带协变量的负二项回归模型中离散参数估计的研究（英文）

带协变量的负二项回归模型中离散参数估计的研究（英文）IntroductionThe negative binomial regression model is commonly used in sta

带协变量的负二项回归模型中离散参数估计的研究 （英文） Introduction Thenegativebinomialregressionmodeliscommonlyusedin statisticalanalysiswhendealingwithcountdata.Inpractice,itis oftennecessarytoincludecovariatesthatarebinaryorcategorical innature.However,thisraisesachallengeintermsofestimating themodelcoefficientsforthesecovariates.Inthispaper,wewill focusontheestimationofdiscreteparametersinnegative binomialregressionmodelswithcovariates. Background Thenegativebinomialdistributionisaprobabilitydistribution thatiscommonlyusedtomodelcountdata.Itisatwo-parameter probabilitydistributionthathasameanandadispersion parameter.Inthecontextofregressionanalysis,thenegative binomialregressionmodelisageneralizedlinearmodel(GLM) thatisusedtomodelcountdatawithcovariates.Themodel assumesthatthelogoftheexpectedcountisalinearcombination ofthecovariates,andthattheresponsevariablefollowsa negativebinomialdistribution. Whenthecovariatesinthemodelarecontinuous,wecan estimatethemodelcoefficientsusingstandardregression techniquessuchasmaximumlikelihoodestimation(MLE). However,whenthecovariatesarebinaryorcategorical,weneed touseslightlydifferenttechniquestoestimatethemodel coefficients. EstimationofDiscreteParameters Whenacovariateisbinary,wecanestimateitscoefficient usingmethodsthataresimilartothoseusedinlogisticregression models.Specifically,wecanuselogisticregressiontoestimatethe probabilityoftheeventoccurring,andthenusethisprobabilityto estimatethenegativebinomialregressioncoefficients. Whenacovariateiscategorical,wecanusedummyvariables torepresentthecategories.Forexample,ifwehaveacategorical variablewithfourlevels,wewouldusethreedummyvariablesin