Journal of Statistical Planning and Inference 129 (2005) 159 – 179 www.elsevier.com/locate/jspi Generalized estimating equations for longitudinal mixed Rasch model Mohand L. Feddag a , ∗ , Mounir Mesbah b a Laboratory SABRES, University of South Brittany, RueYves Mainguy, 56000 Vannes, France b UFR SSI, University of South Brittany, RueYves Mainguy, 56000 Vannes, France Available online 21 August 2004 Abstract In this paper, the problem of estimating the fixed effects parameters and the variance of the random effects (variance components) in longitudinal mixed Rasch model is considered. It is well known that estimating these parameters by the method of maximum likelihood faces computational difficulties. As an alternative, we propose the generalized estimating equations approach. Approximations of the joint moments of the variables are proposed. The estimators obtained are consistent and asymptotically normal. We illustrate the usefulness of the method with simulations and with an analysis of real data from quality of life. © 2004 Elsevier B.V.All rights reserved. Keywords: IRT models; Rasch model; Generalized linear mixed model; Fixed effects; Random effects; Generalized estimating equations; Longitudinal data; Fisher-scoring algorithm; Quality of life 1. Introduction Item response theory (IRT) models (Fischer and Molenaar, 1995) are increasingly used in various fields where subjective variables need to be measured using questionnaires with polychotomous items. This is usual in health sciences and clinical trials, where these sub- jective variables could be pain, depression or quality of life. Other examples come from marketing where satisfaction or attitudes need to be well measured and educational testing services where well calibrated exams need to be produced. One of the most popular IRT models is the Rasch model (Fischer and Molenaar, 1995). For a single administration of ∗ Corresponding author. E-mail address: mohand-larbi.feddag@univ-ubs.fr (M.L. Feddag). 0378-3758/$ - see front matter © 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.jspi.2004.06.045