Mixture of Generalized Latent Trait Analyzers for jointly clustering pediatric patients and their clinical conditions

Understanding how different subsets of clinical conditions manifest in pediatric patients can enhance diagnostic accuracy. We aim at identifying groups of pediatric patients possibly affected by appendicitis being similar with respect to subsets of clinical conditions. To achieve this, we introduce the finite Mixture of Generalized Latent Trait Analyzers (MGLTA), allowing us to 1) handle mixed-type data; 2) group pediatric patients into distinct subsets, called components, and, within each component, identify subsets of qualitative/quantitative clinical conditions, called segments. The latter are identified via a parsimonious and flexible specification of the linear predictor. The continuous latent trait incorporated into the model allows to account for possible residual dependence between clinical conditions from the same patient. An EM algorithm is employed for the estimation of model parameters in a maximum likelihood framework, and a Gauss Hermite quadrature is considered to approximate multidimensional integrals not available in closed-form.