A multidimensional latent Markov IRT model

We introduce a multidimensional extension of the latent Markov model which is suitable for the analysis of longitudinal binary data collected by the administration of batteries of tests which measure more than one latent trait. The model is based on the one-parameter or two-parameter logistic parameterisation of the conditional distribution of the response variables given the latent process. The latter is assumed to follow a first-order Markov chain with transition matrices parameterized according to the application of interest. We outline an EM algorithm for the maximum likelihood estimation of the model parameters and we focus on testing the dimensionality of the problem through a likelihood ratio test on these parameters. To illustrate the approach we analyse data from a study aimed at assessing cognitive development in early childhood.