M/PhFWBdZddlZddlmZddlmcmZddlmcm Z ddl m cm Zddlm cmZddlmcmZddlmcmZddlmZddlmZdgZdZGddejZGdd ejZ Gd d ej!Z"e j#e"e dS) a Robust linear models with support for the M-estimators listed under :ref:`norms `. References ---------- PJ Huber. 'Robust Statistics' John Wiley and Sons, Inc., New York. 1981. PJ Huber. 1973, 'The 1972 Wald Memorial Lectures: Robust Regression: Asymptotics, Conjectures, and Monte Carlo.' The Annals of Statistics, 1.5, 799-821. R Venables, B Ripley. 'Modern Applied Statistics in S' Springer, New York, 2002. N)cache_readonly)ConvergenceWarningRLMctj||||dz z }tj||ko||k S)N)npabsany) criterion iterationtolmaxiterconds f/var/www/html/test/jupyter/venv/lib/python3.11/site-packages/statsmodels/robust/robust_linear_model.py_check_convergencersE 6)I&9q=)AA B BDtcz"":y7': ;;ceZdZdejejZdfd ZdZ dZ dZ dd Z d Z d Zd Zd Z ddZxZS)raE Robust Linear Model Estimate a robust linear model via iteratively reweighted least squares given a robust criterion estimator. {params} M : statsmodels.robust.norms.RobustNorm, optional The robust criterion function for downweighting outliers. The current options are LeastSquares, HuberT, RamsayE, AndrewWave, TrimmedMean, Hampel, and TukeyBiweight. The default is HuberT(). See statsmodels.robust.norms for more information. {extra_params} Attributes ---------- df_model : float The degrees of freedom of the model. The number of regressors p less one for the intercept. Note that the reported model degrees of freedom does not count the intercept as a regressor, though the model is assumed to have an intercept. df_resid : float The residual degrees of freedom. The number of observations n less the number of regressors p. Note that here p does include the intercept as using a degree of freedom. endog : ndarray See above. Note that endog is a reference to the data so that if data is already an array and it is changed, then `endog` changes as well. exog : ndarray See above. Note that endog is a reference to the data so that if data is already an array and it is changed, then `endog` changes as well. M : statsmodels.robust.norms.RobustNorm See above. Robust estimator instance instantiated. nobs : float The number of observations n pinv_wexog : ndarray The pseudoinverse of the design / exogenous data array. Note that RLM has no whiten method, so this is just the pseudo inverse of the design. normalized_cov_params : ndarray The p x p normalized covariance of the design / exogenous data. This is approximately equal to (X.T X)^(-1) Examples -------- >>> import statsmodels.api as sm >>> data = sm.datasets.stackloss.load() >>> data.exog = sm.add_constant(data.exog) >>> rlm_model = sm.RLM(data.endog, data.exog, M=sm.robust.norms.HuberT()) >>> rlm_results = rlm_model.fit() >>> rlm_results.params array([ 0.82938433, 0.92606597, -0.12784672, -41.02649835]) >>> rlm_results.bse array([ 0.11100521, 0.30293016, 0.12864961, 9.79189854]) >>> rlm_results_HC2 = rlm_model.fit(cov="H2") >>> rlm_results_HC2.params array([ 0.82938433, 0.92606597, -0.12784672, -41.02649835]) >>> rlm_results_HC2.bse array([ 0.11945975, 0.32235497, 0.11796313, 9.08950419]) >>> mod = sm.RLM(data.endog, data.exog, M=sm.robust.norms.Hampel()) >>> rlm_hamp_hub = mod.fit(scale_est=sm.robust.scale.HuberScale()) >>> rlm_hamp_hub.params array([ 0.73175452, 1.25082038, -0.14794399, -40.27122257]) )params extra_paramsNnonec ||||ntj|_t t j|j||fd|i|||j ddgdS)Nmissingweights pinv_wexog) _check_kwargsnormsHuberTMsuperbaseLikelihoodModel__init__ _initialize _data_attrextend)selfendogexogrrkwargs __class__s rr"z RLM.__init__ms 6"""m2d"D))25$ N N;B NFL N N N   <899999rctj|j|_tj|jtj|j|_t|jj dtj |jz |_ ttj |jdz |_ t|j j d|_dS)zo Initializes the model for the IRLS fit. Resets the history and number of iterations. rrN)rlinalgpinvr(rdot transposenormalized_cov_paramsfloatshape matrix_rankdf_residdf_modelr'nobsr&s rr#zRLM._initializews )..33%'VDO,.L,I,I&K&K"tyq1!y44TY?? @AA bi33DI>>BCC $**1-.. rctNNotImplementedErrorr&rs rscorez RLM.score!!rctr9r:r<s r informationzRLM.informationr>rc>||j}tj||S)a[ Return linear predicted values from a design matrix. Parameters ---------- params : array_like Parameters of a linear model exog : array_like, optional. Design / exogenous data. Model exog is used if None. Returns ------- An array of fitted values )r(rr.)r&rr(s rpredictz RLM.predicts" <9DvdF###rctr9r:r<s rloglikez RLM.logliker>rc~|j|jz }|||jz S)zQ Returns the (unnormalized) log-likelihood from the M estimator. )r' fittedvaluesrscalesum)r& tmp_results tmp_resids rdeviancez RLM.deviances9J!99 vvi+"334488:::rc|d|j|d|j|dkr/|d||nZ|dkr)|d|j|jz n+|dkr%|d|jj|S)NrrGdevrKsresidr)appendrrGrKresidmodelr)r&rIhistoryconvs r_update_historyzRLM._update_historys  !3444 1222 5== J  & &t}}['A'A B B B B X   H  $ $[%69J%J K K K K Y   I  % %k&7&? @ @ @rczt|jtrJ|jdkrt j|dSt d|jzt|jtjr!||j|j |St j||dzS)zU Estimates the scale based on the option provided to the fit method. madr)centerz&Option %s for scale_est not understood) isinstance scale_eststrlowerrGrV ValueError HuberScaler4r6)r&rPs r_estimate_scalezRLM._estimate_scales dnc * * 5~##%%..yq1111 !I!%"0111 (8 9 9 5>>$-EBB B?4//14 4r2:0yE>rVH1TrMc |dvrtd|z||_|}|dvrtd|z||_|2t j|j|j } ntj |tj  }|jd|jjdks |jdkr2td |jjdt#j|j|jtj|jd } | |} |s|| j|_t1tjgg } |d kr | d} n|dkr7| t1tjg| d} ny|dkr7| t1tjg| d} n<|dkr6| t1tjg| d} || | |} d} d}|s|jdkr ddl}|dt<n|j | j|jz |_ t#j|j|j|j d  } |dur|| j|_|| | |} | dz } tC| | ||}|tE|| j#|j$|j}| | d<| |_%t1|||jj&j'||_(tS|S)a Fits the model using iteratively reweighted least squares. The IRLS routine runs until the specified objective converges to `tol` or `maxiter` has been reached. Parameters ---------- conv : str Indicates the convergence criteria. Available options are "coefs" (the coefficients), "weights" (the weights in the iteration), "sresid" (the standardized residuals), and "dev" (the un-normalized log-likelihood for the M estimator). The default is "dev". cov : str, optional 'H1', 'H2', or 'H3' Indicates how the covariance matrix is estimated. Default is 'H1'. See rlm.RLMResults for more information. init : str Specifies method for the initial estimates of the parameters. Default is None, which means that the least squares estimate is used. Currently it is the only available choice. maxiter : int The maximum number of iterations to try. Default is 50. scale_est : str or HuberScale() 'mad' or HuberScale() Indicates the estimate to use for scaling the weights in the IRLS. The default is 'mad' (median absolute deviation. Other options are 'HuberScale' for Huber's proposal 2. Huber's proposal 2 has optional keyword arguments d, tol, and maxiter for specifying the tuning constant, the convergence tolerance, and the maximum number of iterations. See statsmodels.robust.scale for more information. tol : float The convergence tolerance of the estimate. Default is 1e-8. update_scale : Bool If `update_scale` is False then the scale estimate for the weights is held constant over the iteration. Otherwise, it is updated for each fit in the iteration. Default is True. start_params : array_like, optional Initial guess of the solution of the optimizer. If not provided, the initial parameters are computed using OLS. Returns ------- results : statsmodels.rlm.RLMresults Results instance )rbH2H3z#Covariance matrix %s not understood)rcoefsrMrNz&Convergence argument %s not understoodN)dtyperrz/start_params must by a 1-d array with {} valuesF)r check_weights)rrGrfrrM)rKrKrN)rNr)rzkEstimated scale is 0.0 indicating that the most last iteration produced a perfect fit of the weighted data.Tr )covrZnormrS)*upperr]rjr\rZlmWLSr'r(fitrasarraydoublesqueezer2ndimformat reg_tools _MinimalWLS ones_likeresultsr_rPrGdictinfupdaterTwarningswarnrrrr RLMResultsrr0 fit_historyr*__name__ fit_optionsRLMResultsWrapper)r&rr rZinitrj update_scalerS start_params wls_resultsfake_wlsrRr r convergedr|rxs rrozRLM.fitsb 99;;0 0 0BSHII Iyy{{DHzz|| < < <ELMM M"  &TY77;;==KK:l")DDDLLNNL"1%);;; %** "**0&1C*D*DFFF ,TZ57\$*5M5M;@BBBH#**<88K A--k.?@@DJrvhb111 7??)II U]] NN4"&222 3 3 3 +II X   NN4x000 1 1 1)II Y   NN4111 2 2 2 *I&&{GTBB   OzS   /0BDDD6>>+*;dj*HIIDL#/ DI8< >BDDDDGCEE t##!11+2CDD **;FFG NI*9igNNI O T;#5!7EE ) %"syy{{i(,(8(ANNN!)))r)Nrr9)r`rarVNrbTrMN)r __module__ __qualname__rtr _model_params_doc_missing_param_doc__doc__r"r#r=r@rBrDrKrTr_ro __classcell__r*s@rrr$sDH %D4K   I P:::::: / / /""""""$$$$(""";;;    5 5 5IM8<w*w*w*w*w*w*w*w*rceZdZdZfdZedZedZedZedZ edZ edZ ed Z ed Z ed Z ddZ ddZxZS)r~a Class to contain RLM results Attributes ---------- bcov_scaled : ndarray p x p scaled covariance matrix specified in the model fit method. The default is H1. H1 is defined as ``k**2 * (1/df_resid*sum(M.psi(sresid)**2)*scale**2)/ ((1/nobs*sum(M.psi_deriv(sresid)))**2) * (X.T X)^(-1)`` where ``k = 1 + (df_model +1)/nobs * var_psiprime/m**2`` where ``m = mean(M.psi_deriv(sresid))`` and ``var_psiprime = var(M.psi_deriv(sresid))`` H2 is defined as ``k * (1/df_resid) * sum(M.psi(sresid)**2) *scale**2/ ((1/nobs)*sum(M.psi_deriv(sresid)))*W_inv`` H3 is defined as ``1/k * (1/df_resid * sum(M.psi(sresid)**2)*scale**2 * (W_inv X.T X W_inv))`` where `k` is defined as above and ``W_inv = (M.psi_deriv(sresid) exog.T exog)^(-1)`` See the technical documentation for cleaner formulae. bcov_unscaled : ndarray The usual p x p covariance matrix with scale set equal to 1. It is then just equivalent to normalized_cov_params. bse : ndarray An array of the standard errors of the parameters. The standard errors are taken from the robust covariance matrix specified in the argument to fit. chisq : ndarray An array of the chi-squared values of the parameter estimates. df_model See RLM.df_model df_resid See RLM.df_resid fit_history : dict Contains information about the iterations. Its keys are `deviance`, `params`, `iteration` and the convergence criteria specified in `RLM.fit`, if different from `deviance` or `params`. fit_options : dict Contains the options given to fit. fittedvalues : ndarray The linear predicted values. dot(exog, params) model : statsmodels.rlm.RLM A reference to the model instance nobs : float The number of observations n normalized_cov_params : ndarray See RLM.normalized_cov_params params : ndarray The coefficients of the fitted model pinv_wexog : ndarray See RLM.pinv_wexog pvalues : ndarray The p values associated with `tvalues`. Note that `tvalues` are assumed to be distributed standard normal rather than Student's t. resid : ndarray The residuals of the fitted model. endog - fittedvalues scale : float The type of scale is determined in the arguments to the fit method in RLM. The reported scale is taken from the residuals of the weighted least squares in the last IRLS iteration if update_scale is True. If update_scale is False, then it is the scale given by the first OLS fit before the IRLS iterations. sresid : ndarray The scaled residuals. tvalues : ndarray The "t-statistics" of params. These are defined as params/bse where bse are taken from the robust covariance matrix specified in the argument to fit. weights : ndarray The reported weights are determined by passing the scaled residuals from the last weighted least squares fit in the IRLS algorithm. See Also -------- statsmodels.base.model.LikelihoodModelResults ct||||||_|j|_|j|_|j|_i|_|jdg|j |_ dS)NrN) rr"rQr5r4r6_cache_data_in_cacher% bcov_scaledcov_params_default)r&rQrr0rGr*s rr"zRLMResults.__init__su (=uEEE   J   ""H:..."&"2rcJtj|jj|jSr9)rr.rQr(rr7s rrFzRLMResults.fittedvaluessvdjot{333rc*|jj|jz Sr9)rQr'rFr7s rrPzRLMResults.residsz$"333rcz|jdkr"|j}d|dd<|S|j|jz S)Nri)rGrPcopy)r&rNs rrNzRLMResults.sresidsA :  Z__&&FF111IMzDJ&&rc|jSr9)r0r7s r bcov_unscaledzRLMResults.bcov_unscaleds ))rc|jjSr9)rQrr7s rrzRLMResults.weightss z!!rc |j}tj|j|j}tj|j|j}d|jdz|jz |z|dzz z}|j dkrtj |j |jdz}tj |j|j}|dzd|j z |z|j dzzzd|jz |zdzz |jzStj|j|j|jjz|j}tj|}|j dkr|d|j z ztj |j |jdzz|j dzzd|jz tj |j|jzz |zS|j dkr|dzdz|j z tj |j |jdzz|j dzztjtj|tj|jj|j|zSdS)NrrXrbrdre)rQrmeanr psi_derivrNvarr5r6rjrHpsir4rGr0r.r(Tr,inv) r&rQm var_psiprimekss_psi s_psi_derivWW_invs rrzRLMResults.bcov_scaleds  GEG%%dk22 3 3veg// <<== "di/,>aG G 9  VEGKK 449::F&!2!24;!?!?@@K6Q.7$*/IJdi-+-!35+, ,uw((55 Dz##AIMM!$$EyD  A -.GKK ,,12323359Z1_Ety=&!2!24;!?!?@@ABEJJJd""Bw{T]2RVGKK ,,16363359Z1_EF5"&uz"B"BCC#"rcttjtj|jdzSNrX)statsrksfrr tvaluesr7s rpvalueszRLMResults.pvaluess'z}}RVDL1122Q66rcXtjtj|jSr9)rsqrtdiagrr7s rbsezRLMResults.bseswrwt/00111rc&|j|jz dzSr)rrr7s rchisqzRLMResults.chisqs dh&1,,rNr皙?textc ddddgfd|jdgfd|jdgfd |jd gfd d d d|jdzgfg }gd}|d}ddlm}|} | ||||||| |||||jg} d} | | | r| | | S)z; This is for testing the new summary setup )zDep. Variable:N)zModel:NzMethod:IRLSzNorm:rkz Scale Est.:rZz Cov Type:rj)zDate:N)zTime:NzNo. Iterations:z%dr ))zNo. Observations:N)z Df Residuals:N)z Df Model:NNz&Robust linear Model Regression Resultsr)Summary)gleftgrightynamexnametitle)rralphause_tzIf the model instance has been used for another fit with different fit parameters, then the fit options might not be the correct ones anymore .) rrstatsmodels.iolib.summaryradd_table_2colsadd_table_paramsrrO add_extra_txt) r&rrrr return_fmttop_left top_rightrsmryetextwstrs rsummaryzRLMResults.summarysI -$)t/789"T%5k%B$CD 4#3E#:";<##&0@0M)M(NO   77^722^2--^->A!))))VBE$########rr~ceZdZdS)rN)rrrrrrr5sDrr)$rnumpyr scipy.statsrstatsmodels.base.modelr rQstatsmodels.base.wrapperwrapperwrapstatsmodels.regression._tools regression_toolsru#statsmodels.regression.linear_model linear_modelrmstatsmodels.robust.normsrobustrstatsmodels.robust.scalerGstatsmodels.tools.decoratorsrstatsmodels.tools.sm_exceptionsr__all__rr!rLikelihoodModelResultsr~RegressionResultsWrapperrpopulate_wrapperrrrrs%%%%%%%%%'''''''''111111111000000000((((((((((((((((((777777>>>>>> '<<< V*V*V*V*V*$ V*V*V*ruuuuu,uuup     3   '44444r