Posterior mode estimation in dynamic generalized linear mixed models. (REVISED, June 2000)

Dynamic generalized linear mixed models for longitudinal data
combine the generalized linear mixed model and the dynamic
generalized linear model dealing with the case that both unit- and
time-specific parameters are allowed. We base statistical inference
on posterior mode estimation thus avoiding numerical integrations
in high dimensions or Monte Carlo simulations which are necessary
for posterior mean estimation in a fully Bayesian analysis. This
results in a Fisher scoring algorithm with backfitting steps in
each scoring iteration, since estimating equations of the
unobserved effects mutually contain each other effect. Algorithms
for estimation of random effects and dynamic effects can be used in
each backfitting step due to the additive definition of the model.
Estimation of unknown hyperparameters is done by an EM-type
algorithm where posterior modes and curvatures resulting from the
Fisher scoring algorithm are substituted for posterior means and
covariances. We apply the model to multicategorical business test
data.