An extension of the latent Markov Rasch model is described for the analysis
of binary longitudinal data with covariates when subjects are collected in
clusters, e.g. students clustered in classes. For each subject, the latent
process is used to represent the characteristic of interest (e.g. ability)
conditional on the effect of the cluster to which he/she belongs. The latter
effect is modeled by a discrete latent variable associated with each cluster.
For the maximum likelihood estimation of the model parameters we outline an EM
algorithm. We show how the proposed model may be used for assessing the
development of cognitive Math achievement. This approach is applied to the
analysis of a dataset collected in the Lombardy Region (Italy) and based on
test scores over three years of middle-school students attending public and
private schools.