Abstract:

Item Response Theory (ITR) is an extension of Classical Test Theory (CTT). The mathematical foundation of IRT is a function that relates the probability of a person responding to an item in a specific manner to the standing of that person on the trait that the item is measuring. It means that the function describes, in probabilistic terms, how a person with a higher standing on a trait is likely to provide a response in a different category to a person with a low standing on the trait. In this paper we present multivariate IRT models as an extension of classical and unidimensional IRT models. Multidiensional models explain the probability of a correct response to a given item as a function of a vector of latent traits, instead of a single latent trait. In this paper we present the background, theory, and application of MIRT models for the measurement of social attitudes based on own studies. All calculations will be conducted in R from CRAN.