The Estimation Of Zero-inflated Poisson Model With Robust Random Effects

In the actual problem,there are a large number of repeated measurements with excessive zero-inflated data,about study of this kind of data,the popular treatment method is to use zero-inflated Poisson model with random effect to fit,however,in the actual problem,the assumptions of general normal random effect may not be satisfied,especially when the data appear heavy tail phenomenon,because of this,this paper has made new progress on the basis of what has already been achieved,putting forward a zero-inflated Poisson model with robust random effect,which random effects include not only the classic normal distribution.It also contains the T distribution and Slash distribution which apply to heavy tails.For the establishment of a zero-inflated Poisson model with NI random effect,the paper studies the parameter estimation of the model in detail.First of all,the paper uses the MCEM method to explore the parameter estimation of the model,for the zero components and Poisson components of the model,the paper introduces potential variables to mark these two components,and combined with the hierarchical structure of NI random effects,the paper gives the layered description of the model,and then obtains the log-likelihood function of completely data;Then,combining the Metropolis-Hastings(MH)algorithm and the Gibbs algorithm,the approximate expression of expectation in the EM algorithm is obtained,so that the parameter estimation is obtained by maximizing the expression.Secondly,the paper also uses the Bayes method to study the model parameter estimation,under the a priori distribution of the given parameters,calculates the full condition distribution of the model parameters under the three distributions of NI random effect,and for the unconventional full condition distribution,the paper obtains the corresponding random sample by using MH algorithm and Gibbs algorithm,thus giving the Bayes estimate.Finally,the paper also uses a large number of random simulation studies to further explain the effectiveness of the proposed estimation method,at the same time,the model constructed in this paper is applied to the actual hospital outpatient service utilization data,and combined with the model selection criteria to study the model fitting effect under different random effects.