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.