ? z}}RVDL%9%9::Q>  ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?sA1C8CCCc t|dr|jddvrt}n tj}|&|jt|dst d|||t d||t d|+t|dr|j}n||j}|j|z}|=tj |}|j d kr |||fS||dddf|fS|qtj |}|j d krt d ||}ntj |}||||tj |}|S|S) a Compute the variance/covariance matrix. The variance/covariance matrix can be of a linear contrast of the estimated parameters or all params multiplied by scale which will usually be an estimate of sigma^2. Scale is assumed to be a scalar. Parameters ---------- r_matrix : array_like Can be 1d, or 2d. Can be used alone or with other. column : array_like, optional Must be used on its own. Can be 0d or 1d see below. scale : float, optional Can be specified or not. Default is None, which means that the scale argument is taken from the model. cov_p : ndarray, optional The covariance of the parameters. If not provided, this value is read from `self.normalized_cov_params` or `self.cov_params_default`. other : array_like, optional Can be used when r_matrix is specified. Returns ------- ndarray The covariance matrix of the parameter estimates or of linear combination of parameter estimates. See Notes. Notes ----- (The below are assumed to be in matrix notation.) If no argument is specified returns the covariance matrix of a model ``(scale)*(X.T X)^(-1)`` If contrast is specified it pre and post-multiplies as follows ``(scale) * r_matrix (X.T X)^(-1) r_matrix.T`` If contrast and other are specified returns ``(scale) * r_matrix (X.T X)^(-1) other.T`` If column is specified returns ``(scale) * (X.T X)^(-1)[column,column]`` if column is 0d OR ``(scale) * (X.T X)^(-1)[column][:,column]`` if column is 1d rrl1 l1_cvxopt_cpNrzFneed covariance of parameters for computing (unnormalized) covariancesz3Column should be specified without other arguments.z)other can only be specified with r_matrixr@zr_matrix should be 1d or 2d) rrrrrrrGrrrcrc transpose)r0r_matrixcolumnrcov_potherdot_funrns r2rz!LikelihoodModelResults.cov_paramssf D. ) ) !+.2HHHGGfG Md8@D"677A:;; ;  8#75;L*++ +  !1HII I =t122 ;/= JE2U:  Z''F|r!!VV^,,VAAAtG_f455  !z(++H~## !>???}  5))'(GGE2<3F3F$G$GHHCJLr4cddlm}t|ddd}|jjdkrd|jjjD}n|jjj}|||}|j |j }}|j d}|j d} |&|j t|d std |jd } | | j dkrtd|t!j|}n(t!j|}|}|jdkr |j d|krtd|t|do|j}t!j|| } |dkr>> import numpy as np >>> import statsmodels.api as sm >>> data = sm.datasets.longley.load() >>> data.exog = sm.add_constant(data.exog) >>> results = sm.OLS(data.endog, data.exog).fit() >>> r = np.zeros_like(results.params) >>> r[5:] = [1,-1] >>> print(r) [ 0. 0. 0. 0. 0. 1. -1.] r tests that the coefficients on the 5th and 6th independent variable are the same. >>> T_test = results.t_test(r) >>> print(T_test) Test for Constraints ============================================================================== coef std err t P>|t| [0.025 0.975] ------------------------------------------------------------------------------ c0 -1829.2026 455.391 -4.017 0.003 -2859.368 -799.037 ============================================================================== >>> T_test.effect -1829.2025687192481 >>> T_test.sd 455.39079425193762 >>> T_test.tvalue -4.0167754636411717 >>> T_test.pvalue 0.0015163772380899498 Alternatively, you can specify the hypothesis tests using a string >>> from statsmodels.formula.api import ols >>> dta = sm.datasets.longley.load_pandas().data >>> formula = 'TOTEMP ~ GNPDEFL + GNP + UNEMP + ARMED + POP + YEAR' >>> results = ols(formula, dta).fit() >>> hypotheses = 'GNPDEFL = GNP, UNEMP = 2, YEAR/1829 = 1' >>> t_test = results.t_test(hypotheses) >>> print(t_test) Test for Constraints ============================================================================== coef std err t P>|t| [0.025 0.975] ------------------------------------------------------------------------------ c0 15.0977 84.937 0.178 0.863 -177.042 207.238 c1 -2.0202 0.488 -8.231 0.000 -3.125 -0.915 c2 1.0001 0.249 0.000 1.000 0.437 1.563 ============================================================================== r DesignInforTstrictoptionalrSc6g|]}d|dd|dSyr_rr@rFs r2rCz1LikelihoodModelResults.t_test..i@999'1&&!&&999r4rNrz8Need covariance of parameters for computing T statisticsForderz#r_matrix and params are not aligned7r_matrix and q_matrix must have the same number of rowsrrr)effectrsddf_denomr)r statisticrr distribution)r]rrrrbrr( cov_nameslinear_constraintcoefs constantsrcrrrGr7rrrcsqueezerZrrrrrrr8rr )r0rrrrnamesLCq_matrix num_ttests num_paramsr_effect_sd_trs r2t_testzLikelihoodModelResults.t_test sr %$$$$$%EEE ; q 99"jo7999EEJO-E Z   0 0 : :Xr|(^A& ^A& Md8@D"677A,-- -"""-- a ( (BCC C  x ++HHz(++H''))H =1  ~a J.. "2333 =T7++: E&6** >>'"'$//!#2#0#01122CC'$//85/IIJJC F3KK /4!5t}EE  8"'RC,4666 6#'RC,406888 8r4c:||||dd}|S)a Compute the F-test for a joint linear hypothesis. This is a special case of `wald_test` that always uses the F distribution. Parameters ---------- r_matrix : {array_like, str, tuple} One of: - array : An r x k array where r is the number of restrictions to test and k is the number of regressors. It is assumed that the linear combination is equal to zero. - str : The full hypotheses to test can be given as a string. See the examples. - tuple : A tuple of arrays in the form (R, q), ``q`` can be either a scalar or a length k row vector. cov_p : array_like, optional An alternative estimate for the parameter covariance matrix. If None is given, self.normalized_cov_params is used. invcov : array_like, optional A q x q array to specify an inverse covariance matrix based on a restrictions matrix. Returns ------- ContrastResults The results for the test are attributes of this results instance. See Also -------- t_test : Perform a single hypothesis test. wald_test : Perform a Wald-test using a quadratic form. statsmodels.stats.contrast.ContrastResults : Test results. patsy.DesignInfo.linear_constraint : Specify a linear constraint. Notes ----- The matrix `r_matrix` is assumed to be non-singular. More precisely, r_matrix (pX pX.T) r_matrix.T is assumed invertible. Here, pX is the generalized inverse of the design matrix of the model. There can be problems in non-OLS models where the rank of the covariance of the noise is not full. Examples -------- >>> import numpy as np >>> import statsmodels.api as sm >>> data = sm.datasets.longley.load() >>> data.exog = sm.add_constant(data.exog) >>> results = sm.OLS(data.endog, data.exog).fit() >>> A = np.identity(len(results.params)) >>> A = A[1:,:] This tests that each coefficient is jointly statistically significantly different from zero. >>> print(results.f_test(A)) Compare this to >>> results.fvalue 330.2853392346658 >>> results.f_pvalue 4.98403096572e-10 >>> B = np.array(([0,0,1,-1,0,0,0],[0,0,0,0,0,1,-1])) This tests that the coefficient on the 2nd and 3rd regressors are equal and jointly that the coefficient on the 5th and 6th regressors are equal. >>> print(results.f_test(B)) 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) T)rinvcovuse_fscalar) wald_test)r0rrrrs r2f_testzLikelihoodModelResults.f_tests&znnXU6VZn[[ r4ct|ddd}t|ddd}|t|do|j}ddlm}|jjd krd |jjj D}n|jjj }|j d } || |} | j | j } }|j#|!|t|d stdt!j|| dddf} t%|jd} | t!j| } nt!j| } | jdkr,| dddf} | jd| krtd| | z }||||}t!j|rtdt j|}t j|}|| kr!t9jd| |fzt<|} ||} t|dr3|jddvr$tAtA|j!||}n-t!jt!j|j!||}tE|d|j#}|t9jdtHd}|r,|j%dkr!t%t!j&|}|r|| z}tO||| StO|| |d| fS)a Compute a Wald-test for a joint linear hypothesis. Parameters ---------- r_matrix : {array_like, str, tuple} One of: - array : An r x k array where r is the number of restrictions to test and k is the number of regressors. It is assumed that the linear combination is equal to zero. - str : The full hypotheses to test can be given as a string. See the examples. - tuple : A tuple of arrays in the form (R, q), ``q`` can be either a scalar or a length p row vector. cov_p : array_like, optional An alternative estimate for the parameter covariance matrix. If None is given, self.normalized_cov_params is used. invcov : array_like, optional A q x q array to specify an inverse covariance matrix based on a restrictions matrix. use_f : bool If True, then the F-distribution is used. If False, then the asymptotic distribution, chisquare is used. If use_f is None, then the F distribution is used if the model specifies that use_t is True. The test statistic is proportionally adjusted for the distribution by the number of constraints in the hypothesis. df_constraints : int, optional The number of constraints. If not provided the number of constraints is determined from r_matrix. scalar : bool, optional Flag indicating whether the Wald test statistic should be returned as a sclar float. The current behavior is to return an array. This will switch to a scalar float after 0.14 is released. To get the future behavior now, set scalar to True. To silence the warning and retain the legacy behavior, set scalar to False. Returns ------- ContrastResults The results for the test are attributes of this results instance. See Also -------- f_test : Perform an F tests on model parameters. t_test : Perform a single hypothesis test. statsmodels.stats.contrast.ContrastResults : Test results. patsy.DesignInfo.linear_constraint : Specify a linear constraint. Notes ----- The matrix `r_matrix` is assumed to be non-singular. More precisely, r_matrix (pX pX.T) r_matrix.T is assumed invertible. Here, pX is the generalized inverse of the design matrix of the model. There can be problems in non-OLS models where the rank of the covariance of the noise is not full. rTrrNrrrrSc6g|]}d|dd|dSrr@rFs r2rCz4LikelihoodModelResults.wald_test..Crr4rrrz8need covariance of parameters for computing F statisticsrrrzPr_matrix performs f_test for using dimensions that are asymptotically non-normalzbcovariance of constraints does not have full rank. The number of constraints is %d, but rank is %drrrrzThe behavior of wald_test will change after 0.14 to returning scalar test statistic values. To get the future behavior now, set scalar to True. To silence this message while retaining the legacy behavior, set scalar to False.F)rrdf_numchi2)rrrrdistargs)(rrrr]rrrbrr(rr7rrrrrGrrr#rcrrcrisnanmaxrpinvr"rErFrrrrr8r FutureWarningrZrr )r0rrrrdf_constraintsrrrrrrcparamsJRbqJ_rrs r2rz LikelihoodModelResults.wald_tests~%EEE68D4HHH =T7++: E$$$$$$ ; q 99"jo7999EEJO-E"""-- Z   0 0 : :Xr|(  & .5=wt5I'J'J,-- -&6!!!T'?33 (.# $ $  x{{HHz(++H =A  4(H~a A%% "2333  >OOXUOCCEx""$$ / ".///Y^^E**F&&u--BAvv +./W56BDDD  %A D. ) ) 3!+.2HHHv..44AArvceV,,c22A4!5t}EE > M<    F  %afkkbjmm$$A  G FA"Q*+--- -#A06!GGG Gr4Fcddlm}|}|g}|g}t|jjdd}||t dt jt|j }g} |t} ||j D]} | | } | } || }|D]!}|| vr| ||"|jd}|r|dkrm| | |fg}|D]1}||t j| |f2nt#|jjD]]\}} t j||}|D]!}|| vr| ||"|rF| | |f^g}|D]1}||t j| |f2|j}ddg|}g}g}| |z|zD]|\} }||| }|j|j|jdg}|r||j|||| }gd }|r|d dd lm}|||| }t7d|d|}| |z|z|_|S)a1 Compute a sequence of Wald tests for terms over multiple columns. This computes joined Wald tests for the hypothesis that all coefficients corresponding to a `term` are zero. `Terms` are defined by the underlying formula or by string matching. Parameters ---------- skip_single : bool If true, then terms that consist only of a single column and, therefore, refers only to a single parameter is skipped. If false, then all terms are included. extra_constraints : ndarray Additional constraints to test. Note that this input has not been tested. combine_terms : {list[str], None} Each string in this list is matched to the name of the terms or the name of the exogenous variables. All columns whose name includes that string are combined in one joint test. scalar : bool, optional Flag indicating whether the Wald test statistic should be returned as a sclar float. The current behavior is to return an array. This will switch to a scalar float after 0.14 is released. To get the future behavior now, set scalar to True. To silence the warning and retain the legacy behavior, set scalar to False. Returns ------- WaldTestResults The result instance contains `table` which is a pandas DataFrame with the test results: test statistic, degrees of freedom and pvalues. Examples -------- >>> res_ols = ols("np.log(Days+1) ~ C(Duration, Sum)*C(Weight, Sum)", data).fit() >>> res_ols.wald_test_terms() F P>F df constraint df denom Intercept 279.754525 2.37985521351e-22 1 51 C(Duration, Sum) 5.367071 0.0245738436636 1 51 C(Weight, Sum) 12.432445 3.99943118767e-05 2 51 C(Duration, Sum):C(Weight, Sum) 0.176002 0.83912310946 2 51 >>> res_poi = Poisson.from_formula("Days ~ C(Weight) * C(Duration)", data).fit(cov_type='HC0') >>> wt = res_poi.wald_test_terms(skip_single=False, combine_terms=['Duration', 'Weight']) >>> print(wt) chi2 P>chi2 df constraint Intercept 15.695625 7.43960374424e-05 1 C(Weight) 16.132616 0.000313940174705 2 C(Duration) 1.009147 0.315107378931 1 C(Weight):C(Duration) 0.216694 0.897315972824 2 Duration 11.187849 0.010752286833 3 Weight 30.263368 4.32586407145e-06 4 r) defaultdictNr zno constraints, nothing to dorrr)r)rpvalue df_constraintr)r`)r[rf)table) collectionsrr8rr(rGreyererr,termsslicerWr/rcvstack enumerater}rdrrrrrpandasr`r temp)r0 skip_singleextra_constraints combine_termsrrresultr identity constraintscombinedtermrprWconstraint_matrixcname k_constraintcombined_constraintsrqrrres_waldr[ constraintwtrow col_namesr`rrs r2wald_test_termsz&LikelihoodModelResults.wald_test_termss| ,+++++  $ "   Mfl/EE  #4#<<== =6#fm,,-- ;t$$  "#) > >"((..yy{{$,TN!+BBE}} ../@AAA06q9 !#q(( ""D*;#<====#% & Q Q$++UBIhuo4N4N,OPPPP Q'v|'>?? > > T$&M(3-$@$@!+BBE}} ../@AAA""D*;#<====#% & Q Q$++UBIhuo4N4N,OPPPP }U+  +.B BEV V   D*!!*V!<>> res = ols("np.log(Days+1) ~ C(Weight) + C(Duration)", data).fit() >>> pw = res.t_test_pairwise("C(Weight)") >>> pw.result_frame coef std err t P>|t| Conf. Int. Low 2-1 0.632315 0.230003 2.749157 8.028083e-03 0.171563 3-1 1.302555 0.230003 5.663201 5.331513e-07 0.841803 3-2 0.670240 0.230003 2.914044 5.119126e-03 0.209488 Conf. Int. Upp. pvalue-hs reject-hs 2-1 1.093067 0.010212 True 3-1 1.763307 0.000002 True 3-2 1.130992 0.010212 True )ralpha factor_labels)r )r0 term_namerrrrs r2r z&LikelihoodModelResults.t_test_pairwises)rdIfE,9;;; r4cdddlm}d}|||j|||}|S)aExperimental method for nonlinear prediction and tests 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 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. Returns ------- nl : instance of `NonlinearDeltaCov` with attributes and methods to calculate the results for the prediction or tests r)NonlinearDeltaCovN)deriv func_args)statsmodels.stats._delta_methodrrr)r0funcrrrnls r2_get_wald_nonlinearz*LikelihoodModelResults._get_wald_nonlinearUsT( FEEEEE  tT[$//2C2C%*iAAA r4c|j}|jr?tj}t |d|j}|d|dz z |}n'tj}|d|dz z }|j}|||zz }|||zz} |>tj dttj |}||}| |} tj t|| S)a Construct confidence interval for the fitted parameters. Parameters ---------- alpha : float, optional The significance level for the confidence interval. The default `alpha` = .05 returns a 95% confidence interval. cols : array_like, optional Specifies which confidence intervals to return. .. deprecated: 0.13 cols is deprecated and will be removed after 0.14 is released. cols only works when inputs are NumPy arrays and will fail when using pandas Series or DataFrames as input. You can subset the confidence intervals using slices. Returns ------- array_like Each row contains [lower, upper] limits of the confidence interval for the corresponding parameter. The first column contains all lower, the second column contains all upper limits. Notes ----- The confidence interval is based on the standard normal distribution if self.use_t is False. If self.use_t is True, then uses a Student's t with self.df_resid_inference (or self.df_resid if df_resid_inference is not defined) degrees of freedom. Examples -------- >>> import statsmodels.api as sm >>> data = sm.datasets.longley.load() >>> data.exog = sm.add_constant(data.exog) >>> results = sm.OLS(data.endog, data.exog).fit() >>> results.conf_int() array([[-5496529.48322745, -1467987.78596704], [ -177.02903529, 207.15277984], [ -0.1115811 , 0.03994274], [ -3.12506664, -0.91539297], [ -1.5179487 , -0.54850503], [ -0.56251721, 0.460309 ], [ 798.7875153 , 2859.51541392]]) >>> results.conf_int(cols=(2,3)) array([[-0.1115811 , 0.03994274], [-3.12506664, -0.91539297]]) rrrSNacols is deprecated and will be removed after 0.14 is released. cols only works when inputs are NumPy arrays and will fail when using pandas Series or DataFrames as input. Subsets of confidence intervals can be selected using slices of the full confidence interval array.)rrrrr8rppfrrrErFrrrcr) r0rrprdistrqrloweruppers r2conf_intzLikelihoodModelResults.conf_intpshh : (7Dt%94=IIHUQY11AA:DUQY''AS S    M9     :d##D$KE$KEz$ue,,---r4cVddlm}|r||||dS)ap Save a pickle of this instance. Parameters ---------- fname : {str, handle} A string filename or a file handle. remove_data : bool If False (default), then the instance is pickled without changes. If True, then all arrays with length nobs are set to None before pickling. See the remove_data method. In some cases not all arrays will be set to None. Notes ----- If remove_data is true and the model result does not implement a remove_data method then this will raise an exception. r) save_pickleN)statsmodels.iolib.smpickler  remove_data)r0fnamer r s r2savezLikelihoodModelResults.savesH( ;:::::         D%     r4c$ddlm}||S)a Load a pickled results instance .. warning:: Loading pickled models is not secure against erroneous or maliciously constructed data. Never unpickle data received from an untrusted or unauthenticated source. Parameters ---------- fname : {str, handle, pathlib.Path} A string filename or a file handle. Returns ------- Results The unpickled results instance. r) load_pickle)r r)rlrrs r2loadzLikelihoodModelResults.loads&, ;:::::{5!!!r4c |j}i t|D]3} t||}| |<$#t$rY0wxYw fd D}|D] }d|j|< d}dt |dgD}d|jjD}|j|z|zD]}||vr||||j D]$} d|j| <#ttf$rY!wxYwdS)a Remove data arrays, all nobs arrays from result and model. This reduces the size of the instance, so it can be pickled with less memory. Currently tested for use with predict from an unpickled results and model instance. .. warning:: Since data and some intermediate results have been removed calculating new statistics that require them will raise exceptions. The exception will occur the first time an attribute is accessed that has been set to None. Not fully tested for time series models, tsa, and might delete too much for prediction or not all that would be possible. The lists of arrays to delete are maintained as attributes of the result and model instance, except for cached values. These lists could be changed before calling remove_data. The attributes to remove are named in: model._data_attr : arrays attached to both the model instance and the results instance with the same attribute name. result._data_in_cache : arrays that may exist as values in result._cache result._data_attr_model : arrays attached to the model instance but not to the results instance cJg|]}t|t| Sr@)r^r)r9rZ cls_attrss r2rCz6LikelihoodModelResults.remove_data.. sB@@@A#IaL+>>@a@@@r4Nc|d}|d} tt|g|z}t ||rt ||ddSdS#t $rYdSwxYw)N.rT)splitr&rr8rrNAttributeError)objattpatt_obj_s r2wipez0LikelihoodModelResults.remove_data..wipe$ s #A5599D guqy114&&.D$-----..!    s:A** A87A8cg|]}d|zSzmodel.r@rFs r2rCz6LikelihoodModelResults.remove_data../ sRRRqhlRRRr4_data_attr_modelcg|]}d|zSr!r@rFs r2rCz6LikelihoodModelResults.remove_data..0 sBBBqhlBBBr4) rdirobject__getattribute__rrr8rr*rRrP) r0rlrWattr data_attrsr model_only model_attrrr:rs @r2r z"LikelihoodModelResults.remove_datasBn HH ' 'D '..sD99#' $"    @@@@@@@  % %D $DK     SRGD:Lb,Q,QRRR BBDJ,ABBB ?Z/*<  Cj   DsOOOO&  C #' C  "H-      s!> A  A  CC)(C))Nr)rCTN)NNNNNr)FNNN)rrNr7)rN)F)rrrrr3rr}rrsetterrrrrrrrrrrr rr rrrr rrs@r2rrsHX X z??????<"""EI%);;;;$X \""\"//\/  \ **\*??\?HL\\\\~L8L8L8L8\^^^^B6::>LGLGLGLG\DH37LLLL\=A&*;;;;z6M.M.M.M.^!!!!6""["0IIIIIIIr4rc0eZdZddddddddZeZdddZdS)LikelihoodResultsWrapperrfrowsr)rrrrrrr)rr N)rrr_attrs _wrap_attrs _wrap_methodsr@r4r2r-r-? sH!&FKMMMr4r-ceZdZedZedZedZedZedZedZ edZ edZ ed Z ddZ dZdS) ResultMixinct|jdd}t|dr?t|dr|j}nt|dr|j}nd}|j|z|zS|jjS)zModel WCrrrr)r!r)r8rrr)r!rrrZ)r0rr!s r2 df_modelwczResultMixin.df_modelwcV s $*i33 4 $ $ $t\** ?z** ==8+g5 5;# #r4c,d|jzd|jzzS)zAkaike information criterionrS)rr5rvs r2aiczResultMixin.aich sDH}qDO444r4cZd|jztj|j|jzzS)zBayesian information criterionr7)rrlogrr5rvs r2biczResultMixin.bicm s(DH}rvdi00DODDDr4c@|j|jS)z*cached Jacobian of log-likelihood )rr:rrvs r2 score_obsvzResultMixin.score_obsvr sz##DK000r4c@|j|jS)z)cached Hessian of log-likelihood )rrrrvs r2hessvzResultMixin.hessvx sz!!$+...r4c~|j}tjtj|j|S)zg covariance of parameters based on outer product of jacobian of log-likelihood )r=rrrrr)r0jacvs r2covjaczResultMixin.covjac~ s-y}}RVDFD11222r4c |j}|j}tj|}tj|tjtj|j||S)zcovariance of parameters based on HJJH dot product of Hessian, Jacobian, Jacobian, Hessian of likelihood name should be covhjh )r=r?rrrrr)r0rAr?hessinvs r2covjhjzResultMixin.covjhj sQ )--&&vgrvbfTVT&:&:GDDEEEr4cXtjtj|jS)zBstandard deviation of parameter estimates based on covHJH )rrrrErvs r2bsejhjzResultMixin.bsejhj wrwt{++,,,r4cXtjtj|jS)zBstandard deviation of parameter estimates based on covjac )rrrrBrvs r2bsejaczResultMixin.bsejac rHr4rrrrc g}t|jdrdnd}t|D]}tj|j|j}|j|j|ddf} nd} |j} |jj |j |fd| i| } |r3|jj D]&} t| | t|j| '| ||} || jtj|}|r||_|d|d|fS) a]simple bootstrap to get mean and variance of estimator see notes Parameters ---------- nrep : int number of bootstrap replications method : str optimization method to use disp : bool If true, then optimization prints results store : bool If true, then parameter estimates for all bootstrap iterations are attached in self.bootstrap_results Returns ------- mean : ndarray mean of parameter estimates over bootstrap replications std : ndarray standard deviation of parameter estimates over bootstrap replications Notes ----- This was mainly written to compare estimators of the standard errors of the parameter estimates. It uses independent random sampling from the original endog and exog, and therefore is only correct if observations are independently distributed. This will be moved to apply only to models with independently distributed observations. cloneattrTF)rZNr$)rrr)rrrIrrandomrandintrr$r=rr%rLrNr8rr/rrbootstrap_resultsmeanstd)r0nreprrstoreresults hascloneattrrArvsind exog_resamprfitmodr'fitress r2 bootstrapzResultMixin.bootstrap stF&tz;??JttU t * *AY&&tyty&AAFy$"i 2 "  1133I)TZ)$*V*<II/:I>GIIF E J0EEDFD'$*d*C*CDDDDZZvDZ99F NN6= ) ) ) )(7##  -%,D "||A A77r4ct)z< get_nlfun This is not Implemented r)r0funs r2 get_nlfunzResultMixin.get_nlfun s "!r4N)rrrr)rrrrr5r8r;r=r?rBrErGrJrZr]r@r4r2r3r3T s/$$^$"55^5EE^E11^1 //^/  3 3^ 3 F F^ F--^- --^- :8:8:8:8x"""""r4r3cdeZdZdZd dZedZedZd dZed Z dS) _LLRMixinz4Mixin class for Null model and likelihood ratio mcfc.|}|drd|j|jz z }nX|ds|dvr0dt j|j|jz d|jz zz }ntd|S)zC McFadden's pseudo-R-squared. `1 - (llf / llnull)` r`rcox)cslrrSz)only McFadden and Cox-Snell are available)r startswithrllnullrexprrG)r0kindprsqs r2pseudo_rsquaredz_LLRMixin.pseudo_rsquared szz|| ??5 ! ! Jtx$+--DD __U # # Jt|';';rvt{TX5!di-HIIIDDHII I r4c&d|j|jz zS)zM Likelihood ratio chi-squared statistic; `-2*(llnull - llf)` r7)rfrrvs r2llrz _LLRMixin.llr s 4;)**r4c|j}|j}|j}||z }||_tjj||S)z The chi-squared probability of getting a log-likelihood ratio statistic greater than llr. llr has a chi-squared distribution with degrees of freedom `df_model`. )rlr df_resid_null df_lr_nullr distributionsrr)r0rldf_fulldf_restrlrdfs r2 llr_pvaluez_LLRMixin.llr_pvalue sGh-%7""'**3555r4NTc 6|jdd|jdd|jdd|jddt|dr|`| ||jd<||_||_dS)a Set the fit options for the Null (constant-only) model. This resets the cache for related attributes which is potentially fragile. This only sets the option, the null model is estimated when llnull is accessed, if llnull is not yet in cache. Parameters ---------- llnull : {None, float} If llnull is not None, then the value will be directly assigned to the cached attribute "llnull". attach_results : bool Sets an internal flag whether the results instance of the null model should be attached. By default without calling this method, thenull model results are not attached and only the loglikelihood value llnull is stored. **kwargs Additional keyword arguments used as fit keyword arguments for the null model. The override and model default values. Notes ----- Modifies attributes of this instance, and so has no return. rfNrlrt prsquaredres_null)rr&rrw_attach_nullmodel_optim_kwds_null)r0rfattach_resultsr1s r2set_null_optionsz_LLRMixin.set_null_options s: $''' t$$$  d+++  T*** 4 $ $   $*DK !!/ &r4c|j}|}t|dgD]}||=|j|jt j|jfi|}t|di}d|vr| d}n't|dr| }nd}tdddd }| ||r|jdd|i|}n9||d ddd }||jdddd }t|d ddur||_t#|j|_|j|_|jS)z: Value of the constant-only loglikelihood _null_drop_keysryr_get_start_params_nullNbfgsFi'r)rrrrr)rrrrrrxr@)rr=rr8rr%rrGrr&rr~rrjrrrwrek_nullrrnr) r0rr<r:mod_null optim_kwdssp_nullopt_kwdsrws r2rfz_LLRMixin.llnull= s  ##%%**,,5"3R88  CS "5?5; 0B0BKKdKK T#5r::??AA Z ' ' nn^44GG U4 5 5 2244GGGvu    ###  ;#x|EEEHEEHH ||5:,1$;;H ||5:,1$;;H 4,e 4 4E A A$DM(/** %.|r4)r`rM) rrrrrjrrlrtr{rfr@r4r2r_r_ s    ++^+  6 6^ 6''''''''R--^---r4r_c4eZdZdZdZ d dZd d ZdS) rHa A results class for the discrete dependent variable models. ..Warning : The following description has not been updated to this version/class. Where are AIC, BIC, ....? docstring looks like copy from discretemod Parameters ---------- model : A DiscreteModel instance mlefit : instance of LikelihoodResults This contains the numerical optimization results as returned by LikelihoodModel.fit(), in a superclass of GnericLikelihoodModels Attributes ---------- aic : float Akaike information criterion. -2*(`llf` - p) where p is the number of regressors including the intercept. bic : float Bayesian information criterion. -2*`llf` + ln(`nobs`)*p where p is the number of regressors including the intercept. bse : ndarray The standard errors of the coefficients. df_resid : float See model definition. df_model : float See model definition. fitted_values : ndarray Linear predictor XB. llf : float Value of the loglikelihood llnull : float Value of the constant-only loglikelihood llr : float Likelihood ratio chi-squared statistic; -2*(`llnull` - `llf`) llr_pvalue : float The chi-squared probability of getting a log-likelihood ratio statistic greater than llr. llr has a chi-squared distribution with degrees of freedom `df_model`. prsquared : float McFadden's pseudo-R-squared. 1 - (`llf`/`llnull`) cz||_|j|_|j|_|jjd|_t |jdd}t |dr&tj|j s |j |_ n7t|j |jj z |z }||_ ||j_ t |dr&tj|j s |j |_ n3|jjd|j z |z |_ |j |j_ i|_|j|jt|j }|j |jj z|z|krt#jdt&|j |j|z krt#jddSdS)Nrrrrz5df_model + k_constant + k_extra differs from k_paramsz%df_resid differs from nobs - k_params)rr%r$rcrr8rrrrrerr)rrrOrjrErF UserWarning)r0rrrrrs r2r3z&GenericLikelihoodModelResults.__init__ s [ J K%a( $*i33 5* % % +bhu~.F.F +!NDMM6=))DJ,AAGKH$DM"*DJ  5* % % 0bhu~.F.F 0!NDMM J,Q/$-?'IDM"&-DJ   V_---v}%% =4:0 07 :h F F M23> @ @ @ =DI0 0 0 MA B B B B B 1 0r4NrPTFc <ddlm}|} ||||||||| } | S)a Compute prediction results when endpoint transformation is valid. Parameters ---------- exog : array_like, optional The values for which you want to predict. transform : bool, optional If the model was fit via a formula, do you want to pass exog through the formula. Default is True. E.g., if you fit a model y ~ log(x1) + log(x2), and transform is True, then you can pass a data structure that contains x1 and x2 in their original form. Otherwise, you'd need to log the data first. which : str Which statistic is to be predicted. Default is "mean". The available statistics and options depend on the model. see the model.predict docstring row_labels : list of str or None If row_lables are provided, then they will replace the generated labels. average : bool If average is True, then the mean prediction is computed, that is, predictions are computed for individual exog and then the average over observation is used. If average is False, then the results are the predictions for all observations, i.e. same length as ``exog``. agg_weights : ndarray, optional Aggregation weights, only used if average is True. The weights are not normalized. **kwargs : Some models can take additional keyword arguments, such as offset, exposure or additional exog in multi-part models like zero inflated models. See the predict method of the model for the details. Returns ------- prediction_results : PredictionResults The prediction results instance contains prediction and prediction variance and can on demand calculate confidence intervals and summary dataframe for the prediction. Notes ----- Status: new in 0.14, experimental r)get_prediction)r$whichre row_labelsaverage agg_weights pred_kwds)&statsmodels.base._prediction_inferencer) r0r$rrerrrr1rrrs r2rz,GenericLikelihoodModelResults.get_prediction sRr JIIIII n !#    r4rcddddgfddddd g}d d d |jzgfd d |jzgfg}||jjjdzdz}ddlm}|}|||||||||||||j |S)a,Summarize the Regression Results Parameters ---------- yname : str, optional Default is `y` xname : list[str], optional Names for the exogenous variables, default is "var_xx". Must match the number of parameters in the model title : str, optional Title for the top table. If not None, then this replaces the default title alpha : float significance level for the confidence intervals Returns ------- smry : Summary instance this holds the summary tables and text, which can be printed or converted to various output formats. See Also -------- statsmodels.iolib.summary.Summary : class to hold summary results )zDep. Variable:N)zModel:NzMethod:zMaximum Likelihood)zDate:N)zTime:N)zNo. Observations:N)z Df Residuals:N)z Df Model:N)zLog-Likelihood:NzAIC:z%#8.4gzBIC:N rOr)Summary)gleftgrightynamexnametitle)rrrr) r8r;rrrstatsmodels.iolib.summaryradd_table_2colsadd_table_paramsr) r0rrrrtop_left top_rightrsmrys r2rpz%GenericLikelihoodModelResults.summary s6-$!5 67##/+'/x$(234x$(234 =J(1C7)CE 655555wyy T)#(U  D D D d%uE$(J  0 0 0 r4)NrPTNFN)NNNr)rrrrr3rrpr@r4r2rHrHn ss,,\#C#C#CNGGGGR555555r4rH): __future__rstatsmodels.compat.pythonr functoolsrrEnumpyrrr\scipyrstatsmodels.base.datarstatsmodels.base.optimizerrstatsmodels.base.wrapperbasewrapperwrapstatsmodels.formular statsmodels.stats.contrastr r r statsmodels.tools.datar statsmodels.tools.decoratorsrrrr=rrrrstatsmodels.tools.toolsrrstatsmodels.tools.validationrrrrrrrrrOrResultsWrapperr-populate_wrapperr3r_rHr@r4r2rs""""""******------000000'''''''''333333 433333 433333433333332222223> F"F"F"F"F"F"F"F"R|<|<|<|<|