Parameter-Driven Models for Time Series of Count Data

• Activity Number: 82
• Type: Contributed
• Date/Time: Monday, August 9, 2004 : 8:30 AM to 10:20 AM
• Sponsor: Biometrics Section
• Author(s): Rachel M. Altman*+ and Brian G. Leroux
• Companies: University of Washington and University of Washington
• Keywords: count data ; generalized linear mixed models ; latent variables ; hidden Markov models

Abstract

Modelling correlated count data is a challenging problem. Unlike the situation for continuous data, for which the multivariate normal distribution is available, for count data there is no convenient and flexible class of multivariate distributions that can capture the shape of the distribution and the autocorrelation. Furthermore, techniques which have been developed for assessing the fit of models for normally distributed data do not extend readily to the count data setting. We propose a general class of parameter-driven (latent variable) models for count data. This class includes the generalized linear mixed model, hierarchical generalized linear model, and the hidden Markov model. We consider the interpretation of these models and discuss a parameter estimation method which yields estimates of the regression coefficients that are both efficient and robust to misspecification of the latent process. We apply these ideas to the analysis of multiple sclerosis and polio incidence data.