A Survey on Quasi-Likelihood Estimation Approaches for Longitudinal Set-ups

The Com-Poisson (CMP) model is one of the most popular discrete generalized linear models (GLMS) that handles both equi-, overand under-dispersed data. In longitudinal context, an integer-valued autoregressive (INAR(1)) process that incorporates covariate specification has been developed to model longitudinal CMP counts. However, the joint likelihood CMP function is difficult to specify and thus restricts the likelihood-based estimating methodology. The joint generalized quasi-likelihood approach (GQL-I) was instead considered but is rather computationally intensive and may not even estimate the regression effects due to a complex and frequently ill-conditioned covariance structure. This paper proposes a new GQL approach for estimating the regression parameters (GQL-III) that is based on a single score vector representation. The performance of GQL-III is compared with GQL-I and separate marginal GQLs (GQL-II) through some simulation experiments and is proved to yield equally efficient estimates as GQL-I and is far more computationally stable. Keywords—Longitudinal, Com-Poisson, Ill-conditioned, INAR(1), GLMS, GQL.