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Biometrika 1999 86(1):169-181; doi:10.1093/biomet/86.1.169
© 1999 by Biometrika Trust
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A state space model for multivariate longitudinal count data

B JørgensenA1, S Lundbye-ChristensenA2, PX-K SongA3 and L SunA4

A1 Department of Statistics and Demography, Odense University, Campusvej 55, DK-5230 Odense M, Denmark A2 Department of Mathematics and Computer Science, Institute for Electronic Systems, Aalborg University, Fredrik Bajers Vej 7, DK-9220 Aalborg Ø, Denmark A3 Department of Mathematics and Statistics, York University, 4700 Keele Street, North York, Ontario, Canada M3J 1P3 song@mathstat.yorku.ca A4 Department of Statistics, University of British Columbia, Vancouver, B.C., Canada B6T 1Z2 lisun@stat.ubc.ca

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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