Vakgroep Methodenleer en Statistiek
Faculteit der Sociale Wetenschappen
P.O. Box 80.140
3508 TC Utrecht
Brian W. Junker
Department of Statistics
Carnegie Mellon University
Pittsburgh PA 15213
May 29, 1994
In this paper we review a class of nonparametric unidimensional item response models in which the ordinal properties of items (and persons) can be studied, and survey both old and new methods for the investigaton of invariant item ordering in empirical data sets. Our model formulation derives in particular from the work of Mokken (1971), Holland Rosenbaum (1986) and Junker (1993). We survey methods based on the work of Mokken (1971), Rosenbaum (1987a, 1987b), and Sijtsma Meijer (1992), and we also discuss some new proposals for checking invariant item ordering. When violations are detected, these methods allow a rough assessment of where on the latent scale the item response functions cross.
We also study similarities and differences between these various methods and provide guidelines for their use. Finally, the methods are illustrated with data from a developmental psychology experiment in which the ability to draw inferences about transitive relations is explored.