GLMM applications in some binary count models

Abstract

In this paper, we employed the generalized linear mixed models for the binomial, the beta binomial, the multiplicative binomial and the Com-Poisson Binomial distributions. These are applied to two examples of over-dispersed binomial data with covariates. The logistic linear model is employed for comparative purposes only. SAS PROC NLMIXED is employed for implementing these models. For the logistic-normal model, we also compare our results from PROC NLMIXED with those from PROC GLIMMIX in SAS, and R packages glimmer, and STATA program melogit. For this case, our results agree with those obtained from PROC NLMIXED.The conditional log-likelihoods functions are integrated out using the adaptive Gaussian Quadrature (usually with 32 q-points) and the optimized by using either the Newton-Raphson or Nelder-Mead Simplex algorithms. Starting values are obtained by specifying a large range of grid values for each parameter of the models