Abstract
Establishing model parameters is fast becoming more complex especially with generalized
linear mixed models (GLMMs); which comprises of generalized linear models and
classical linear mixed models. Evaluating generalized linear mixed models (GLMMs)
parameters with maximum likelihood techniques involves some levels of complexity, to
proffer solutions to this challenge, techniques involving approximation of integrals were
considered in this paper. Some approximation methods for parameter estimation were
considered to establish the most effective and adaptive model using a good number of
model performance metrics/criteria. Penalized quasi-likelihood, adaptive gauss-Hermite
quadrature, and Laplace approximation estimation techniques were considered to fit the
real clinical data set with binary outcomes. Real-life data analysis showed some better
fitness and superiority of an adaptive gauss-Hermit quadrature technique over some other
existing estimation techniques using a set of model performance metrics. Data users at
various levels of analysis may now consider adaptive gauss-Hermite quadrature technique
over other estimation techniques in fitting GLMMs with binary responses. Coefficients of
the model with good performance metrics were also considered in establishing effects of
clinical follow-up on medical diagnoses of individual patients.