An Extended Multidimensional IRT Formulation for the Linear Item Factor Analysis Model

Abstract

Abstract. In previous research Spearman’s factor-analytic (FA) model has been formulated as a linear Item Response Theory (IRT) model for (approximately) continuous item responses. Furthermore, some generalized IRT-based indices have been proposed for multidimensional FA. However, to date no explicit IRT formulation has existed for this model. This article extends previous proposals in two directions. First, it proposes a Lord’s-type parameterization of the multidimensional FA model in which each item is characterized by a difficulty index in each dimension. Second, it proposes two multidimensional IRT-based item-person-distance indices. The characteristics and advantages of all the proposed measures as well as their relations to existing indices are discussed. The usefulness of the proposal in item analysis and validity assessment is also discussed and illustrated with two empirical examples.