The Estimation Of Two-component Poisson Mixture Model With Robust Random Effects

In the fields of biomedicine,economics,agriculture,insurance,etc.,there are a large number of count data,which sometimes come from different populations and have the characteristics of repeated measurement.Researchers often use discrete models with random effects for research.However,the widely used assumptions of normal random effects sometimes contradict reality.In order to describe this type of data reasonably,the paper constructs a two-component mixed Poisson random effects model,in which the random effects are assumed to obey the two-dimensional NI-type distribution.It includes not only the normal distribution but also the heavy-tailed T distribution and the Slash distribution,so that the model built has a certain degree of flexibility and robustness.The paper uses Monte Carlo Expectation-Maximization(MCEM)method and Bayesian method to study the model parameter estimation in detail for the built model.In the MCEM method,the paper uses the characteristics of the flexible hierarchical structure of the NI class distribution and gives the model log-likelihood function.Then,the Metropolis-Hastings(MH)algorithm is used to sample from the conditional density of random effects to obtain the approximate estimation of the highdimensional integral involved in the algorithm,and then obtain the specific algorithm of parameter estimation.In addition,under the Bayesian framework,the paper derives the full condition posterior distribution of each parameter under the condition of the prior distribution of the model parameters.At the same time,for the posterior density without conventional distribution,the paper uses the Gibbs sampler with MH algorithm to give a sampling method based on the full conditional distribution,and then obtain the Bayesian estimation of the parameters.Subsequently,this paper conducts a series of numerical simulation studies for the two-component mixed Poisson random effect model under different sample sizes and different random effect distributions,and further illustrates the effectiveness of the estimation method in this paper.Finally,this paper also uses one-component and two-component mixed Poisson random effects regression models to fit the actual data and give parameter estimates.Through the study of the selection criteria such as AIC,BIC and DIC and fitting effects,it shows that the two-component mixed Poisson random effects model performs better than the one-component Poisson random effects model when fitting the actual data in the text,and the two-component Poisson mixed model under the T random effect is better than other models in the comparison.