Comparions of Estimation Methods in Generalized Linear Mixed Models with an Application

In statistics, a Generalized Linear Mixed Model (GLMM) is a particular type of mixed model. It is an extension to the generalized linear model in which the linear predictor contains random effects in addition to the usual fixed effects. Fitting such models by maximum likelihood involves integrating over these random effects. In general, these integrals cannot be expressed in analytical form. Various approximate methods have been developed, but none has good properties for all possible models and data sets. For this reason, methods involving Laplace, Numerical Quadrature or Markov Chain Monte Carlo have increased in use as increasing computing power and advances in methods have made them more practical. This study compares different approaches that are applied for interpreting the parameters in mixture experiments and measuring the effects of the components in the case of the response, which has a Binary or a Poisson distribution, with application to Trabzon Youth survey data.