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Assessing Parameter Invariance in the BLIM: Bipartition Models

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  • Debora Chiusole
  • Luca Stefanutti
  • Pasquale Anselmi
  • Egidio Robusto

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. Copyright The Psychometric Society 2013

Suggested Citation

  • Debora Chiusole & Luca Stefanutti & Pasquale Anselmi & Egidio Robusto, 2013. "Assessing Parameter Invariance in the BLIM: Bipartition Models," Psychometrika, Springer;The Psychometric Society, vol. 78(4), pages 710-724, October.
    • Handle: RePEc:spr:psycho:v:78:y:2013:i:4:p:710-724
    DOI: 10.1007/s11336-013-9325-5
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    References listed on IDEAS

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    1. Jimmy Torre & Jeffrey Douglas, 2004. "Higher-order latent trait models for cognitive diagnosis," Psychometrika, Springer;The Psychometric Society, vol. 69(3), pages 333-353, September.
    2. Curtis Tatsuoka, 2002. "Data analytic methods for latent partially ordered classification models," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 51(3), pages 337-350, July.
    3. Erling Andersen, 1973. "A goodness of fit test for the rasch model," Psychometrika, Springer;The Psychometric Society, vol. 38(1), pages 123-140, March.
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    Cited by:

    1. Luca Stefanutti & Debora Chiusole & Pasquale Anselmi & Andrea Spoto, 2020. "Extending the Basic Local Independence Model to Polytomous Data," Psychometrika, Springer;The Psychometric Society, vol. 85(3), pages 684-715, September.

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