Abstract: In this paper, a mixture of generalized linear model is proposed and the parameter estimation to fit the practical data is performed. Firstly, based on the existence of the first, second order moments of a heterogeneous population, the mixture of generalized linear models is applied to establish the mean model in the subpopulation, and the extended quasi-likelihood and pseudo-likelihood functions are constructed. Moreover, by using EM algorithm, the mean parameter, dispersion and mixing ratio are estimated, and Monte Carlo simulation studies are indicated the effectiveness. Finally, a real example illustrates that the model and method is scientific and useful.

Key words: mixture of generalized linear models, extended quasi-likelihood, pseudo-likelihood, EM algorithm