This article is concerned with hierarchical generalized linear models. It includes generalized linear models and generalized linear mixed models, which are related to linear models.
In generalized linear mixed models, the dependent variable and the standard error follow any distribution from the exponential family, e.g. normal, Poisson, binomial, gamma, etc. We studied counting data, and then use the Poisson-gamma model,where the dependentvariable follows the Poisson distribution and the standard error follow the gamma distribution. Several estimation techniques can be used for generalized linear mixed model. In this paperthe hierarchical likelihood estimation technique was used to prove the performance of H-likelihood methodwhen thecounting data were balanced or unbalanced.
Real data were used to test the performance of Poisson-gamma H-likelihood estimation method in case of balanced and unbalanced counting data.When real data used in the past research for another problem, it was noticed that the performance of the hierarchical likelihood estimation technique gave a close approximations in the event of balanced and unbalanced counting data, and the output of the technique was approximately equivalent in both instances.
A comparative study of approximation methods for maximum likelihood estimation in generalized linear mixed models (GLMM)