Bayesian Modeling of Longitudinal Multiple-Group IRT Data with Skewed Latent Distributions and Growth Curves

In this work, we introduce a multiple-group longitudinal IRT model that accounts for skewed latent trait distributions. Our approach extends the model proposed by Santos et al. in 2022, which introduced a general class of longitudinal IRT models. The latent traits follow a multivariate skew-normal distribution, induced by an antedependence structure with centered skew-normal errors. Additionally, latent mean trajectories are modeled using quadratic curves, while structured covariance matrices capture within-participant dependencies. A three-parameter probit model is employed for dichotomous items. Bayesian parameter estimation and model fit assessment are conducted through a hybrid MCMC algorithm, combining the FFBS sampler with Metropolis-Hastings steps. The model's effectiveness is demonstrated through an application to real data from the Longitudinal Study of the 2005 School Generation in Brazil (GERES project), where it outperforms the normal model by better capturing asymmetry in latent traits. A simulation study further supports its robustness across various test conditions.