Abstract: Mosaic plots are state-of-the-art graphics for multivariate categor ical data in statistical visualization. Knowledge structures are mathematical models that belong to the theory of knowledge spaces in psychometrics. This paper presents an application of mosaic plots to psychometric data arising from underlying knowledge structure models. In simulation trials and with empirical data, the scope of this graphing method in knowledge space theory is investigated.
Abstract: A crucial problem in knowledge space theory, a modern psy chological test theory, is the derivation of a realistic knowledge structure representing the organization of knowledge in an information domain and examinee population under reference. Often, one is left with the problem of selecting among candidate competing knowledge structures. This article proposes a measure for the selection among competing knowledge structures. It is derived within an operational framework (prediction paradigm), and is partly based on the unitary method of proportional reduction in predictive error as advocated by the authors Guttman, Goodman, and Kruskal. In particular, this measure is designed to trade off the (descriptive) fit and size of a knowledge structure, which is of high interest in knowledge space theory. The proposed approach is compared with the Correlational Agreement Coef ficient, which has been recently discussed for the selection among competing surmise relations. Their performances as selection measures are compared in a simulation study using the fundamental basic local independence model in knowledge space theory