Approximate estimation in generalized linear mixed models with applications to the Rasch model

This article discusses two different approaches to estimate the difficulty parameters (fixed effects parameters) and the variance of latent traits (variance components) in the mixed Rasch model. The first one is the generalized estimating equations (GEE2) which uses an approximation of the marginal likelihood to derive the joint moments whilst the second approach uses the maximum of the approximate likelihood. We illustrate these methods with a simulation study and with an analysis of real data from a quality of life.