On a Unified Generalized Quasi-likelihood Approach for Familial-Longitudinal Non-Stationary Count Data

Abstract

In this paper, conditional on random family effects, we consider an auto-regres- sion model for repeated count data and their corresponding time-dependent covariates, collected from the members of a large number of independent families. The count responses, in such a set up, unconditionally exhibit a non-stationary familial-longitudinal correlation structure. We then take this two-way correlation structure into account, and develop a generalized quasilikelihood (GQL) approach for the estimation of the regression effects and the familial correlation index para- meter, whereas the longitudinal correlation parameter is estimated by using the well-known method of moments. The performance of the proposed estimation approach is examined through a simula- tion study. Some model mis-specification effects are also studied. The estimation methodology is illustrated by analysing real life healthcare utilization count data collected from 36 families of size four over a period of 4 years.