Statistical Inference For Mixture Of Generalized Linear Models

Linear model is a statistical model for studying the relationship between variables and widely used in biology,medicine,management,economics and other fields.Since the dependent variable may be discrete,it is necessary to extend the linear model to generalized linear model.In actual problems,if only the overall data is analyzed,the conclusions obtained tend to show deviations.To solve this type of problem,it is necessary to simultaneously model heterogeneous populations.In the heterogeneous population,the mixture regression model is an important analytical tool.In order to understand the source of variance and effectively control variance,it is necessary to model variance at the same time.In the classical generalized linear model,there may be a correlation between the response variables.The so-called "overdispersion" may occur.Its distribution is no longer the standard form of the exponential family distribution.Then the maximum likelihood method is no longer suitable for estimating the parameters.Therefore,the quasi-likelihood estimation method was developed.In the quasi-likelihood estimation method,it is only necessary to assume that the first and second moments of the variable exist.This article is structured as follows:Firstly,according to different statistical characteristics,the population was divided into two or more categories,Only the mean value is used to establish the model and the mixture of generalized linear model is obtained.Using EM algorithm to get pseudo-likelihood and extended quasi-likelihood estimation of parameters.Then the Monte Carlo simulation was used to verify the validity of the model,and the practicality and feasibility of the model were verified by example data.Secondly,for heterogeneous heteroscedasticity data,mean parameters and dispersion parameters are modeled and mixture of double generalized linear model is obtained.Then,the EM algorithm is used to estimate the parameters.The validity and practicability of the model are verified by Monte Carlo and a real example data.Finally,the variable selection is made by the penalty likelihood function with the mixture of double generalized linear model.According to the three different penalty functions,the corresponding penalty likelihood function is obtained.The BIC criterion is used to select the adjustment parameters of the mean model and the variance model.Then iterative algorithm is used to get the specific calculation process of variable selection.Furthermore,the method of variable selection proposed by simulation test is scientific.