p7]c@sdZddlZddljZddlmZddljj Z ddl jj Z ddljjZddljjZddljjZddljjZdgZdZdejfdYZdejfdYZd e jfd YZ ej!e ee"d krddl#j$Z%ej&d d ddddddddddddddddddd d!d"d#d$gZ'ej&d%d&d&d'd(d%d)d%d*d+d,d-d'd(d.d-d(d%d&d/d-d0d.d1d'gd2d3d4d5d6d7d8d9d:d;d<d=d>d?d@dAdBdCdDdEdFdGdHdId6ggZ(e(j)Z(e%j*e(Z(ddJl+m,Z,e,dKe-Z.e%j*e.j(e._(ee.j'e.j(dLej/Z0e0j1dMej2Z3ndS(Ns 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. iN(tcache_readonlytRLMcCs9tjtj||||d|ko7||k S(Ni(tnptanytfabs(t criteriont iterationttoltmaxiter((sElib/python2.7/site-packages/statsmodels/robust/robust_linear_model.pyt_check_convergencescBseZdiejd6ejd6ZdddZdZdZ dZ ddZ d Z d Z d Zd Zd ddddeddZRS(sR Robust Linear Models Estimate a robust linear model via iteratively reweighted least squares given a robust criterion estimator. %(params)s 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)s 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 : array 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 : array 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 : array 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 : array 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(as_pandas=False) >>> 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]) tparamst extra_paramstnonecKsj|dk r|n tj|_ttj|j||d|||j|j j ddgdS(Ntmissingtweightst pinv_wexog( tNonetnormstHuberTtMtsupertbasetLikelihoodModelt__init__t _initializet _data_attrtextend(tselftendogtexogRR tkwargs((sElib/python2.7/site-packages/statsmodels/robust/robust_linear_model.pyRls !  cCstjj|j|_tj|jtj|j|_tj|jj dtjj |j|_ tjtjj |jd|_ t|j j d|_dS(so Initializes the model for the IRLS fit. Resets the history and number of iterations. iiN(RtlinalgtpinvRRtdott transposetnormalized_cov_paramstfloattshapet matrix_ranktdf_residtdf_modelRtnobs(R((sElib/python2.7/site-packages/statsmodels/robust/robust_linear_model.pyRus %cCs tdS(N(tNotImplementedError(RR ((sElib/python2.7/site-packages/statsmodels/robust/robust_linear_model.pytscorescCs tdS(N(R*(RR ((sElib/python2.7/site-packages/statsmodels/robust/robust_linear_model.pyt informationscCs(|dkr|j}ntj||S(s Return linear predicted values from a design matrix. Parameters ---------- params : array-like, optional after fit has been called Parameters of a linear model exog : array-like, optional. Design / exogenous data. Model exog is used if None. Returns ------- An array of fitted values Notes ----- If the model as not yet been fit, params is not optional. N(RRRR!(RR R((sElib/python2.7/site-packages/statsmodels/robust/robust_linear_model.pytpredicts  cCs tdS(N(R*(RR ((sElib/python2.7/site-packages/statsmodels/robust/robust_linear_model.pytloglikescCs$|j|j|j|jjS(sQ Returns the (unnormalized) log-likelihood from the M estimator. (RRt fittedvaluestscaletsum(Rt tmp_results((sElib/python2.7/site-packages/statsmodels/robust/robust_linear_model.pytdeviancescCs|dj|j|dj|j|dkrQ|dj|j|nP|dkr{|dj|j|jn&|dkr|dj|jjn|S(NR R0tdevR3tsresidR(tappendR R0R3tresidtmodelR(RR2thistorytconv((sElib/python2.7/site-packages/statsmodels/robust/robust_linear_model.pyt_update_historys   cCst|jtrP|jjdkr:tj|ddStd|jnBt|jtjr~|j|j|j |Stj||dSdS(sU Estimates the scale based on the option provided to the fit method. tmadtcenteris&Option %s for scale_est not understoodiN( t isinstancet scale_esttstrtlowerR0R<t ValueErrort HuberScaleR'R)(RR7((sElib/python2.7/site-packages/statsmodels/robust/robust_linear_model.pyt_estimate_scalesi2g:0yE>R<tH1R4c Cs|jdkr%td|n|j|_|j}|dkr_td |n||_tj|j|jj }|s|j |j |_ nt d tjgd g} |dkr| d } n|dkr | jt d tjg| d } nj|dkrB| jt dtjg| d} n5|dkrw| jt dtjg| d} n|j|| |} d } d} x| sH|jj|j |j |_tj|j|jd|jdtj }|tkr|j |j |_ n|j|| |} | d 7} t| | ||} qWt||j|j|j } | | d<| | _t d|jd|d|jjjd|| _t| S(s 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 : string 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 : string, optional 'H1', 'H2', or 'H3' Indicates how the covariance matrix is estimated. Default is 'H1'. See rlm.RLMResults for more information. init : string 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 : string 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. Returns ------- results : object statsmodels.rlm.RLMresults REtH2tH3s#Covariance matrix %s not understoodRtcoefsR4R5s&Convergence argument %s not understoodR R0R3iit check_weightsRtcovR?tnormR:(RERFRG(RRHR4R5( tupperRBRJRAR?tlmtWLSRRtfitRDR7R0tdictRtinftupdateR;RRt reg_toolst _MinimalWLStTrueR t RLMResultsR R#t fit_historyt __class__t__name__t fit_optionstRLMResultsWrapper(RRRR?tinitRJt update_scaleR:t wls_resultsR9RRt convergedtresults((sElib/python2.7/site-packages/statsmodels/robust/robust_linear_model.pyROsV.                   N(RYt __module__Rt_model_params_doct_missing_param_doct__doc__RRRR+R,R-R.R3R;RDRURO(((sElib/python2.7/site-packages/statsmodels/robust/robust_linear_model.pyR#sF       RVcBseZdZdZedZedZedZedZedZ edZ edZ ed Z ed Z ddd d d dZdddd ddZRS(s Class to contain RLM results Attributes ---------- bcov_scaled : array 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 : array The usual p x p covariance matrix with scale set equal to 1. It is then just equivalent to normalized_cov_params. bse : array 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 : array An array of the chi-squared values of the paramter 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 : array 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 : array See RLM.normalized_cov_params params : array The coefficients of the fitted model pinv_wexog : array See RLM.pinv_wexog pvalues : array The p values associated with `tvalues`. Note that `tvalues` are assumed to be distributed standard normal rather than Student's t. resid : array 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 : array The scaled residuals. tvalues : array 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 : array The reported weights are determined by passing the scaled residuals from the last weighted least squares fit in the IRLS algortihm. See Also -------- statsmodels.base.model.LikelihoodModelResults cCsqtt|j||||||_|j|_|j|_|j|_i|_dg|_|j |_ dS(NR5( RRVRR8R(R'R)t_cachet data_in_cachet bcov_scaledtcov_params_default(RR8R R#R0((sElib/python2.7/site-packages/statsmodels/robust/robust_linear_model.pyRs       cCstj|jj|jS(N(RR!R8RR (R((sElib/python2.7/site-packages/statsmodels/robust/robust_linear_model.pyR/scCs|jj|jS(N(R8RR/(R((sElib/python2.7/site-packages/statsmodels/robust/robust_linear_model.pyR7scCs|j|jS(N(R7R0(R((sElib/python2.7/site-packages/statsmodels/robust/robust_linear_model.pyR5scCs|jS(N(R#(R((sElib/python2.7/site-packages/statsmodels/robust/robust_linear_model.pyt bcov_unscaledscCs |jjS(N(R8R(R((sElib/python2.7/site-packages/statsmodels/robust/robust_linear_model.pyRscCs|j}tj|jj|j}tj|jj|j}d|jd|j||d}|j dkr|dd|j tj |jj |jd|j dd|jtj |jj|jd|jStj|jj|j|jj|j}tjj|}|j dkr|d|j tj |jj |jd|j dd|jtj |jj|j|S|j dkr|dd|j tj |jj |jd|j dtjtj|tj|jj|j|SdS(NiiRERFRGi(R8RtmeanRt psi_derivR5tvarR(R)RJR'R1tpsiR0R#R!RtTRtinv(RR8tmt var_psiprimetktWtW_inv((sElib/python2.7/site-packages/statsmodels/robust/robust_linear_model.pyRgs $p" egcCs tjjtj|jdS(Ni(tstatsRKtsfRtabsttvalues(R((sElib/python2.7/site-packages/statsmodels/robust/robust_linear_model.pytpvaluesscCstjtj|jS(N(RtsqrttdiagRg(R((sElib/python2.7/site-packages/statsmodels/robust/robust_linear_model.pytbsescCs|j|jdS(Ni(R R|(R((sElib/python2.7/site-packages/statsmodels/robust/robust_linear_model.pytchisqsig?ttextc Cs1dd ddgfd|jdgfd|jdgfd |jd gfd!d"d d|jdgfg }d#d$d%g}|dk rd}nddlm}|} | j|d|d|d|d|d|| j|d|d|d|d|jg} d} | j| | r-| j | n| S(&s; This is for testing the new summary setup sDep. Variable:sModel:sMethod:tIRLSsNorm:RKs Scale Est.:R?s Cov Type:RJsDate:sTime:sNo. Iterations:s%dRsNo. Observations:s Df Residuals:s Df Model:s&Robust linear Model Regression Resultsi(tSummarytglefttgrighttynametxnamettitletalphatuse_tsIf the model instance has been used for another fit with different fit parameters, then the fit options might not be the correct ones anymore .N(sDep. Variable:N(sModel:N(sDate:N(sTime:N(sNo. Observations:N(s Df Residuals:N(s Df Model:N( RRZRWtstatsmodels.iolib.summaryRtadd_table_2colstadd_table_paramsRR6t add_extra_txt( RRRRRt return_fmtttop_leftt top_rightRtsmrytetexttwstr((sElib/python2.7/site-packages/statsmodels/robust/robust_linear_model.pytsummarys4       s%.4fc CsNddlm}|j}|jd|d|d|d|d|d||S( sExperimental summary function for regression results Parameters ---------- xname : List of strings of length equal to the number of parameters Names of the independent variables (optional) yname : string Name of the dependent variable (optional) title : string, optional Title for the top table. If not None, then this replaces the default title alpha : float significance level for the confidence intervals float_format: string print format for floats in parameters summary 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.summary2.Summary : class to hold summary results i(tsummary2R`Rt float_formatRRR(tstatsmodels.iolibRRtadd_base(RRRRRRRR((sElib/python2.7/site-packages/statsmodels/robust/robust_linear_model.pyRs  N(RYRaRdRRR/R7R5RiRRgRyR|R}RRR(((sElib/python2.7/site-packages/statsmodels/robust/robust_linear_model.pyRV*sS   + R[cBseZRS((RYRa(((sElib/python2.7/site-packages/statsmodels/robust/robust_linear_model.pyR[st__main__gGz0@g'@g(\(@g(\-@g+@g\(2@g @gGz1@g(\S@g5@g ףp=*D@g5@g+@g3@g8@g=@g33333.@g3@g#@ǧA@gfffff1@g)\(J@g2@gGz3@g%@iiiiiiiii i iiii0iiTiPiiJiniii]iiiiiiiii$iii*ii{(tloadt as_pandasRR?(4RdtnumpyRt scipy.statsRutstatsmodels.tools.decoratorsRt#statsmodels.regression.linear_modelt regressiont linear_modelRMtstatsmodels.regression._toolst_toolsRStstatsmodels.robust.normstrobustRtstatsmodels.robust.scaleR0tstatsmodels.base.modelRR8tstatsmodels.base.wrappertwrappertwrapt__all__R RRtLikelihoodModelResultsRVtRegressionResultsWrapperR[tpopulate_wrapperRYtstatsmodels.apitapitsmtarrayRRRnt add_constanttstatsmodels.datasets.stacklossRtFalsetdataRt m1_Huber_HRORCtresults_Huber1_H(((sElib/python2.7/site-packages/statsmodels/robust/robust_linear_model.pyts@    96- %!