Simple Structure Detection Through Bayesian Exploratory Multidimensional IRT Models

In modern validity theory, a major concern is the construct validity of a test, which is commonly assessed through confirmatory or exploratory factor analysis. In the framework of Bayesian exploratory Multidimensional Item Response Theory (MIRT) models, we discuss two methods aimed at investigating the underlying structure of a test, in order to verify if the latent model adheres to a chosen simple factorial structure. This purpose is achieved without imposing hard constraints on the discrimination parameter matrix to address the rotational indeterminacy. The first approach prescribes a 2-step procedure. The parameter estimates are obtained through an unconstrained MCMC sampler. The simple structure is, then, inspected with a post-processing step based on the Consensus Simple Target Rotation technique. In the second approach, both rotational invariance and simple structure retrieval are addressed within the MCMC sampling scheme, by introducing a sparsity-inducing prior on the discrimination parameters. Through simulation as well as real-world studies, we demonstrate that the proposed methods are able to correctly infer the underlying sparse structure and to retrieve interpretable solutions.