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Assessing Parameter Invariance in the BLIM: Bipartition Models

Published online by Cambridge University Press:  01 January 2025

Debora de Chiusole,
Luca Stefanutti,
Pasquale Anselmi and
Egidio Robusto
Debora de Chiusole*
Affiliation:
Fisppa Department, University of Padua
Luca Stefanutti
Affiliation:
Fisppa Department, University of Padua
Pasquale Anselmi
Affiliation:
Fisppa Department, University of Padua
Egidio Robusto
Affiliation:
Fisppa Department, University of Padua
*
Requests for reprints should be sent to Debora de Chiusole, FISPPA Department, University of Padua, Via Venezia, 8, 35131, Padova, Italy. E-mail: deboratn@libero.it
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Abstract

In knowledge space theory, the knowledge state of a student is the set of all problems he is capable of solving in a specific knowledge domain and a knowledge structure is the collection of knowledge states. The basic local independence model (BLIM) is a probabilistic model for knowledge structures. The BLIM assumes a probability distribution on the knowledge states and a lucky guess and a careless error probability for each problem. A key assumption of the BLIM is that the lucky guess and careless error probabilities do not depend on knowledge states (invariance assumption). This article proposes a method for testing the violations of this specific assumption. The proposed method was assessed in a simulation study and in an empirical application. The results show that (1) the invariance assumption might be violated by the empirical data even when the model’s fit is very good, and (2) the proposed method may prove to be a promising tool to detect invariance violations of the BLIM.

Keywords

basic local independence modelknowledge space theoryparameter invariance

Information

Type
Original Paper
Information
Psychometrika , Volume 78 , Issue 4 , October 2013, pp. 710 - 724
Copyright
Copyright © 2013 The Psychometric Society

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