Multidimensional Three-Mode Rasch Models

Abstract

Rasch’s measurements model has been generalized in many different ways (see Chapter 1, this volume). One direction of generalizing the Rasch model is to consider not only two factors of the response probability, i.e., persons and items, but an additional third factor. This means to extend the twodimensional data matrix to a three-dimensional data cube and extending the RM accordingly. Those extensions have been proposed in various contexts, e.g., in the context of measuring change, where the third factor or “mode” is time (Rost &Spada, 1983, Spiel, 1994), in the context of multitraitmultimethod measurement, where the third factor or “mode” is the method (Rost & Walter, 2005), in the context of assessing inter-rater agreement, where the third factor or mode is the rater or judge (Linacre, 1989), and in the context of facet-designed tests, where the item factor is split up into two facets like content domain knowledge and cognitive processes (Rost & Carstensen, 2002).