Multidimensional Bayesian IRT Model for Hierarchical Latent Structures

Abstract: It is reasonable to consider, in many cases, that individuals' latent traits have a hierarchical structure such that more general traits are a suitable composition of more specific ones. Existing item response models that account for such hierarchical structure feature have considerable limitations in terms of modelling and/or inference. Motivated by those limitations and the importance of the theme, this paper aims at proposing an improved methodology in terms of both modelling and inference to deal with hierarchically structured latent traits in an item response theory context. From a modelling perspective, the proposed methodology allows for genuinely multidimensional items and all of the latent traits in the assumed hierarchical structure are on the same scale. Items are allowed to be dichotomous or of graded response. An efficient MCMC algorithm is carefully devised to sample from the joint posterior distribution of all the unknown quantities of the proposed model. In particular, all the latent trait parameters are jointly sampled from their full conditional distribution in a Gibbs sampling algorithm. The proposed methodology is applied to simulated data and a real dataset concerning the Enem exam in Brazil.