Uncovering hidden mental health patterns via a dynamic mixture of Latent Trait Analyzers.

We propose an extension of the Mixture of Latent Trait Analyzers (MLTA) model for clustering longitudinal data on mental health. In detail, we focus on a data set from SHARE (Survey of Health, Ageing and Retirement in Europe), composed of several indicators of mental health, emotional well-being, cognitive function, and behavioural symptoms experienced over the past month by various individuals over four years. Specifically, we move from a Mixture of latent trait analyzers (MLTA) to a Latent Markov Model (LMM) framework with the aim to: (i) enable dynamic clustering of individuals based on their mental health status over time, allowing for time-varying cluster memberships; (ii) account for possible unobserved factors related to psychological well-being. The proposed model can capture both time-constant and time-varying sources of unobserved heterogeneity, which are typical in longitudinal data settings. For parameter estimation, we extend the Baum-Welch algorithm, typically used with LMMs, to handle the presence of a multidimensional continuous latent trait. Since the model involves multidimensional integrals that lack closed-form solutions, suitable approximation methods are required. The obtained results demonstrate the model’s effectiveness in identifying latent states that clearly reflect individuals’ propensity to poor mental health. Further details and an in-depth discussion of the empirical findings will be provided.