M/Ph7@ddlZddlmZddlmcmZddlmZddl m Z ddl m Z ddl m Z ddlmcmZddlmcmZddlmZGdd ZGd d eZGd d eZGddeZGddejZGddejZGddejZ ej!e edS)N) defaultdict)families)GLM)links)varfuncs)cache_readonlyceZdZdZdZdS) QIFCovarianceay A covariance model for quadratic inference function regression. The mat method returns a basis matrix B such that the inverse of the working covariance lies in the linear span of the basis matrices. Subclasses should set the number of basis matrices `num_terms`, so that `mat(d, j)` for j=0, ..., num_terms-1 gives the basis of dimension d.` ct)zX Returns the term'th basis matrix, which is a dim x dim matrix. )NotImplementedErrorselfdimterms V/var/www/html/test/jupyter/venv/lib/python3.11/site-packages/statsmodels/genmod/qif.pymatzQIFCovariance.mats "!N)__name__ __module__ __qualname____doc__rrrr r s-  """""rr ceZdZdZdZdZdS)QIFIndependenceaQ Independent working covariance for QIF regression. This covariance model gives identical results to GEE with the independence working covariance. When using QIFIndependence as the working covariance, the QIF value will be zero, and cannot be used for chi^2 testing, or for model selection using AIC, BIC, etc. cd|_dS)N num_termsrs r__init__zQIFIndependence.__init__+ rc:|dkrtj|SdS)Nr)npeyer s rrzQIFIndependence.mat.s 1996#;; 4rNrrrrr rrrrrr"s<rrceZdZdZdZdZdS)QIFExchangeablez= Exchangeable working covariance for QIF regression. cd|_dS)Nrrs rr zQIFExchangeable.__init__:r!rcr|dkrtj|S|dkrtj||fSdS)Nrr)r#r$onesr s rrzQIFExchangeable.mat=s; 1996#;;  QYY7C:&& &4rNr%rrrr'r'5s<rr'ceZdZdZdZdZdS)QIFAutoregressivez? Autoregressive working covariance for QIF regression. cd|_dS)Nrrs rr zQIFAutoregressive.__init__Kr!rc8|dkrd}t||dkrtj|S|dkr2tj||f}d|jdd|dz<||jz }|S|dkr*tj||f}d|d<d||dz |dz f<|SdS)Nr/z?Groups must have size at least 3 for autoregressive covariance.rrr)rr) ValueErrorr#r$zerosflatT)rrrmsgrs rrzQIFAutoregressive.matNs 770CS// ! 1996#;;  QYY(C:&&C#$CHQZQZ 35LCJ QYY(C:&&CCI !CAs1u J4rNr%rrrr-r-Fs<rr-cbeZdZdZ d fd ZdZdZdZedfd Z dd Z xZ S)QIFa Fit a regression model using quadratic inference functions (QIF). QIF is an alternative to GEE that can be more efficient, and that offers different approaches for model selection and inference. Parameters ---------- endog : array_like The dependent variables of the regression. exog : array_like The independent variables of the regression. groups : array_like Labels indicating which group each observation belongs to. Observations in different groups should be independent. family : genmod family An instance of a GLM family. cov_struct : QIFCovariance instance An instance of a QIFCovariance. References ---------- A. Qu, B. Lindsay, B. Li (2000). Improving Generalized Estimating Equations using Quadratic Inference Functions, Biometrika 87:4. www.jstor.org/stable/2673612 Nnonec  |tj}n.t|jtjst d||_tt|_ |t}n$t|tst d||_ tj|}t!j||f||d|tt%||_t)|j|_tt t/|D] \}} | |! fd|jD|_||dS)Nz.QIF: `family` must be a genmod family instancez2QIF: `cov_struct` must be a QIFCovariance instance)groupsmissingc g|] }| Srr).0na groups_ixs r z QIF.__init__..sCCCB)B-CCCr)rGaussian issubclass __class__Familyr2familyrlist _fit_historyr isinstancer cov_structr#asarraysuperr set group_nameslenendognobs enumerateappendr@ _check_args) rrPexogr;rFrJr<kwargsigr@rDs @rr z QIF.__init__s >&((FFf.@@ 4 "3444 '--  (**JJj-88 J HJJJ$F## 4 &  ;A    F ,, OO %% f%% # #DAq aL   " " " "CCCC$2BCCC      rct|t|jkrd}t|t|j|jjdkrd}t|dS)Nz1QIF: groups and endog should have the same lengthrzGQIF: the length of endog should be equal to the number of rows of exog.)rOrPr2rUshape)rr;r6s rrTzQIF._check_argssc v;;#dj// ) )ECS// ! tz??dioa0 0 0-CS// ! 1 0rc  |j}|j}tj||}|jj|}|j|}|jj|}|jj |}|jj |} |j j } |j d} | | z} tj| } tj| }tj| | f}tj| | f}dg| z}tj| | f}|jjtju}t#|jjt$jt$jf}|jD]}tj||}||||z }||z }||ddf||dfz}d}t/| D]}|j t3||}tj|||z }tj|j||||| z<tj|| |dddfz |dddfz }tj|j||||| zddf<|r|st/| D]}tj||ddfj|||||fz|z} |sd| |z|dd|fz||dzz }!tj|j|!tj||z}"tj|jtj||!|z|z }#nd\}"}#|||| z|fxx| |"z|#zz cc<|| z }t/| D]9}tj||dd|f}$||xx|$|$jzz cc<:| |z } ||z }|tj||z }t3|j}%| |%z} ||%z}||%dzz}tj| tj|| }&tj| }'t/| D]}||xxt3|jdzzcc<tj|||j}$tj||$}$tj| tj|$| |'|<dtj|jtj|| z|'z }(|&|(|| |fS)a Calculate the gradient of the QIF objective function. Parameters ---------- params : array_like The model parameters at which the gradient is evaluated. Returns ------- grad : array_like The gradient vector of the QIF objective function. gn_deriv : array_like The gradients of each estimating equation with respect to the parameter. rrNgg?r1r))rPrUr#dotrFlinkinversevariance inverse_derivinverse_deriv2derivrJrrZr3rconstantrIrIdentityidentityr@sqrtrangerrOr5outerlinalgsolve))rparamsrPrUlprmeanvaidlidl2vdmpdgngigi_derivgn_derivcn_derivcmatfastvarfastlinkixsdresidsresidrbjjjccrs1crs2km1vxm2m3ungrpqifgcggrads) r objectivez QIF.objectives=$ yfT6""{'',, [ ! !$ ' 'k,,S11{..s33 [ ! ' ' - - O % JqM E Xa[[ Xa[[8QF##8QF##37xA+&(*;; K  ^U^ ,   .% %% %BBB"IR(ERZFQQQK#b$h-/EB1XX   O''B33va((2- fUWd332bd7 va%"QQQW+!566AAAtGD')vegt'<'<BqD!!!$ =W ="1XX = =VDQQQKM$(HtBE{$:T$ACC&*!%2qqq!t!"" d D afRr2233hqkkq / /A QKKK3t~..1 1KKK hqk224A a((AVBq" ..CFF26(*bioodB&?&?@@@3FD$H,,rctt|jtjtjfrdSt |dr|j}n |jd}tj |j|}|jj |}|j |z }tj |dz|j|z z }|S)z Estimate the dispersion/scale. The scale parameter for binomial and Poisson families is fixed at 1, otherwise it is estimated from the data. g? ddof_scalerr))rIrFrBinomialPoissonhasattrrrUr#r\r]r^rPsumrQ)rrkrrlrmrscales restimate_scalezQIF.estimate_scales dkH$5x7G#H I I 2 4 & & &JJ1JfTY''{'',, T!uax  DI $:; rct|tr||}tj|g|R|||d|}|S)a Create a QIF model instance from a formula and dataframe. Parameters ---------- formula : str or generic Formula object The formula specifying the model groups : array_like or string Array of grouping labels. If a string, this is the name of a variable in `data` that contains the grouping labels. data : array_like The data for the model. subset : array_like An array_like object of booleans, integers, or index values that indicate the subset of the data to used when fitting the model. Returns ------- model : QIF model instance )datasubsetr;)rIstrrL from_formula) clsformular;rrargsrVmodelrDs rrzQIF.from_formula2si2 fc " " "&\F$$3#'33!%f 33+133 rdư>-C6?c ||jjd|_n||_|=t|j|j|j}|}|j}n|}t|D]@} | |\} } } } } tj tj | | z}|j d| |j d|||krndtj| jtj| | z}tj|| }tj tj ||z}|j d|||krn||z}Btj| jtj| | }tj|}||}t+||||z |}|j |_t/t0|_ t3|S)a, Fit a GLM to correlated data using QIF. Parameters ---------- maxiter : int Maximum number of iterations. start_params : array_like, optional Starting values tol : float Convergence threshold for difference of successive estimates. gtol : float Convergence threshold for gradient. ddof_scale : int, optional Degrees of freedom for the scale parameter Returns ------- QIFResults object Nr)rFrgradnormr)stepnorm)rUrZrrrPrFfitrkrgrr#rfrrHrSr\r5rirjinvr QIFResults fit_historyrrGQIFResultsWrapper)rmaxiter start_paramstolgtolrrresultrk_rrrzrxgnormcjacstepsnormvcovrrslts rrzQIF.fitTs 0  "ioa0DOO(DO   DIdkBBBEYY[[F]FF!Fw  A+/>>&+A+A (CtQGBF4$;//00E  e $ + +C 0 0 0  j ) 0 0 7 7 7t||rvhj")//$*I*IJJJD9??4..DGBF4$;//00E  j ) 0 0 7 7 7s{{ dNFFvhj")//$"A"ABBy}}T""##F++$u e<<,'-- &&&r)NNr9)N)rNrrN) rrrrr rTrr classmethodrr __classcell__rDs@rr8r8es648*0%!%!%!%!%!%!N " " "f-f-f-P.[BBF@'@'@'@'@'@'@'@'rr8cpeZdZdZ d fd ZedZedZedZd d Z xZ S) rz Results class for QIF RegressionFc t|||||j|\|_}}}}dS)N)normalized_cov_paramsr)rLr rrr) rrrk cov_paramsruse_tkwdsrrDs rr zQIFResults.__init__sX  6     $z33F;;!Q111rct|jjtrd}t ||jjjd}|jd|zzS)zA An AIC-like statistic for models fit using QIF. z1AIC not available with QIFIndependence covariancerr))rIrrJrr2rUrZrrr6dfs raiczQIFResults.aicsM dj+_ = = "ECS// ! Z_ "1 %x!B$rct|jjtrd}t ||jjjd}|jtj |jj |zzS)z@ A BIC-like statistic for models fit using QIF. z1BIC not available with QIFIndependence covariancer) rIrrJrr2rUrZrr#logrQrs rbiczQIFResults.bics] dj+_ = = "ECS// ! Z_ "1 %x"&11"444rc|jjjt j|jj|jS)z; Returns the fitted values from the model. )rrFr]r^r#r\rUrkrs r fittedvalueszQIFResults.fittedvaluess9 z %--tz 4466 6rN皙?c ndddgfd|jjjjgfd|jjjjgfddg}d|jjD}d t |gfd t|gfd t|gfd t|gfd dtj |zgfdd|j zgfg}||jjjdzdz}| |jj }| |jj}ddlm}|} | ||||||| ||||d| S)ag Summarize the QIF regression results Parameters ---------- yname : str, optional Default is `y` xname : list[str], optional Names for the exogenous variables, default is `var_#` for ## in the number of regressors. 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:NzMethod:r8zFamily:zCovariance structure:)zDate:N)zTime:Nc,g|]}t|Sr)rO)r>ys rrAz&QIFResults.summary..s 3 3 3c!ff 3 3 3rzNo. Observations:z No. clusters:zMin. cluster size:zMax. cluster size:zMean cluster size:z%.1fzScale:z%.3fN zRegression Resultsr)Summary)gleftgrightynamexnametitleF)rralphar)rrFrDrrJr@rrOminmaxr#rmr exog_names endog_namesstatsmodels.iolib.summaryradd_table_2colsadd_table_params) rrrrrtop_leftNY top_rightrsmrys rsummaryzQIFResults.summarys:-(!2!?A## 4 3dj2 3 3 3)CGG95%By1*SWWI6*SWWI6*Vbgbkk-A,BC$*!4 56   =J(1C7$%E =J)E =J*E 655555wyy T)#(#(  * * * d%u$)  8 8 8 r)F)NNNr) rrrrr rrrrrrrs@rrrs**<<<<<<^55^566^6EEEEEEEErrceZdZdS)rN)rrrrrrrrsDrr)"numpyr# collectionsrstatsmodels.base.modelbaserstatsmodels.genmodr+statsmodels.genmod.generalized_linear_modelrstatsmodels.genmod.familiesrr#statsmodels.regression.linear_model regression linear_modellmstatsmodels.base.wrapperwrapperwrapstatsmodels.tools.decoratorsrr rr'r-Modelr8LikelihoodModelResultsrRegressionResultsWrapperrpopulate_wrapperrrrrs*######%%%%%%%%%'''''';;;;;;------000000000000000'''''''''777777""""""""*m&m" >o'o'o'o'o'$*o'o'o'd nnnnn,nnnb     3   '44444r