Approximate Inference for Mixtures of Latent Trait Analyzers

The Mixture of Latent Trait Analyzers (MLTA) model com- bines 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 in- tractable integrals in the likelihood can be approximated using either Gauss–Hermite quadrature or a variational approximation. A simulation study is conducted to compare the two approximation methods under different scenarios, evaluating their performance in terms of parameters’ recovery, clustering accuracy, and computational time. The results high- light 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.