Abstract
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-varying covariates may enter via either the Poisson model or the latent gamma process. Estimation is based on the Kalman smoother, and we consider analysis of residuals from both the Poisson model and the latent process. A reanalysis of Zeger's (1988) polio data shows that the choice between a stationary and nonstationary model is crucial for the correct assessment of the evidence of a long-term decrease in the rate of U.S. polio infection. Keywords:EM algorithm; Estimation function; Generalised linear model; Kalman filter; Kalman smoother; Latent process; Mixed Poisson distribution; Overdispersion; Regression model; Residual analysis; Time-varying covariate.
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