The Estimate Of Dynamic Zero-inflated Poisson Model With Random Effects

Zero-inflated count data is widespread in the fields of biomedicine,agriculture,insurance industry and so on.In order to characterize this data,researchers have done a lot of research on the zero-inflated model.However,in practical problems,some zero-inflated count data is collected by time.In this case,the classical zero-inflated model may be no longer suitable.Therefore,based on the ZIP model with random effects,this paper will study the dynamic zero-inflated Poisson model with random effects and the semiparametric dynamic zero-inflated Poisson model with random effects.Firstly,we establish a dynamic ZIP model with random effects by introducing lag item,and two different methods of parameter estimation are discussed,including MCEM algorithm and Nonparametric Maximum Likelihood(NPML)method.This model can not only describe the correlation within individuals,but also describe the influence of the previous moment on the present moment.Secondly,the correlation between the count data and the time is unknown,and if there is a linear relationship between them,it may lead to the unreasonable structure of the model.For this reason,we introduce an unknown smooth function in the model,and establish a semiparametric dynamic zero-inflated Poisson model with random effects.In this paper,we approximate the unknown function based on p-spline,and combine penalized log-likelihood function to discuss the parameter estimation of the model under the framework of MCEM algorithm.In addition,stochastic simulation are provided under finite sample to evaluate the effectiveness of the parameter estimation methods of two model.Finally,we apply two dynamic models to the practical problems and analysis the relevant data.At the same time,in order to illustrate the fitting situation of two dynamic models,we also use ZIP model with random effects and semiparametric ZIP model with random effects to fit the real data,based on the AIC criterion,we found that the dynamic models presented in this paper is superior to the corresponding non-dynamic models.