Three Stochastic Versions of the EM Algorithm for Estimating Longitudinal Rasch Model

Abstract

The Rasch model is a latent variable model which is widely used for the analysis of psychological data and recently for the study of quality of life data in medicine. In this article we propose an extension of the Rasch model to the case of repeated measurements of quality of life. The complex form of the likelihood function implies that it is impossible to find directly estimates. The classical EM algorithm is not a practical solution in the present context. So we propose to use three stochastic versions of the EM: the MCEM, SEM algorithms and a new algorithm we call SGEM. Some theoretical properties of these three algorithms are exposed. Illustrations with simulated and real data are given.

Keywords:

• Rasch model
• Stochastic algorithm
• Longitudinal binary data