ABSTRACT
In the psychometric literature, most applications of the linear logistic test model (LLTM), cf. Volume One, Chapter 13, aim at explaining item difficulty parameters in terms of cognitive operations involved, of rules that have to be applied in the solution process, and/or other properties of the items. Such applications require, however, (a) that all test items satisfy the assumptions of the Rasch model (RM; Rasch, 1960; cf. Volume One, Chapter 3) and (b) that a sound and sufficiently concrete hypothesis on the cognitive structure of the tasks is available. More often than not, these prerequisites for the item material are hard to meet in practice. Many applications have therefore failed to achieve psychological or psychometric relevance. “Relevance” in this context means that a study either (i) contributes significantly to the psychological theory of cognitive complexity of a universe of items/tasks or (ii) results in a practical procedure for constructing unidimensional items with prespecified difficulties, based on a set of components, operations, rules, or the like.
