We introduce new applications of the skew-probit IRT model by considering a flexible skew-normal distribution for the latent variables and by extending this model to include an additional random effect for modeling dependence between items within the same testlet. A Bayesian hierarchical structure is presented using a double data augmentation approach. This can be easily implemented in WinBUGS or SAS by considering MCMC algorithms. Several Bayesian model selection criteria, such as DIC, EAIC and EBIC, have been considered; in addition, we use posterior sum of squares of the latent residuals as a global discrepancy measure to model comparison. Two applications illustrate the methodology, one data set related to a mathematical test and another related to reading comprehension, both applied to Peruvian students. Results indicate better performance of the more flexible models proposed in this paper.
"Extensions of the skew-normal ogive item response model." Braz. J. Probab. Stat. 28 (1) 1 - 23, February 2014. https://doi.org/10.1214/12-BJPS191