Assessment structures in psychological testing

Abstract

Abstract Based on the notion of an assessment structure introduced by Falmagne (2015) the present paper characterizes the so-called quasi ordinal assessment spaces. It establishes a one-to-one correspondence to certain binary relations on an extended item set, containing a positive instance and a negative instance for each of the items. This result allows for building quasi ordinal assessment spaces from data through a generalized version of a well-established procedure, known as item tree analysis. Analyzing data from psychological testing constitutes a prototypical application that calls for this generalization of knowledge spaces, as it allows for describing dependencies between positive and negative answers to the items in a questionnaire. Empirical application of the approach is illustrated for a published data set on the Woodworth Psychoneurotic Inventory.