Markov Chain Monte Carlo Simulation in Dynamic Generalized Linear Mixed Models.
Collaborative Research Center 386, Discussion Paper 8
Dynamic generalized linear mixed models are proposed as a regression tool for nonnormal longitudinal data. This framework is an interesting combination of dynamic models, by other name state space models, and mixed models, also known as random effect models. The main feature is, that both time- and unit-specific parameters are allowed, which is especially attractive if a considerable number of units is observed over a longer period. Statistical inference is done by means of Markov chain Monte Carlo techniques in a full Bayesian setting. The algorithm is based on iterative updating using full conditionals. Due to the hierarchical structure of the model and the extensive use of Metropolis-Hastings steps for updating this algorithm mainly evaluates (log-)likelihoods in multivariate normal distributed proposals. It is derivative-free and covers a wide range of different models, including dynamic and mixed models, the latter with slight modifications. The methodology is illustrated through an analysis of artificial binary data and multicategorical business test data.