Testing homogeneity in clustered (longitudinal) count data regression model with over-dispersion

Abstract

Clustered (longitudinal) count data arise in many bio-statistical practices in which a number of repeated count responses are observed on a number of individuals. The repeated observations may also represent counts over time from a number of individuals. One important problem that arises in practice is to test homogeneity within clusters (individuals) and between clusters (individuals). As data within clusters are observations of repeated responses, the count data may be correlated and/or over-dispersed. For over-dispersed count data with unknown over-dispersion parameter we derive two score tests by assuming a random intercept model within the framework of (i) the negative binomial mixed effects model and (ii) the double extended quasi-likelihood mixed effects model (Lee and Nelder, 2001). These two statistics are much simpler than a statistic derived by Jacqmin-Gadda and Commenges (1995) under the framework of the over-dispersed generalized linear model. The first statistic takes the over-dispersion more directly into the model and therefore is expected to do well when the model assumptions are satisfied and the other statistic is expected to be robust. Simulations show superior level property of the statistics derived under the negative binomial and double extended quasi-likelihood model assumptions. A data set is analyzed and a discussion is given.