Parameter Maximum Likelihood Estimations From Incomplete Data In Generalized Linear Models

The generalized linear model (GLM) which is suitable for the continuous data and the discrete data has great application in biology, medicine, economy and society field, etc. The objective of this paper is to carry on the parameter estimations of the model when incomplete data appear in the GLM.It is firstly introduced that the background and the development of the GLM in the domestic and foreign in this paper. And then the necessary theoretical knowledges such as Newton-Raphson algorithm, EM algorithm and the Metropolis-Hasting algorithm of Markov chain sample are presented.The central work of the paper is from the chapter 3 to chapter 5. In chapter 3, based on the covariate and the response variable both are discrete variables, at the same time covariate and response variable both are missing at random, the expressions of EM algorithm for parameter estimation are obtained and the asymptotic variances of the parameter estimation of models are presented through Louis method. In chapter 4, when the missing data mechanism of covariate and response variable is non-ignorable and missing variables could be discrete, continuous or mixed, the EM algorithm of parameter estimation of model is derived and approaches of modeling for the missing data mechanism is discussed. In chapter 5, the maximum likelihood estimation of model parameters which are incomplete data in the General linear mixed model (GLMM) in which the missing mechanism is non-ignorable are studied. The Monte Carlo EM (MCEM) algorithm and the Monte Carlo Newton-Raphson (MCNR) algorithm of estimation parameters are also presented.The typical algorithms mentioned in this paper are random simulated, especially when the missing data mechanism is non-ignorable. The results of the simulation show that eliminating the missing observation without considering the missing data mechanism will lead to large deviations.