Modeling Count Data from Dependent Clusters with Poisson Mixed Models
K. A. N. K. Karunarathna *
Department of Mathematics, Faculty of Science, Eastern University, Sri Lanka and Postgraduate Institute of Science, University of Peradeniya, Sri Lanka
Pushpakanthie Wijekoon
Department of Statistics and Computer Science, University of Peradeniya, Sri Lanka
*Author to whom correspondence should be addressed.
Abstract
Responses collected from dependent clusters are affected by the dependence among clusters and it should be taken into account in modeling such responses. In this study, a new approach was evaluated to incorporate cluster dependence in generalized linear Poisson mixed models for count responses from dependent clusters. Performance of this approach was evaluated by using a simulation process under three different designs and different covariates. The Marginal Generalized Quasi-likelihood (GQL) method was used for estimation of parameters with the cluster dependence. Monte Carlo likelihood (MCL) and Penalized Quasi-likelihood (PQL) estimates also were obtained for the purpose of comparison. Proposed approach was tested with a real data set also.
The proposed approach, with the incorporation of cluster dependence, gives better estimates for both fixed effects and variance of random effects with low standard errors with compared to the estimates obtained by ignoring the cluster dependence. Therefore, the proposed approach can be used for modeling count responses from a dependent cluster set up.
Keywords: Poisson mixed model, cluster counts, inter correlations, dependent clusters