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
Highlights
Knowledge structures and surmise relations are mathematical models that belong to the theory of knowledge spaces
We summarize the κ procedure based on the special truncation constant, and the corresponding Maximum likelihood estimates (MLEs) in terms of the data
We describe the results of an application of modified version of ITA (MITA) to the simulated basic local independence model (BLIM) data
Summary
A crucial problem in KST is the derivation of a ‘realistic’ knowledge structure from empirical data, representing the organization of ‘knowledge’ in an information domain and examinee population under reference. In this regard, often one has to make a choice among candidate competing knowledge structures. (For instance, Section 5 describes how the candidate competing knowledge structure models may be obtained data-analytically, based on a modified Item Tree Analysis procedure. The competing models under consideration may be derived theoretically, based on different psychological theories/postulates.)
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