Showing papers by "Paul De Boeck published in 1995"

The Conjunctive Model of Hierarchical Classes.

Abstract: This paper describes the conjunctive counterpart of De Boeck and Rosenberg's hierarchical classes model. Both the original model and its conjunctive counterpart represent the set-theoretical structure of a two-way two-mode binary matrix. However, unlike the original model, the new model represents the row-column association as a conjunctive function of a set of hypothetical binary variables. The conjunctive nature of the new model further implies that it may represent some conjunctive higher order dependencies among rows and columns. The substantive significance of the conjunctive model is illustrated with empirical applications. Finally, it is shown how conjunctive and disjunctive hierarchical classes models relate to Galois lattices, and how hierarchical classes analysis can be useful to construct lattice models of empirical data.

Componential IRT Models for Polytomous Items

Abstract: Componential IRT models for polytomous items are of particular interest in two contexts: componential research and test development. We assume that there are basic components, such as processes and knowledge structures, involved in solving cognitive tasks. In componential research, the subtask paradigm may be used to isolate such components in subtasks. In test development, items may be composed such that their response alternatives correspond with specific combinations of such components. In both cases the data may be modeled as polytomous items. With Bock's (1972) nominal model as a general framework, transformation matrices can be used to constrain the parameters of the response categories so as to reflect the componential design of the response categories. In this way, both main effects and interaction effects of components can be studied. An application to a spelling task demonstrates this approach. In item response theory (IRT), the probability that a person will solve an item correctly is modeled in terms of both the characteristics of the item and the ability of the person. Both refer to latent traits that are required more or less by the item or possessed more or less by the person. As Mislevy (1993) has written, a promising prospect is to incorporate cognitive principles into IRT. One such principle is that solving an item can be decomposed into elementary cognitive requirements called components. The term component in the present context is used in a broader sense than it was by Steinberg (1977) and denotes aspects of