Adequacy of H-Likelihood Estimation Method for Unbalanced Clustered Counting Data Models.

Abstract

     This article would concentrate on hierarchical generalized linear models, including generalized linear mixed-models, which are the extension of linear models. In generalized linear models, the dependent variable assumes every distribution from exponential family distributions, e.g., normal, poisson, binomial, gamma, etc.

      The poisson-gamma method was applied, where the dependent variable represents the poisson distribution and the standard error is defined by the gamma distribution. In generalized linear models, several estimation methods have been used. Throughout this study, the hierarchical likelihood estimation method was used to determine the effectiveness of this methodology for both data balanced and unbalanced.

      This article compares the Adequacy of poisson-gamma H-Likelihood estimation method of mixed effects clustered data models with equal and unequal cluster sizes. This was evaluated in terms of probability of type-I error rate, power and standard error by applying computer simulation. Simulation is performed using different cluster numbers and different cluster sizes. The results show that the performance of the hierarchical likelihood estimation technique provided close approximations in the event of balanced and unbalanced data, while the output of the technique was approximately equivalent in both instances, regardless of cluster size inequality.