M/PhzdZddlZddlmZddlZddlmcm Z ddl m cm ZddlmZddlmZmZmZddlmZdZGdd eZGd d eeZGd d ejZe jeedS)u Beta regression for modeling rates and proportions. References ---------- Grün, Bettina, Ioannis Kosmidis, and Achim Zeileis. Extended beta regression in R: Shaken, stirred, mixed, and partitioned. No. 2011-22. Working Papers in Economics and Statistics, 2011. Smithson, Michael, and Jay Verkuilen. "A better lemon squeezer? Maximum-likelihood regression with beta-distributed dependent variables." Psychological methods 11.1 (2006): 54. N)gammaln)cache_readonly)GenericLikelihoodModelGenericLikelihoodModelResults _LLRMixin)familiesa Beta regression with default of logit-link for exog and log-link for precision. >>> mod = BetaModel(endog, exog) >>> rslt = mod.fit() >>> print(rslt.summary()) We can also specify a formula and a specific structure and use the identity-link for precision. >>> from sm.families.links import identity >>> Z = patsy.dmatrix('~ temp', dat, return_type='dataframe') >>> mod = BetaModel.from_formula('iyield ~ C(batch, Treatment(10)) + temp', ... dat, exog_precision=Z, ... link_precision=identity()) In the case of proportion-data, we may think that the precision depends on the number of measurements. E.g for sequence data, on the number of sequence reads covering a site: >>> Z = patsy.dmatrix('~ coverage', df) >>> formula = 'methylation ~ disease + age + gender + coverage' >>> mod = BetaModel.from_formula(formula, df, Z) >>> rslt = mod.fit() cbeZdZdeZdejej ffd Z e dfd Z dZ d dZdd Zd!d Zd Zd Zd ZfdZddZ d"dZdZddZd#dZd$dZ d%fd ZdZdZd!dZd!dZxZ S)& BetaModelaMBeta Regression. The Model is parameterized by mean and precision. Both can depend on explanatory variables through link functions. Parameters ---------- endog : array_like 1d array of endogenous response variable. exog : array_like A nobs x k array where `nobs` is the number of observations and `k` is the number of regressors. An intercept is not included by default and should be added by the user (models specified using a formula include an intercept by default). See `statsmodels.tools.add_constant`. exog_precision : array_like 2d array of variables for the precision. link : link Any link in sm.families.links for mean, should have range in interval [0, 1]. Default is logit-link. link_precision : link Any link in sm.families.links for precision, should have range in positive line. Default is log-link. **kwds : extra keywords Keyword options that will be handled by super classes. Not all general keywords will be supported in this class. Notes ----- Status: experimental, new in 0.13. Core results are verified, but api can change and some extra results specific to Beta regression are missing. Examples -------- {example} See Also -------- :ref:`links` )exampleNc ~tj|}tjd|k|dkzsJ|)dg}tjt |dfd}n?dt |dr|jntd|jddzD}||d<tj ||fd |i|||_ ||_ |j jd|_d|_|jd z |_|j|jz |_t |jt |j ksJd |_d |jvr|jd g|jd d gd g|_|d=||t2|_t6|_dS)Nr precisionf)dtypecg|]}d|zS)z precision-%s).0zcs \/var/www/html/test/jupyter/venv/lib/python3.11/site-packages/statsmodels/othermod/betareg.py z&BetaModel.__init__..ns/III2>B.IIIcolumnsextra_params_namesexog_precisionoimlinklink_precision)nparrayalloneslenhasattrrrangeshapesuper__init__rrendognobsk_extranparamsdf_modeldf_residr hess_type _init_keysextend_null_drop_keys _check_kwargs BetaResults results_classBetaResultsWrapperresults_class_wrapper) selfr)exogrrrkwdsetmp extra_names __class__s rr(zBetaModel.__init__dsxvq4xD1H-.....  !&-KWc%jj!_C@@@NNII&~yAAGN22!&q.*>q*AA*E!F!FIIIK &1 !"LL^LtLLL ,J$Q'   q(  DL0 4&''3tz??:::: 4? 2 2 O " "$4#5 6 6 6 (89::: 01 % & 4   (%7"""rc|Gd|vr)|j|d}tj||}ntj||}||d<tj||g|Ri|S)Nsubsetr)ixpatsydmatrixr' from_formula) clsformuladataexog_precision_formulaargskwargsdZr=s rrCzBetaModel.from_formulas " -6!!GF8,-M"8!<<M"8$??'(F# $#uww#GTCDCCCFCCCrc|j|jfSNr9rr8s r _get_exogszBetaModel._get_exogss 4.//rmeanc|dkrd}|dvrd}|jjd}|dvrN||j}|d|}tj||}|dkr|j|}|} n|} n|d vrN||j}||d} tj|| } |d kr|j| } | } n4| } n1|d kr|||| } ntd |z| S)aPredict values for mean or precision Parameters ---------- params : array_like The model parameters. exog : array_like Array of predictor variables for mean. exog_precision : array_like Array of predictor variables for precision parameter. which : str - "mean" : mean, conditional expectation E(endog | exog) - "precision" : predicted precision - "linear" : linear predictor for the mean function - "linear-precision" : linear predictor for the precision parameter Returns ------- ndarray, predicted values linpredlinear)linpred_precisionlinear_precisionlinear-precisionr )rQrTNrQ)rrWrvarrNzwhich = %s is not available) r9r&rdotrinverserr _predict_var ValueError) r8paramsr9rwhichk_mean params_meanrSmures params_prec linpred_precphis rpredictzBetaModel.predictsE. I  E = = =&E# ' ' '|y &/KfT;//GY&&w// 7 7 7%!%!4 /K6.+>>L ##)11,??" e^^##-$CC:UBCC C rc||j}|jjd}||d}tj||}|j|}|S)aGPredict values for precision function for given exog_precision. Parameters ---------- params : array_like The model parameters. exog_precision : array_like Array of predictor variables for precision. Returns ------- Predicted precision. Nr )rr9r&rrYrrZ)r8r]rr_params_precisionrdres r_predict_precisionzBetaModel._predict_precisions[  !!0N#!&''?vn.>?? !)),77 rc~|||}|||}|d|z zd|zz }|S)apredict values for conditional variance V(endog | exog) Parameters ---------- params : array_like The model parameters. exog : array_like Array of predictor variables for mean. exog_precision : array_like Array of predictor variables for precision. Returns ------- Predicted conditional variance. r9)rr )rfri)r8r]r9rrQr var_endogs rr[zBetaModel._predict_varsY ||F|..++F;I,KK AH%Y7 rcP||j|j|j|S)a Loglikelihood for observations of the Beta regressionmodel. Parameters ---------- params : ndarray The parameters of the model, coefficients for linear predictors of the mean and of the precision function. Returns ------- loglike : ndarray The log likelihood for each observation of the model evaluated at `params`. )_llobsr)r9r)r8r]s r loglikeobszBetaModel.loglikeobs s# {{4:ty$2EvNNNrc|||}}}|jd}|d| } || d} tj|| } tj|| } |j| } |j| }d}tj| |z|tj}tjd| z |z|tj}t|t|z t|z | |zdz tj |zzd| z |zdz tj d|z zz}|S)a Loglikelihood for observations with data arguments. Parameters ---------- endog : ndarray 1d array of endogenous variable. exog : ndarray 2d array of explanatory variables. exog_precision : ndarray 2d array of explanatory variables for precision. params : ndarray The parameters of the model, coefficients for linear predictors of the mean and of the precision function. Returns ------- loglike : ndarray The log likelihood for each observation of the model evaluated at `params`. r NN~h) r&rrYrrZrclipinflgammalog)r8r)r9rr]yXrKnzr`rcrSrdrareeps_lbalphabetalls rrnzBetaModel._llobss2,~a1 WQZTrcTl bSTTl &K((va-- Y  w ' '!)),77S&"&11wB#~vrv66SkkF5MM)t cA*+r6S.A%A67  rc||\}}tj||j}tj||j}tj||fS)ak Returns the score vector of the log-likelihood. http://www.tandfonline.com/doi/pdf/10.1080/00949650903389993 Parameters ---------- params : ndarray Parameter at which score is evaluated. Returns ------- score : ndarray First derivative of loglikelihood function. ) score_factorrrYr9r concatenater8r]sf1sf2d1d2s rscorezBetaModel.scoreHsV $$V,,S VC # # VC, - -~r2h'''rcFt|S)zInherited score with finite differences Parameters ---------- params : ndarray Parameter at which score is evaluated. Returns ------- score based on numerical derivatives )r'r)r8r]r=s r _score_checkzBetaModel._score_check^sww}}V$$$rcBddlm}|j}||jn|}|j|j}}|jd}|d| } || d} |jtj || } |j tj || } d} tj | | z| tj }tj d| z | z| tj }tj|d|z z }||}|||z }tjd|z }||| z }d|j| z }d|j | z }| |z||z z}|| ||z z|z|z z}||fS)aKDerivative of loglikelihood function w.r.t. linear predictors. This needs to be multiplied with the exog to obtain the score_obs. Parameters ---------- params : ndarray Parameter at which score is evaluated. Returns ------- score_factor : ndarray, 2-D A 2d weight vector used in the calculation of the score_obs. Notes ----- The score_obs can be obtained from score_factor ``sf`` using - d1 = sf[:, :1] * exog - d2 = sf[:, 1:2] * exog_precision rspecialNr rq?)scipyrpsir)r9rr&rrZrrYrrrrsruderiv)r8r]r)rdigammarvrwrKrxXparamsZparamsrareryrzr{ystardig_betamustarytmutthrrs rr~zBetaModel.score_factorls. "!!!!!+-DJJUy$-1 WQZ2#,",Y  rva11 2 2!))"&G*<*<==S&"&11wB#~vrv66qBF|$$74==(* VAE]]% $$ $ $**3// /Ag(2(2-34SzrFTc$ddlm$$j}|j|j|j}}}|jd}|d| } || d} |jtj || } |j tj || } d} tj | | z| tj }tj d| z | z| tj }tj|d|z z }||}|||z }tjd|z }||| z }d|j| z }d|j | z }||z }| |z|z}|| |z|z|z z}|r$fd}||}|||z}||| z }| }|j| }|j | } | |z|z}!|r|!||dzz|zz }!|!|| zz}!| |z|z| |z|zz}"|r |"||z|zz}"|dz| dz|zd| z|zz|zz}#|r|#| |z|z|z | z|d zzz }#||f|! |" |# ffS||fS) aDerivatives of loglikelihood function w.r.t. linear predictors. This calculates score and hessian factors at the same time, because there is a large overlap in calculations. Parameters ---------- params : ndarray Parameter at which score is evaluated. return_hessian : bool If False, then only score_factors are returned If True, the both score and hessian factors are returned observed : bool If True, then the observed Hessian is returned (default). If False, then the expected information matrix is returned. Returns ------- score_factor : ndarray, 2-D A 2d weight vector used in the calculation of the score_obs. (-jbb, -jbg, -jgg) : tuple A tuple with 3 hessian factors, corresponding to the upper triangle of the Hessian matrix. TODO: check why there are minus rrr Nrqrc0d|S)Nr ) polygamma)xrs rz0BetaModel.score_hessian_factor..s!2!21a!8!8rr)rrrr)r9rr&rrZrrYrrrrsrurderiv2)%r8r]return_hessianobservedrrvrwrKrxrrrareryrzr{rrrrrrrymu_starrrtrigamma trig_betavar_starvar_tcsqjbbjbgjggrs% @rscore_hessian_factorzBetaModel.score_hessian_factors6 "!!!!!+*di)U " "HHH))&3;*==2dDy{T!&&ty11y{T!&&t':;;"$t+001DEEx#sceS\2333rc<||d|\}}|S)zHDerivatives of loglikelihood function w.r.t. linear predictors. Tr)r)r8r]rrrs rhessian_factorzBetaModel.hessian_factor,s.))&3;*==2 rrcddlm}m}|||j|j}|j|j}|j|z }|d|z ztj tj |ddzz dz }|| ||j } |j | j} t|D]d} d| z|d|z zz } | |j|dzz } |||j|j| }|j|j}|j|z }|d|z ztj tj |ddzz dz }d|j | dzz }|| ||j |}|j |j} tj|j|jf}f|r|||fS|S)afind starting values Parameters ---------- niter : int Number of iterations of WLS approximation return_intermediate : bool If False (default), then only the preliminary parameter estimate will be returned. If True, then also the two results instances of the WLS estimate for mean parameters and for the precision parameters will be returned. Returns ------- sp : ndarray start parameters for the optimization res_m2 : results instance (optional) Results instance for the WLS regression of the mean function. res_p2 : results instance (optional) Results instance for the WLS regression of the precision function. Notes ----- This calculates a few iteration of weighted least squares. This is not a full scoring algorithm. r)OLSWLSr g{Gz?r)weightsr)#statsmodels.regression.linear_modelrrrr)r9fitrZ fittedvaluesrmaximumabsrrr%rrr])r8niterreturn_intermediaterrres_mfittedresidprec_ires_p prec_fittedr y_var_inv ylink_var_invres_m2resid2prec_i2w_pres_p2sp2s r _start_paramszBetaModel._start_params3sp> A@@@@@@@DIIdj))495599;;""5#566 V#1v:&BF5MM4)H)H!)KKaOD''//1DEEIIKK)11%2DEE u A AA[Vq6z-BCI& (?(?(BBMS4:.. !.00003 Y&&v':;;FZ&(FV,z"&..$77:;=>?Gt*00==q@@CS,,W55t7J!$&&&&)cee -55f6IJJK.&-!?@@CC  '& & rbfgsc ||}d|vr)|ddkr d|_|d=nd|_tjd||||d|}t |t st |}|S)a2 Fit the model by maximum likelihood. Parameters ---------- start_params : array-like A vector of starting values for the regression coefficients. If None, a default is chosen. maxiter : integer The maximum number of iterations disp : bool Show convergence stats. method : str The optimization method to use. kwds : Keyword arguments for the optimizer. Returns ------- BetaResults instance. Ncov_typerr) start_paramsmaxitermethoddispr)rlowerr/r'r isinstancer6)r8rrrrr:rbr=s rrz BetaModel.fitss0  --//L   J%%''500!&$"DNeggk-|")&#--'+--#122 *$S))C rc|j}||d}||}|j|dddfz}t j|t j|jjfS)ag Derivative of the expected endog with respect to the parameters. not verified yet Parameters ---------- params : ndarray parameter at which score is evaluated Returns ------- The value of the derivative of the expected endog with respect to the parameter vector. rTr^N) rrf inverse_derivr9rrzerosrr&)r8r]rlin_predidldmats r_deriv_mean_dparamszBetaModel._deriv_mean_dparamssp y<<h<77  **y3qqq$w<'bht/B/H&I&IJKKKrcddlm}fd}|jdddf|}|ddddfjz}|ddddfjz}t j||fS)a#derivative of score_obs w.r.t. endog Parameters ---------- params : ndarray parameter at which score is evaluated Returns ------- derivative : ndarray_2d The derivative of the score_obs with respect to endog. r)_approx_fprime_cs_scalarc|jdkr|jddkr |dddf}|}tj|S)Nrr r)r))ndimr&r~rr)rvsfr]r8s rrz,BetaModel._deriv_score_obs_dendog..fsUv{{qwqzQaaadG""6"33B?2&& &rNr r)statsmodels.tools.numdiffrr)r9rrr)r8r]rrdsfrrs`` r_deriv_score_obs_dendogz!BetaModel._deriv_score_obs_dendogs GFFFFF ' ' ' ' ' ' '&tz!!!T'':A>> BQBZ$) # AaC[4. .Bx(((rcz|||}|||d}||z|d|z zfS)a Return distribution parameters converted from model prediction. Parameters ---------- params : array_like The model parameters. exog : array_like Array of predictor variables for mean. exog_precision : array_like Array of predictor variables for mean. Returns ------- (alpha, beta) : tuple of ndarrays Parameters for the scipy distribution to evaluate predictive distribution. rkr)rr^r rf)r8r]r9rrQrs rget_distribution_paramsz!BetaModel.get_distribution_paramssQ&||F|..LL'2!44 4a$h!777rcVddlm}||||}|j|}|S)a Return a instance of the predictive distribution. Parameters ---------- params : array_like The model parameters. exog : array_like Array of predictor variables for mean. exog_precision : array_like Array of predictor variables for mean. Returns ------- Instance of a scipy frozen distribution based on estimated parameters. See Also -------- predict Notes ----- This function delegates to the predict method to handle exog and exog_precision, which in turn makes any required transformations. Due to the behavior of ``scipy.stats.distributions objects``, the returned random number generator must be called with ``gen.rvs(n)`` where ``n`` is the number of observations in the data set used to fit the model. If any other value is used for ``n``, misleading results will be produced. rstatsrNrrrr{)r8r]r9rrrHdistrs rget_distributionzBetaModel.get_distributionsMB ++F;I,KK D! rrM)NNrQ)NN)FT)T)rF)NrFr)!__name__ __module__ __qualname__format _init_example__doc__rlinksLogitLogr( classmethodrCrPrfrir[rornrrr~rrrrrrrrrr __classcell__)r=s@rr r 9s<(P }%%Q T48n**,, ( 2 2 4 4$8$8$8$8$8$8L D D D D D[ D000????B0.OOO$***X(((, % % % % %4444l;@&*SSSSj))),4444>>>>>@9>++++++ZLLL,)))888880%%%%%%%%rr ceZdZdZedZedZedZedZedZ d d Z d d Z d Z d Z dS)r4zResults class for Beta regression This class inherits from GenericLikelihoodModelResults and not all inherited methods might be appropriate in this case. c@|j|jS)z2In-sample predicted mean, conditional expectation.modelrfr]rOs rrzBetaResults.fittedvaluessz!!$+...rcD|j|jdS)zIn-sample predicted precisionrrr rOs rfitted_precisionzBetaResults.fitted_precisions!z!!$+[!AAArc*|jj|jz S)zResponse residual)r r)rrOs rrzBetaResults.resid$sz$"333rc|tj|j|jd}|j|z S)zPearson standardize residualrXr)rsqrtr rfr]r)r8stds r resid_pearsonzBetaResults.resid_pearson)s7gdj((E(BBCCzCrc.|dS)zdCox-Snell Likelihood-Ratio pseudo-R-squared. 1 - exp((llnull - .llf) * (2 / nobs)) lr)kind)pseudo_rsquaredrOs r prsquaredzBetaResults.prsquared/s ###...rNTcz|||}||d|}||z|d|z zfS)ag Return distribution parameters converted from model prediction. Parameters ---------- params : array_like The model parameters. exog : array_like Array of predictor variables for mean. transform : bool If transform is True and formulas have been used, then predictor ``exog`` is passed through the formula processing. Default is True. Returns ------- (alpha, beta) : tuple of ndarrays Parameters for the scipy distribution to evaluate predictive distribution. )r9 transformr)rr^rr r)r8r9rrrQrs rrz#BetaResults.get_distribution_params7sS*|||;;LL'2i!II 4a$h!777rcnddlm}||||}d|D}|j|}|S)ak Return a instance of the predictive distribution. Parameters ---------- exog : array_like Array of predictor variables for mean. exog_precision : array_like Array of predictor variables for mean. transform : bool If transform is True and formulas have been used, then predictor ``exog`` is passed through the formula processing. Default is True. Returns ------- Instance of a scipy frozen distribution based on estimated parameters. See Also -------- predict Notes ----- This function delegates to the predict method to handle exog and exog_precision, which in turn makes any required transformations. Due to the behavior of ``scipy.stats.distributions objects``, the returned random number generator must be called with ``gen.rvs(n)`` where ``n`` is the number of observations in the data set used to fit the model. If any other value is used for ``n``, misleading results will be produced. rr)r9rrc3>K|]}tj|VdSrM)rasarray)rargs r z/BetaResults.get_distribution..ws*00C 3000000rr)r8r9rrrrHrs rrzBetaResults.get_distributionQscD ++;I6?,AA104000 D! rc$ddlm}||S)a Get an instance of MLEInfluence with influence and outlier measures Returns ------- infl : MLEInfluence instance The instance has methods to calculate the main influence and outlier measures as attributes. See Also -------- statsmodels.stats.outliers_influence.MLEInfluence Notes ----- Support for mutli-link and multi-exog models is still experimental in MLEInfluence. Interface and some definitions might still change. Note: Difference to R betareg: Betareg has the same general leverage as this model. However, they use a linear approximation hat matrix to scale and studentize influence and residual statistics. MLEInfluence uses the generalized leverage as hat_matrix_diag. Additionally, MLEInfluence uses pearson residuals for residual analusis. References ---------- todo r) MLEInfluence)$statsmodels.stats.outliers_influencer!)r8r!s r get_influencezBetaResults.get_influence{s'> FEEEEE|D!!!rctrM)NotImplementedError)r8rHrIs r bootstrapzBetaResults.bootstraps!!r)NNT)rrrrrrrrrrrrr#r&rrrr4r4s//^/BB^B44^4  ^ //^/AE*.88884((((T " " "D"""""rr4ceZdZdS)r6N)rrrrrrr6r6sDrr6)rnumpyr scipy.specialrrtrAstatsmodels.base.wrapperbasewrapperwrapr regression linear_modellmstatsmodels.tools.decoratorsrstatsmodels.base.modelrrrstatsmodels.genmodrrr r4RegressionResultsWrapperr6populate_wrapperrrrr6s  ++++++ '''''''''000000000777777FFFFFFFFFF''''''