Two-tier latent class IRT models in r

Abstract

In analyzing data deriving from the administration of a questionnaire to a group of individuals, Item Response Theory (IRT) models provide a flexible framework to account for several aspects involved in the response process, such as the existence of multiple latent traits. In this paper, we focus on a class of semi-parametric multidimensional IRT models, in which these traits are represented through one or more discrete latent variables; these models allow us to cluster individuals into homogeneous latent classes and, at the same time, to properly study item characteristics. In particular, we follow a within-item multidimensional formulation similar to that adopted in the two-tier models, with each item measuring one or two latent traits. The proposed class of models may be estimated through the package MLCIRTwithin, whose functioning is illustrated in this paper with examples based on data about quality-of-life measurement and about the propensity to commit a crime.