Approximate estimation in generalized linear mixed models, with applications to Rasch models

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

Pairwise likelihood for the longitudinal mixed Rasch model

Inference in Generalized linear mixed models with multivariate random effects is often made cumbersome by the high-dimensional intractable integrals involved in the marginal likelihood. An inferential methodology based on the marginal pairwise likelihood approach is proposed. This method belonging to the broad class of composite likelihood involves marginal pairs probabilities of the responses which has analytical expression for the probit version of the model, from where we derived those of the logit version. The different results are illustrated with a simulation study and with an analysis of a real data from health-related quality of life. (C) 2008 Elsevier B.V. All rights reserved

Pairwise likelihood for the longitudinal mixed Rasch model

Inference in Generalized linear mixed models with multivariate random effects is often made cumbersome by the high-dimensional intractable integrals involved in the marginal likelihood. An inferential methodology based on the marginal pairwise likelihood approach is proposed. This method belonging to the broad class of composite likelihood involves marginal pairs probabilities of the responses which has analytical expression for the probit version of the model, from where we derived those of the logit version. The different results are illustrated with a simulation study and with an analysis of a real data from health-related quality of life.

Statistical inference for the multidimensional mixed Rasch model

Inference in generalized linear mixed models with multivariate random effects is often made cumbersome by the high-dimensional intractable integrals involved in the marginal likelihood. This article presents an inferential methodology based on the GEE approach. This method involves the approximations of the marginal likelihood and joint moments of the variables. It is also proposed an approximate Akaike and Bayesian information criterions based on the approximate marginal likelihood using the estimation of the parameters by the GEE approach. The different results are illustrated with a simulation study and with an analysis of real data from health-related quality of life