Approximate Inference for Mixtures of Latent Trait Analyzers

The Mixture of Latent Trait Analyzers (MLTA) model combines finite mixture models and latent trait analysis to cluster units while also accounting for within-cluster dependence among variables. Parameter estimation is performed via an EM algorithm, where the intractable integrals in the likelihood can be approximated using either Guass-Hermite quadrature or variational approximation. A simulation study is conducted to compare the two approximation methods under different scenarios, evaluating their performance in terms o f parameters’ recovery, clustering accuracy, and computational time. The results highlight the trade-off between precision and efficiency, suggesting that the choice of approximation should balance the desired level of accuracy with the available computational resources.