Title: An unconstrained approach to rotational indeterminacy in Bayesian exploratory multidimensional IRT models
Authors: Sara Fontanella - The Open University (United Kingdom) [presenting]
Lara Fontanella - University of Chieti-Pescara (Italy)
Pasquale Valentini - University of Chieti-Pescara (Italy)
Nickolay Trendafilov - Open University (United Kingdom)
Abstract: Within the social and behavioural sciences, item-level data are often categorical in nature and item factor analysis (IFA) represents an appropriate tool for their analysis. We consider only a specific class of factor analytic models, namely Multidimensional Item Response Theory (MIRT) models. These models can be defined in terms of both exploratory and confirmatory perspectives. In the former context, identification problems have to be considered. We focus on the rotational indeterminacy. Following a Bayesian perspective, we address this issue by considering an ex-ante approach, which imposes a minimal number of constraints on the model parameters, as well as an ex-post approach, proposed in classical exploratory factor analysis. Specifically, the first method represents a constrained version of MIRT models where the rotation indeterminacy is removed by imposing a positive lower triangular structure on the factor loadings matrix. On the contrary, the ex-post procedure relies on the definition of an unconstrained Gibbs sampler where the rotational invariance is addressed in a post-processing procedure based on the Orthogonal Procrustes approach. However, in the context of MIRT models, one has to take into account the correlations between the latent traits. For this reason, the post-processing procedure is replaced by Oblique Procrustes.