A state space model for multivariate longitudinal count data

We propose a nonstationary state space model for multivariate longitudinal count data driven by a latent gamma Markov process. The Poisson counts are assumed to be conditionally independent given the latent process, both over time and across categories. We consider a regression model where time-vary ing covariates may enter via either the Poisson model or the latent gamma p rocess. Estimation is based on the Kalman smoother, and we consider analysi s of residuals from both the Poisson model and the latent process. A reanal ysis of Zeger's (1988) polio data shows that the choice between a stationar y and nonstationary model is crucial for the correct assessment of the evid ence of a long-term decrease in the rate of U.S. polio infection.