Likelihood inference for the latent Markov Rash model

We present a latent Markov version of the Rasch model which is suitable for the analysis of binary longitudinal data. For the maximum likelihood estimation of this model we illustrate an EM algorithm implemented by means of certain recursions known in the hidden Markov literature. We also illustrate how certain hypotheses on the transition matrix may be tested by using a likelihood ratio statistic. As an illustration, we analyze data coming from a study on the level of dementia of a sample of elderly people. We also show how the model can be extended to deal with discrete response variables having more than two levels and to deal with multivariate longitudinal data.