Representation of Competencies in Multidimensional IRT Models with Within-Item and Between-Item Multidimensionality

Multidimensional item response theory (MIRT) holds considerable promise for the development of psychometric models of competence. It provides an ideal foundation for modeling performance in complex domains, simultaneously taking into account multiple basic abilities. The aim of this paper is to illustrate the relations between a two-dimensional IRT model with between-item multidimensionality and a nested-factor model with within-item multidimensionality, and the different substantive meanings of the ability dimensions in the two models. Both models are applied to empirical data from a large-scale assessment of reading and listening comprehension in a foreign language. In the between-item model, performance in the reading and listening items is modeled by two separate dimensions. In the within-item model, one dimension represents the abilities common to both tests, and a second dimension represents abilities specific to listening comprehension. Distinct relations of external variables, such as gender and cognitive abilities, with ability scores demonstrate that the alternative models have substantively different implications.