>hCBSSKrSSKJr SSKJs Jr SSKJr SSK J r SSK J r SSK J r SSKJs Jr SSKJs Jr SSKJr "SS 5r"S S \5r"S S \5r"SS\5r"SS\R65r"SS\R:5r"SS\R>5r \RB"\ \5 g)N) defaultdict)families)GLM)links)varfuncs)cache_readonlyc\rSrSrSrSrSrg) QIFCovariance aY 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.` c[e)z@ Returns the term'th basis matrix, which is a dim x dim matrix. )NotImplementedErrorselfdimterms iC:\Users\julio\OneDrive\Documentos\Trabajo\Ideas Frescas\venv\Lib\site-packages\statsmodels/genmod/qif.pymatQIFCovariance.mats "!N)__name__ __module__ __qualname____firstlineno____doc__r__static_attributes__rrrr r s  "rr c$\rSrSrSrSrSrSrg)QIFIndependence"a9 Independent working covariance for QIF regression. This covariance model gives identical results to GEE with the independence working covariance. When using QIFIndependence as the working covariance, the QIF value will be zero, and cannot be used for chi^2 testing, or for model selection using AIC, BIC, etc. cSUlg)N num_termsrs r__init__QIFIndependence.__init__+ rc<US:Xa[R"U5$g)Nr)npeyers rrQIFIndependence.mat.s 1966#; rr"Nrrrrrr%rrrrrrr"srrc$\rSrSrSrSrSrSrg)QIFExchangeable5z5 Exchangeable working covariance for QIF regression. cSUlg)Nr"r$s rr%QIFExchangeable.__init__:r'rcvUS:Xa[R"U5$US:Xa[R"X45$g)Nrr!)r)r*onesrs rrQIFExchangeable.mat=s2 1966#;  QY77C:& &rr"Nr,rrrr.r.5srr.c$\rSrSrSrSrSrSrg)QIFAutoregressiveFz7 Autoregressive working covariance for QIF regression. cSUlg)Nr"r$s rr%QIFAutoregressive.__init__Kr'rcFUS:a Sn[U5eUS:Xa[R"U5$US:Xa<[R"X45nSURSSUS-2'XDR - nU$US:Xa*[R"X45nSUS'SXAS- US- 4'U$g)Nr:z?Groups must have size at least 3 for autoregressive covariance.rr!r1rr) ValueErrorr)r*zerosflatT)rrrmsgrs rrQIFAutoregressive.matNs 70CS/ ! 1966#;  QY((C:&C#$CHHQZQZ 55LCJ QY((C:&CCI !CAs1u Jrr"Nr,rrrr7r7Fsrr7cn^\rSrSrSrS U4SjjrSrSrSr\ S U4Sjj5r S Sjr S r U=r $) QIFea( Fit a regression model using quadratic inference functions (QIF). QIF is an alternative to GEE that can be more efficient, and that offers different approaches for model selection and inference. Parameters ---------- endog : array_like The dependent variables of the regression. exog : array_like The independent variables of the regression. groups : array_like Labels indicating which group each observation belongs to. Observations in different groups should be independent. family : genmod family An instance of a GLM family. cov_struct : QIFCovariance instance An instance of a QIFCovariance. References ---------- A. Qu, B. Lindsay, B. Li (2000). Improving Generalized Estimating Equations using Quadratic Inference Functions, Biometrika 87:4. www.jstor.org/stable/2673612 c >Uc[R"5nO4[UR[R5(d [ S5eX@l[[5Ul Uc [5nO [U[5(d [ S5eXPl [R"U5n[ T U]D"X4X6S.UD6 [[%U55Ul[)UR*5Ul[[5n[/U5HupXR1U 5 M UR&V s/sHoU PM sn UlUR5U5 gs sn f)Nz.QIF: `family` must be a genmod family instancez2QIF: `cov_struct` must be a QIFCovariance instance)groupsmissing)rGaussian issubclass __class__Familyr>familyrlist _fit_historyr isinstancer cov_structr)asarraysuperr%set group_nameslenendognobs enumerateappend groups_ix _check_args) rrXexogrHrNrRrIkwargsr\ignarLs rr% QIF.__init__s6 >&&(Ff..@@ "344 '-  (*Jj-88 HJJ$F#   & ;A  F , O % f%DA L   "&262B2BC2BBB-2BC  Ds=E%c[U5[UR5:wa Sn[U5e[UR5URRS:wa Sn[U5eg)Nz1QIF: groups and endog should have the same lengthrzGQIF: the length of endog should be equal to the number of rows of exog.)rWrXr>r^shape)rrHrBs rr]QIF._check_argssX v;#djj/ )ECS/ ! tzz?diiooa0 0-CS/ ! 1rc  URnURn[R"X15nURR R U5nURRU5nURR RU5nURR RU5nURRRU5n URRn URSn X-n [R"U 5n [R"U 5n[R"X45n[R"X45nS/U -n[R"X45nURR[R Ln[#URR [$R&[$R(45nUR*GHn[R,"UU5nUUUU- nUU- nUUSS24UUS4-nSn[/U 5GHnURR1[3U5U5n[R"UU5U- n[R"UR4U5UUUU -&[R"UU*USS2S4- 5USS2S4- n[R"UR4U5UUUU -2SS24'U(aU(d[/U 5Hn[R"UUSS24R4UUUUU4-U-5n U(dSU U-USS2U4-UUS-- n![R"UR4U![R"UU5-5n"[R"UR4[R"UU!U-5U- 5n#OSun"n#UUUU -2U4==U U"-U#-- ss'M UU - nGM [/U 5H:n[R6"XSS2U45n$UU==U$U$R4-- ss'M< X- n UU- nU[R6"X5- nGM [3UR*5n%U U%-n UU%-nUU%S--n[R"U [R8R;UU 55n&[R"U 5n'[/U 5HnUU==[3UR*5S--ss'[R8R;UUU5R4n$[R8R;UU$5n$[R"U [R"U$U 55U'U'M S[R"UR4[R8R;UU 55-U'- n(U&U(UU U4$)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. r!rNgg?r=r1)rXr^r)dotrNlinkinversevariance inverse_derivinverse_deriv2derivrRr#rer?rconstantrQrIdentityidentityr\sqrtrangerrWrAouterlinalgsolve))rparamsrXr^lprmeanvaidlidl2vdmpdgngigi_derivgn_derivcn_derivcmatfastvarfastlinkixsdresidsresidrnjjjccrs1crs2km1vxm2m3ungrpqifgcggrads) r objective QIF.objectives$ yyffT"{{'', [[ ! !$ 'kk,,S1{{..s3 [[ ! ! ' ' - OO % % JJqM E XXa[ XXa[88QF#88QF#37xx++&&(*;*;; KK   ^^U^^ ,  ..BBB"IR(ERZFQK#b$h-/EB1X OO''B3vva(2- ffUWWd32bd vva%"QW+!56AtGD')vveggt'<BqD!$ W"1XVVDQKMM$(HtBE{$:T$AC&!%2q!t!>" d D affRr23hhqkqA QK3t~~.1 1K hqk244A a(AVVBq" .CF  266(**biioodB&?@@3FD$H,,rc[UR[R[R45(ag[ US5(a UR nOURSn[R"URU5nURRRU5nURU- n[R"US-5URU- - nU$)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_scaler!r1)rQrNrBinomialPoissonhasattrrr^r)rhrirjrXsumrY)rrwrrxryrscales restimate_scaleQIF.estimate_scales dkkH$5$5x7G7G#H I I 4 & &J1JffTYY'{{'', T!uax DII $:; rch>[U[5(aX2n[TU] "U/UQ7X4US.UD6nU$)a4 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 )datasubsetrH)rQstrrT from_formula) clsformularHrrargsr_modelrLs rrQIF.from_formula2sM2 fc " "\F$3#'3!% 3+13 rc UcURRSUlOXPlUcF[URURUR S9nUR 5nURnOUn[U5GH@n URU5uppn [R"[R"X-55nURSRU 5 URSRU5 X:a OS[R"U R [R"R%X55-n[R"R%X5n[R"[R"UU-55nURSRU5 UU:a O UU-nGMC [R"W R [R"R%W U 55n[R"R'U5nUR)U5n[+XUU- U5nURUl[/[05Ul [3U5$)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 r!)rNrgradnormr1stepnorm)r^rerrrXrNfitrwrsrr)rrrrPr[rhrArurvinvr QIFResults fit_historyrrOQIFResultsWrapper)rmaxiter start_paramstolgtolrrresultrw_rrrrgnormcjacstepsnormvcovrrslts rrQIF.fitTs0  "iiooa0DO(O   DIIdkkBEYY[F]]F!FwA+/>>&+A (CtGGBFF4;/0E   e $ + +C 0   j ) 0 0 7|rvvhjj"))//$*IJJD99??4.DGGBFF4$;/0E   j ) 0 0 7s{ dNF% (vvhjj"))//$"AByy}}T"##F+$u e<,,'- &&r)rPrRrrNrVr\rY)NNnone)N)dNgư>g-C6?N)rrrrrr%r]rr classmethodrrr __classcell__rLs@rrErEesR648*0%!N "f-P.BBF@'@'rrEcl^\rSrSrSrS U4Sjjr\S5r\S5r\S5r S Sjr Sr U=r $) riz Results class for QIF Regressionc p>[TU]XUUS9 URRU5uUl ng)N)normalized_cov_paramsr)rTr%rrr) rrrw cov_paramsruse_tkwdsrrLs rr%QIFResults.__init__sB     $zz33F;!Q1rc[URR[5(a Sn[ U5eURR R SnURSU--$)z1 An AIC-like statistic for models fit using QIF. z1AIC not available with QIFIndependence covariancer!r1)rQrrRrr>r^rerrrBdfs raicQIFResults.aicsT djj++_ = =ECS/ ! ZZ__ " "1 %xx!B$rc([URR[5(a Sn[ U5eURR R SnUR[R"URR5U--$)z0 A BIC-like statistic for models fit using QIF. z1BIC not available with QIFIndependence covariancer!) rQrrRrr>r^rerr)logrYrs rbicQIFResults.bicsg djj++_ = =ECS/ ! ZZ__ " "1 %xx"&&1"444rcURRRR[R "URR UR55$)z+ Returns the fitted values from the model. )rrNrirjr)rhr^rwr$s r fittedvaluesQIFResults.fittedvaluessA zz  %%--tzz 46 6rc  SSS/4SURRRR/4SURRRR/4SS/nURR Vs/sHn[ U5PM nnS[U5/4S [ U5/4S [U5/4S [U5/4S S [R"U5-/4SSUR-/4/nUc&URRRS-S-nUcURRnUcURRnSSKJn U "5n U R#XUXUS9 U R%XUUSS9 U $s snf)a Summarize the QIF regression results Parameters ---------- yname : str, optional Default is `y` xname : list[str], optional Names for the exogenous variables, default is `var_#` for ## in the number of regressors. Must match the number of parameters in the model title : str, optional Title for the top table. If not None, then this replaces the default title alpha : float significance level for the confidence intervals Returns ------- smry : Summary instance this holds the summary tables and text, which can be printed or converted to various output formats. See Also -------- statsmodels.iolib.summary.Summary : class to hold summary results )zDep. Variable:NzMethod:rEzFamily:zCovariance structure:)zDate:N)zTime:NzNo. Observations:z No. clusters:zMin. cluster size:zMax. cluster size:zMean cluster size:z%.1fzScale:z%.3f zRegression Resultsr)Summary)gleftgrightynamexnametitleF)rralphar)rrNrLrrRr\rWrminmaxr)ryr exog_names endog_namesstatsmodels.iolib.summaryradd_table_2colsadd_table_params) rrrrrtop_leftyNY top_rightrsmrys rsummaryQIFResults.summarys:-(!2!2!>?A## #jj22 32c!f2 3)CG95%By1*SWI6*SWI6*Vbggbk-A,BC$**!4 56   =JJ((11C7$%E =JJ))E =JJ**E 6y T)#(#(  * du$)  8 ?4s:F)r)F)NNNg?) rrrrrr%rrrrrrrrs@rrrsV*<5566EErrc\rSrSrSrg)rirN)rrrrrrrrrrsrr)"numpyr) collectionsrstatsmodels.base.modelbaserstatsmodels.genmodr+statsmodels.genmod.generalized_linear_modelrstatsmodels.genmod.familiesrr#statsmodels.regression.linear_model regression linear_modellmstatsmodels.base.wrapperwrapperwrapstatsmodels.tools.decoratorsrr rr.r7ModelrELikelihoodModelResultsrRegressionResultsWrapperrpopulate_wrapperrrrr s#%%';-000''7""*m&m" >o'$**o'd n,,nb 33 '4r