The Extensions Of Three Multivariate Statistical Models And The EM Algorithm

This paper is devoted to extending three multivariate statistical models, and the EM algorithm is used to estimate parameters of them based on maximum likelihood estimates. In the Chapter 2, we extend common factors and categorical variables in the models of finite mixture of factor analyzers based on multivariate generalized linear models and the principle of maximum random utility in the probabilistic choice theory. The EM algorithm is used to estimate parameters of the extended models, and the Newton-Raphson iteration is embedded in M-step of EM algorithm for some parameters. The algorithm is illustrated with the numerical simulation and real example. For analyzing correlated unordered categorical data, in the Chapter 3 we propose multinomial probit latent variables models that are defined with a factor analysis and covariates, and discuss its identification. Some useful multinomial probit models are special cases of the proposed model. The MCECM algorithm is used to estimate parameters of the proposed models, and is illustrated with a simulation study, which shows MCECM algorithm for the proposed model is rather efficient and flexible. Based on the generalized linear mixed models with varying coefficients and the finite mixture models, we propose the finite mixture generalized linear random effects models with varying coefficients in the Chapter 4. The proposed models can be used to analysis longitudinal data which comes from nonhomogeneous population and varies with time. Meanwhile, we also give out the MCEM algorithm for the proposed models and the simulation example for this algorithm.