Dynamic mixture of latent trait analyzers for clustering longitudinal data

The Mixture of Latent Trait Analyzers (MLTA) is a model- based clustering approach specifically designed for categorical data anal- ysis. It enables clustering of units through a Finite Mixture (FM) frame- work, while also addressing the standard local independence assumption typically underlying FMs. This is achieved by incorporating a multidi- mensional continuous latent trait into the model, which captures resid- ual heterogeneity among units within the same cluster. We propose an extension of the MLTA model to accommodate longitudinal data. Specif- ically, we move from a static FM specification to a Latent Markov Model (LMM) framework, which (i) captures the dynamic nature of the data and (ii) enables dynamic clustering of units over time. For parameter estimation, the standard Baum-Welch algorithm is extended to account for the presence of the continuous latent trait in the model. Nevertheless, the solution of multidimensional integrals not available in closed form is required. Suitable approximation methods are considered to overcome the issue.