Parameter Estimation Of Two-component Negative Binomial Mixture Regression Model With Bivariate Random Effects

For a long time, Negative Binomial regression model has been paid much at-tention due to its adaptation to overdispersion. Random effects can be incorporated into the regression model to account for with-cluster correlation when outcomes come from different clusters. Therefore, the Negative Binomial mixture regression model with random effects has played an important role in theory and practice.In this paper, we discuss two-component mixture regression model to describe outcomes that arise from two sub-populations, and we extend the two-component Poisson mixture regression model with bivariate random effects to the case of two-component Negative Binomial mixture regression model. In this way, we can better deal with the overdispersed data in the situation that two components are correlated. After a brief introduction of the theory model and basic properties of the model, three different methods of parameter estimation are discussed, including the best linear un-biased prediction (BLUP)-type estimation with restricted maximum quasi-likelihood (REMQL), Gaussian Quadrature method and non-parametric maximum likelihood (NPML) estimation method, and we derive parameter estimations based on EM al-gorithm and iterative formula. Stochastic simulations are provided to discuss and compare the three methods we present in this paper, and we find that all the three methods perform well, while Gaussian Quadrature method performs slightly better. What's more, the greater the sample size is, the closer the estimations are to the true values. Besides, small mean samples exhibit larger bias for the estimations. Finally, annual measles data are given to illustrate the methods in our paper.