Markov Chain Monte Carlo Simulation in Dynamic Generalized Linear Mixed Models

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.