Empirical indistinguishability: From the knowledge structure to the skills. (10th November 2022)

• Record Type: Journal Article
• Authors: Spoto, Andrea; Stefanutti, Luca
• Is Part Of: British journal of mathematical & statistical psychology. Volume 76:Part 2(2023)
• Page Start: 312
• Page End: 326
• Publication Date: 2022-11-10
• Subjects: basic local independence model -- competence‐based knowledge space theory -- empirical indistinguishability -- identifiability -- knowledge space theory -- skill map; Psychometrics -- Periodicals; Psychology -- Mathematical models -- Periodicals; Psychology -- Statistical methods -- Periodicals; 150.727
• DOI: 10.1111/bmsp.12291
• Languages: English
• ISSNs: 0007-1102

Abstract

Abstract: Recent literature has pointed out that the basic local independence model (BLIM) when applied to some specific instances of knowledge structures presents identifiability issues. Furthermore, it has been shown that for such instances the model presents a stronger form of unidentifiability named empirical indistinguishability, which leads to the fact that the existence of certain knowledge states in such structures cannot be empirically tested. In this article the notion of indistinguishability is extended to skill maps and, more generally, to the competence‐based knowledge space theory. Theoretical results are provided showing that skill maps can be empirically indistinguishable from one another. The most relevant consequence of this is that for some skills there is no empirical evidence to establish their existence. This result is strictly related to the type of probabilistic model investigated, which is essentially the BLIM. Alternative models may exist or can be developed in knowledge space theory for which this indistinguishability problem disappears.