Hostname: page-component-cd9895bd7-p9bg8 Total loading time: 0 Render date: 2025-01-06T00:43:56.639Z Has data issue: false hasContentIssue false
  • English
  • Français

Uncovering the Best Skill Multimap by Constraining the Error Probabilities of the Gain-Loss Model

Published online by Cambridge University Press:  01 January 2025

Pasquale Anselmi ,
Egidio Robusto  and
Luca Stefanutti
Pasquale Anselmi*
Affiliation:
Department Fisppa, University of Padua
Egidio Robusto
Affiliation:
Department Fisppa, University of Padua
Luca Stefanutti
Affiliation:
Department Fisppa, University of Padua
*
Requests for reprints should be sent to Pasquale Anselmi, Department FISPPA, University of Padua, via Venezia 8, 35131 Padua, Italy. E-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

The Gain-Loss model is a probabilistic skill multimap model for assessing learning processes. In practical applications, more than one skill multimap could be plausible, while none corresponds to the true one. The article investigates whether constraining the error probabilities is a way of uncovering the best skill assignment among a number of alternatives. A simulation study shows that this approach allows the detection of the models that are closest to the correct one. An empirical application shows that it allows the detection of models that are entirely derived from plausible assumptions about the skills required for solving the problems.

Keywords

knowledge space theoryknowledge structureGain-Loss modelskill multimaplearning processconstrained parameter estimation
Type
Original Paper
Information
Psychometrika , Volume 77 , Issue 4 , October 2012 , pp. 763 - 781
Copyright
Copyright © 2012 The Psychometric Society

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Anselmi, P., Stefanutti, L., & Robusto, E. (2012). Uncovering the true skill assignment with the constrained gain-loss model. Manuscript (submitted for publication).Google Scholar
Bamber, D., & van Santen, J. (1985). How many parameters can a model have and still be testable?. Journal of Mathematical Psychology, 29, 443–473.CrossRefGoogle Scholar
Bamber, D., & van Santen, J. (2000). How to assess a model’s testability and identifiability. Journal of Mathematical Psychology, 44, 20–40.CrossRefGoogle ScholarPubMed
de la Torre, J., & Douglas, J. (2008). Model evaluation and multiple strategies in cognitive diagnosis: an analysis of fraction subtraction data. Psychometrika, 73, 595–624.CrossRefGoogle Scholar
Dempster, A.P., Laird, N.M., & Rubin, D.B. (1977). Maximum likelihood from incomplete data via the EM algorithm. Journal of the Royal Statistical Society. Series B. Methodological, 39, 1–38.CrossRefGoogle Scholar
Doignon, J.-P. (1994). Knowledge spaces and skill assignments. In Fischer, G.H., & Laming, D. (Eds.), Contributions to mathematical psychology, psychometrics, and methodology (pp. 111121). New York: Springer.CrossRefGoogle Scholar
Doignon, J.-P., & Falmagne, J.-C. (1985). Spaces for the assessment of knowledge. International Journal of Man-Machine Studies, 23, 175–196.CrossRefGoogle Scholar
Doignon, J.-P., & Falmagne, J.-C. (1999). Knowledge spaces. Berlin: Springer.CrossRefGoogle Scholar
Falmagne, J.-C., & Doignon, J.-P. (1988). A class of stochastic procedures for the assessment of knowledge. British Journal of Mathematical & Statistical Psychology, 41, 1–23.CrossRefGoogle Scholar
Haberman, S. (1979). Qualitative data analysis (vols. 1, 2). New York: Academic Press.Google Scholar
Junker, B.W., & Sijtsma, K. (2001). Cognitive assessment models with few assumptions, and connections with nonparametric item response theory. Applied Psychological Measurement, 25, 258–272.CrossRefGoogle Scholar
Langeheine, R., Pannekoek, J., & van de Pol, F. (1996). Bootstrapping goodness-of-fit measures in categorical data analysis. Sociological Methods & Research, 24, 492–516.CrossRefGoogle Scholar
Lazarsfeld, P.F., & Henry, N.W. (1968). Latent structure analysis. .Google Scholar
Robusto, E., Stefanutti, L., & Anselmi, P. (2010). The gain-loss model: a probabilistic skill multimap model for assessing learning processes. Journal of Educational Measurement, 47, 373–394.CrossRefGoogle Scholar
Rupp, A.A., & Templin, J. (2008). The effects of Q-matrix misspecification on parameter estimates and classification accuracy in the DINA model. Educational and Psychological Measurement, 68, 78–96.CrossRefGoogle Scholar
Stefanutti, L., Anselmi, P., & Robusto, E. (2011). Assessing learning processes with the gain-loss model. Behavior Research Methods, 43 16676.CrossRefGoogle ScholarPubMed
Stefanutti, L., & Robusto, E. (2009). Recovering a probabilistic knowledge structure by constraining its parameter space. Psychometrika, 74, 83–96.CrossRefGoogle Scholar
von Davier, M. (1997). Bootstrapping goodness-of-fit statistics for sparse categorical data: results of a Monte Carlo study. Methods of Psychological Research, 2, 29–48.Google Scholar