Monte Carlo EM algorithm for generalized linear models with linear structural random effects
We propose generalized linear mixed models with linear structural random effects based on generalized linear mixed models. In this article, an Monte Carlo EM type algorithm is developed for maximum likelihood estimations of the proposed models. To avoid computation of the complicated multiple integrals involved, the E-step is completed by Monte Carlo techniques. The M-step is carried out efficiently by simple Conditional Maximization. Standard errors of MLEs are obtained via Louis's identity.
The study of the stability of many stochastic processes as Markov chains needs sometimes to use eigenvalues and eigenvectors of the transition matrix. This paper is an investigation on a methodology which computes fuzzy eigenvalues and fuzzy eigenvectors within the context of a fuzzy Markov chain transition matrix, under max-min composition.