Parameter recovery of skew multidimensional multiple-group item response models (MGM-MIRT): a comparison of MCMC algorithms and assessment of effects of interest

• Published in: Journal of statistical computation and simulation Vol. 95; no. 3; pp. 467 - 489
• Main Authors: Padilla G., Juan L., Azevedo, Caio L.N., Lachos, Victor H.
• Format: Journal Article
• Language: English
• Published: Abingdon Taylor & Francis 11.02.2025; Taylor & Francis Ltd
• Subjects: Algorithms; Bayesian inference; Data augmentation; item response theory; Markov chains; MCMC algorithms; multidimensional models; Multivariate analysis; multivariate centred skew-normal distribution; Normal distribution; Parameter estimation; parameter recovery; Parameterization; Recovery; Regression models; Response data analysis; Simulation; Skewed distributions; Statistical analysis
• ISSN: 0094-9655; 1563-5163
• DOI: 10.1080/00949655.2024.2428785

Multidimensional item response theory (MIRT) models are powerful tools to analyse item response data. Most of them rely on the assumption that the latent traits are normally distributed. However, when such assumption does not hold, the item and the latent traits estimates can be inaccurate. This paper deals, in a very detailed way, through simulation studies, with the utility of the class of the MIRT models developed by Padilla et al. [Multidimensional multiple-group IRT models with skew normal latent trait distributions. J Multivariate Anal 2018;167:250-268], where the multivariate skew-normal distribution under the centred parameterization is employed for modelling the latent traits. The impact of important factors of interest on the parameter recovery is investigated. Such factors are the number of subjects, number of items, number of groups and asymmetry level. In a general way, the results show that our approach outperforms some traditional models when the latent traits follow asymmetric distributions. In addition, different Monte Carlo Markov Chain (MCMC) algorithms for parameter estimation are compared, by considering two schemes of data augmentation and a proposal to speed up their convergence, based on approaches found in the literature, for binary regression models. Guidelines are provided for the correct using of Bayesian inferential methods for the MIRT models.