Multidimensional multiple group IRT models with skew normal latent trait distributions

Abstract

Multidimensional item response theory (MIRT) models are quite useful to analyze datasets involving multiple skills or latent traits, which occur in many applications. However, most of the works consider the usual multivariate (symmetric) normal distribution to model the latent traits and do not deal with the multiple group framework. Also, in general, the works consider a limited number of model fit assessment tools and do not investigate the measurement instrument dimensionality in a detailed way. When the assumption of normality of the latent traits distributions does not hold, misleading results and conclusions can be obtained. Our goal is to propose a MIRT multiple group model with multivariate skew normal distributions under the centered parameterization to model the distribution of the latent traits of each group, presenting simple and feasible conditions for model identification. Such an approach is more flexible than the usual multivariate (symmetric) normal one. In addition, a full Bayesian approach for parameter estimation, structural selection (model comparison and determination of the dimensionality of the measurement instrument) and model fit assessment are developed through Markov Chain Monte Carlo algorithms. The proposed tools are illustrated through the analysis of a real dataset related to the first stage of the University of Campinas 2013 admission exam.