Semiparametric Approach to the Multivariate Mixed Rasch Model

Abstract

The multivariate mixed Rasch model is used to analyse binary reponses of questionnaires with several subscales. The responses of our model are two-way correlated. First, at a given subscale of questionnaire, the binary responses of a single individual are correlated: second, they are repeated over the subscales and also become correlated. It is, however, well known that a full likelihood analysis for such mixed models is hampered by the need for numerical integrations. To overcome such integration problems, we propose the generalized estimating equations approach. Approximations of the joint moments of the variables are proposed. The estimators of the fixed effects parameters and variance components are consistent and asymptotically normal. We illustrate the usefulness method with simulations and with an analysis of real data from quality of life.KeywordsGeneralized linear mixed modelfixed effects andvariance componentscorrelated datageneralized estimating equationsmodelsRasch modelquality of life