A new family of asymmetric models for item response theory: A Skew-Normal IRT family

A new family of asymmetric models for item response theory: A Skew-Normal IRT family Normal assumptions for the latent variable and symmetric item characteristics curves have been used in the last 50 years in many psychometric methods for item-response theory (IRT) models. This paper introduces a new family of asymmetric models for item response theory, namely the skew-normal item- response theory (SN-IRT) model. This family extends the ogive normal (symmetric probit-normal) model by considering: a) an accumulated skew-normal distribution for the item characteristic curve and b) skew-normal distributions are assumed as priors for latent variables for modeling individuals ’ ability. Four models compose the SN-IRT family: skew-probit-skew-normal, skew-probit-normal, probit-skew-normal and probit-normal models as a particular case. Hence, the SN-IRT is a more flexible model for fitting data sets with dichotomous responses. Bayesian inference methodology using two data augmentation approaches for implementing the MCMC methodology is developed. Model selection between symmetric and asymmetric models is considered by using the deviance information criterion (DIC) and th