Multidimensional Linear Logistic Models for Change

The chapter presents a family of multidimensional logistic models for change, which are based on the Rasch model (RM) and on the linear logistic test model (LLTM; see Fischer, this volume), but unlike these models do not require unidimensionality of the items. As will be seen, to abandon the unidimensionality requirement becomes possible under the assumption that the same items are presented to the testees on two or more occasions. This relaxation of the usual unidimensionality axiom of IRT is of great advantage especially in typical research problems of educational, applied, or clinical psychology, where items or symptoms often are heterogeneous. [See Stout (1987, 1990) for a quite different approach to weakening the strict unidimensionality assumption.] Consider, for example, the problem of monitoring cognitive growth in children: A set of items appropriate for assessing intellectual development will necessarily contain items that address a number of different intelligence factors. If we knew what factors there are, and which of the items measure what factor, we might construct several unidimensional scales. This is unrealistic, however, because the factor structures in males and females, above- and below-average children, etc., generally differ, so that there is little hope of arriving at sufficiently unidimensional scales applicable to all children. Therefore, a model of change that makes no assumption about the latent dimensionality of the items is a very valuable tool for applied research.