DjCBddlZddlmZddlmcmZddlmZddl m Z ddl m Z ddl m Z ddlmcmZddlmcmZddlmZGdd ZGd d eZGd d eZGddeZGddej6ZGddej:ZGddej>Z ejBe ey)N) defaultdict)families)GLM)links)varfuncs)cache_readonlyceZdZdZdZy) 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 ZC:\Crop_Prediction\Backend\crop-ai-system\venv\Lib\site-packages\statsmodels/genmod/qif.pymatzQIFCovariance.mats "!N)__name__ __module__ __qualname____doc__rrrr r s  "rr ceZdZdZdZdZy)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|_y)N num_termsrs r__init__zQIFIndependence.__init__+ rc8|dk(rtj|Sy)Nr)npeyer s rrzQIFIndependence.mat.s 1966#; rNrrrrr rrrrrr"srrceZdZdZdZdZy)QIFExchangeablez= Exchangeable working covariance for QIF regression. cd|_y)Nrrs rr zQIFExchangeable.__init__:r!rcp|dk(rtj|S|dk(rtj||fSy)Nrr)r#r$onesr s rrzQIFExchangeable.mat=s4 1966#;  QY77C:& &rNr%rrrr'r'5srr'ceZdZdZdZdZy)QIFAutoregressivez? Autoregressive working covariance for QIF regression. cd|_y)Nrrs rr zQIFAutoregressive.__init__Kr!rc@|dkr d}t||dk(rtj|S|dk(r=tj||f}d|jdd|dz<||j z }|S|dk(r+tj||f}d|d<d||dz |dz f<|Sy)Nr/z?Groups must have size at least 3 for autoregressive covariance.rrr)rr) ValueErrorr#r$zerosflatT)rrrmsgrs rrzQIFAutoregressive.matNs 70CS/ ! 1966#;  QY((C:&C#$CHHQZQZ 355LCJ QY((C:&CCI !CAs1u JrNr%rrrr-r-Fsrr-c\eZdZdZ dfd ZdZdZdZed fd Z d dZ xZ S) QIFa Fit a regression model using quadratic inference functions (QIF). QIF is an alternative to GEE that can be more efficient, and that offers different approaches for model selection and inference. Parameters ---------- endog : array_like The dependent variables of the regression. exog : array_like The independent variables of the regression. groups : array_like Labels indicating which group each observation belongs to. Observations in different groups should be independent. family : genmod family An instance of a GLM family. cov_struct : QIFCovariance instance An instance of a QIFCovariance. References ---------- A. Qu, B. Lindsay, B. Li (2000). Improving Generalized Estimating Equations using Quadratic Inference Functions, Biometrika 87:4. www.jstor.org/stable/2673612 c |tj}n/t|jtjs t d||_tt|_ | t}nt|ts t d||_ tj|}t! |D||f||d|tt%||_t)|j*|_tt}t/|D]\} } || j1| |j&D cgc]} ||  c} |_|j5|ycc} w)Nz.QIF: `family` must be a genmod family instancez2QIF: `cov_struct` must be a QIFCovariance instance)groupsmissing)rGaussian issubclass __class__Familyr2familyrlist _fit_historyr isinstancer cov_structr#asarraysuperr set group_nameslenendognobs enumerateappend groups_ix _check_args) rrJexogr:r@rDr;kwargsrNignar>s rr z QIF.__init__s= >&&(Ff..@ "344 '-  (*Jj-8 HJJ$F#  4 & ;A  F , O % f% #DAq aL   " #262B2BCB)B-C  Ds2 Ect|t|jk7r d}t|t|j|jjdk7r d}t|y)Nz1QIF: groups and endog should have the same lengthrzGQIF: the length of endog should be equal to the number of rows of exog.)rIrJr2rPshape)rr:r6s rrOzQIF._check_argssX v;#djj/ )ECS/ ! tzz?diiooa0 0-CS/ ! 1rc  |j}|j}tj||}|jj j |}|jj|}|jj j|}|jj j|}|jjj|} |jj} |jd} | | z} tj| } tj| }tj| | f}tj| | f}dg| z}tj| | f}|jjtj u}t#|jj t$j&t$j(f}|j*D]q}tj,||}||||z }||z }||ddf||dfz}d}t/| D]}|jj1t3||}tj|||z }tj|j4||||| ztj|| |dddfz |dddfz }tj|j4||||| zddf<|r|st/| D]}tj||ddfj4|||||fz|z} |sd| |z|dd|fz||dzz }!tj|j4|!tj||z}"tj|j4tj||!|z|z }#nd\}"}#|||| z|fxx| |"z|#zz cc<|| z }t/| D]9}tj6||dd|f}$||xx|$|$j4zz cc<;| |z } ||z }|tj6||z }tt3|j*}%| |%z} ||%z}||%dzz}tj| tj8j;|| }&tj| }'t/| D]}||xxt3|j*dzzcc<tj8j;|||j4}$tj8j;||$}$tj| tj|$| |'|<dtj|j4tj8j;|| z|'z }(|&|(|| |fS)a Calculate the gradient of the QIF objective function. Parameters ---------- params : array_like The model parameters at which the gradient is evaluated. Returns ------- grad : array_like The gradient vector of the QIF objective function. gn_deriv : array_like The gradients of each estimating equation with respect to the parameter. rrNgg?r1r))rJrPr#dotr@linkinversevariance inverse_derivinverse_deriv2derivrDrrVr3rconstantrCrIdentityidentityrNsqrtrangerrIr5outerlinalgsolve))rparamsrJrPlprmeanvaidlidl2vdmpdgngigi_derivgn_derivcn_derivcmatfastvarfastlinkixsdresidsresidr^jjjccrs1crs2km1vxm2m3ungrpqifgcggrads) r objectivez QIF.objectives$ yyffT6"{{'', [[ ! !$ 'kk,,S1{{..s3 [[ ! ! ' ' - OO % % JJqM E XXa[ XXa[88QF#88QF#37xxA++&&(*;*;; KK   ^^U^^ ,  ..% %BBB"IR(ERZFQK#b$h-/EB1X  OO''B3vva(2- ffUWWd32bd vva%"QW+!56AtGD')vveggt'<BqD!$ W"1X =VVDQKMM$(HtBE{$:T$AC&!%2q!t!>" d D affRr23hhqkq /A QK3t~~.1 1K hqk244A a(AVVBq" .CF  / 266(**biioodB&?@@3FD$H,,rct|jtjtjfryt |dr |j }n|jd}tj|j|}|jjj|}|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))rCr@rBinomialPoissonhasattrrrPr#rXrYrZrJsumrK)rrgrrhrir{scales restimate_scalezQIF.estimate_scales dkkH$5$5x7G7G#H I 4 &J1JffTYY'{{'', T!uax DII $:; rc`t|tr||}t| |g||||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:)rCstrrF from_formula) clsformular:rrargsrQmodelr>s rrzQIF.from_formula2sN2 fc "&\F$3#'3!%f 3+13 rc ||jjd|_n||_|It|j|j|j }|j }|j}n|}t|D]>} |j|\} } } } } tjtj| | z}|jdj| |jdj|||krndtj| j tj"j%| | z}tj"j%|| }tjtj||z}|jdj|||krn||z}Atj j tj"j% | }tj"j'|}|j)|}t+||||z |}|j|_t/t0|_ t3|S)a, Fit a GLM to correlated data using QIF. Parameters ---------- maxiter : int Maximum number of iterations. start_params : array_like, optional Starting values tol : float Convergence threshold for difference of successive estimates. gtol : float Convergence threshold for gradient. ddof_scale : int, optional Degrees of freedom for the scale parameter Returns ------- QIFResults object r)r@rgradnormr)stepnorm)rPrVrrrJr@fitrgrcrr#rbrrBrMrXr5rerfinvr QIFResults fit_historyrrAQIFResultsWrapper)rmaxiter start_paramstolgtolrrresultrg_rrrvrtgnormcjacstepsnormvcovrrslts rrzQIF.fitTs0  "iiooa0DO(DO   DIIdkkBEYY[F]]F!Fw A+/>>&+A (CtQGGBFF4$;/0E   e $ + +C 0   j ) 0 0 7t|rvvhjj"))//$*IJJD99??4.DGGBFF4$;/0E   j ) 0 0 7s{ dNF% (vvhjj"))//$"AByy}}T"##F+$u e<,,'- &&r)NNnone)N)dNgư>g-C6?N) rrrrr rOrr classmethodrr __classcell__r>s@rr8r8esL648*0%!N "f-P.BBF@'rr8c^eZdZdZ dfd ZedZedZedZddZ xZ S) rz Results class for QIF Regressionc xt||||||jj|\|_}}}}y)N)normalized_cov_paramsr)rFr rrr) rrrg cov_paramsruse_tkwdsrr>s rr zQIFResults.__init__sD  6   $zz33F;!Q1rct|jjtr d}t ||jj j d}|jd|zzS)zA An AIC-like statistic for models fit using QIF. z1AIC not available with QIFIndependence covariancerr))rCrrDrr2rPrVrrr6dfs raiczQIFResults.aicsQ djj++_ =ECS/ ! ZZ__ " "1 %xx!B$rct|jjtr d}t ||jj j d}|jtj|jj|zzS)z@ A BIC-like statistic for models fit using QIF. z1BIC not available with QIFIndependence covariancer) rCrrDrr2rPrVrr#logrKrs rbiczQIFResults.bicsd djj++_ =ECS/ ! ZZ__ " "1 %xx"&&1"444rc|jjjjt j |jj |jS)z; Returns the fitted values from the model. )rr@rYrZr#rXrPrgrs r fittedvalueszQIFResults.fittedvaluessA zz  %%--tzz 46 6rc dddgfd|jjjjgfd|jjjjgfddg}|jj Dcgc] }t |}}dt|gfd t |gfd t|gfd t|gfd d tj|zgfdd|jzgfg}|&|jjjdzdz}||jj}||jj}ddlm} | } | j#||||||| j%||||d| Scc}w)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:NzNo. Observations:z No. clusters:zMin. cluster size:zMax. cluster size:zMean cluster size:z%.1fzScale:z%.3f zRegression Resultsr)Summary)gleftgrightynamexnametitleF)rralphar)rr@r>rrDrNrIrminmaxr#rir exog_names endog_namesstatsmodels.iolib.summaryradd_table_2colsadd_table_params) rrrrrtop_leftyNY top_rightrsmrys rsummaryzQIFResults.summarys:-(!2!2!>?A## #jj22 3c!f 3 3)CG95%By1*SWI6*SWI6*Vbggbk-A,BC$**!4 56   =JJ((11C7$%E =JJ))E =JJ**E 6y T)#(#(  * d%u$)  8 ?4s:F)F)NNNg?) rrrrr rrrrrrrs@rrrsP*<5566Errc eZdZy)rN)rrrrrrrrsrr)"numpyr# collectionsrstatsmodels.base.modelbaserstatsmodels.genmodr+statsmodels.genmod.generalized_linear_modelrstatsmodels.genmod.familiesrr#statsmodels.regression.linear_model regression linear_modellmstatsmodels.base.wrapperwrapperwrapstatsmodels.tools.decoratorsrr rr'r-Modelr8LikelihoodModelResultsrRegressionResultsWrapperrpopulate_wrapperrrrrs#%%';-000''7""*m&m" >o'$**o'd n,,nb 33 '4r