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Naïve Tests of Basic Local Independence Model’s Invariance

Published online by Cambridge University Press:  28 April 2015

Debora de Chiusole ,
Luca Stefanutti ,
Pasquale Anselmi  and
Egidio Robusto
Debora de Chiusole*
Affiliation:
Università di Padova (Italy)
Luca Stefanutti
Affiliation:
Università di Padova (Italy)
Pasquale Anselmi
Affiliation:
Università di Padova (Italy)
Egidio Robusto
Affiliation:
Università di Padova (Italy)
*
*Correspondence concerning this article should be addressed to Debora de Chiusole. Università di Padova. FISPPA Department. Via Venenzia, 12. 35131. Padua (Italy). E- mail: [email protected]
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Abstract

The basic local independence model (BLIM) is a probabilistic model for knowledge structures, characterized by the property that lucky guess and careless error parameters of the items are independent of the knowledge states of the subjects. When fitting the BLIM to empirical data, a good fit can be obtained even when the invariance assumption is violated. Therefore, statistical tests are needed for detecting violations of this specific assumption. This work provides an extension to theoretical results obtained by de Chiusole, Stefanutti, Anselmi, and Robusto (2013), showing that statistical tests based on the partitioning of the empirical data set into two (or more) groups are not adequate for testing the BLIM’s invariance assumption. A simulation study confirms the theoretical results.

Keywords

knowledge space theorybasic local independence modelparameter invariance assumptionbipartition models
Type
Research Article
Information
The Spanish Journal of Psychology , Volume 18 , 2015 , E26
Copyright
Copyright © Universidad Complutense de Madrid and Colegio Oficial de Psicólogos de Madrid 2015 

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References

Andersen, E. B. (1973). A goodness of fit test for the Rasch model. Psychometrika, 38, 123–140. http://dx.doi.org/10.1007/BF02291180 Google Scholar
de la Torre, J., & Lee, Y.-S. (2010). A note on the invariance of the DINA model parameters. Journal of Educational Measurement, 47, 115–127. http://dx.doi.org/10.1111/j.1745-3984.2009.00102.x Google Scholar
de Chiusole, D., Anselmi, P., Stefanutti, L., & Robusto, E. (2013). The gain-loss model: Bias and variance of the parameter estimates. Electronic Notes in Discrete Mathematics, 42, 33–40.Google Scholar
de Chiusole, D., & Stefanutti, L. (2013). Modeling skill dependence in probabilistic competence structures. Electronic Notes in Discrete Mathematics, 42, 41–48. http://dx.doi.org/10.1016/j.endm.2013.05.144 Google Scholar
de Chiusole, D., Stefanutti, L., Anselmi, P., & Robusto, E. (2013). Assessing parameter invariance in the BLIM: Bipartition Models. Psychometrika, 78, 710–724. http://dx.doi.org/10.1007/s11336-013-9325-5 Google Scholar
Doignon, J.-P., & Falmagne, J.-C. (1985). Spaces for the assessment of knowledge. International Journal of Man-Machine Studies, 23, 175–196. http://dx.doi.org/10.1016/S0020-7373(85)80031-6 Google Scholar
Doignon, J.-P., & Falmagne, J.-C. (1999). Knowledge Spaces. Berlin, Heidelberg, and New York, NY: Springer-Verlag.CrossRefGoogle Scholar
Falmagne, J.-C., & Doignon, J.-P. (1988a). A class of stochastic procedures for the assessment of knowledge. British Journal of Mathematical and Statistical Psychology, 41, 1–23. http://dx.doi.org/10.1111/j.2044-8317.1988.tb00884.x Google Scholar
Falmagne, J.-C., & Doignon, J.-P. (1988b). A Markovian procedure for assessing the state of a system. Journal of Mathematical Psychology, 32, 232–258. http://dx.doi.org/10.1016/0022-2496(88)90011-9 Google Scholar
Falmagne, J.-C., & Doignon, J.-P. (2011). Learning spaces. New York, NY: Springer.Google Scholar
Glas, C. A. W., & Verhelst, N. D. (1995). Testing the Rasch model. In Fischer, G. H. & Molenaar, I. W., editors, Rasch Models: Foundations, Recent Developments, and Applications. New York, NY: Springer.Google Scholar
Heller, J., Stefanutti, L., Anselmi, P., & Robusto, E. (2014). Cognitive diagnostic models and knowledge space theory. The non-missing link. Manuscript submitted for publication.Google Scholar
Heller, J., & Wickelmaier, F. (2013). Minimum discrepancy estimation in probabilistic knowledge structures. Electronic Notes in Discrete Mathematics, 42, 49–56. http://dx.doi.org/10.1016/j.endm.2013.05.145 CrossRefGoogle 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. http://dx.doi.org/10.1177/01466210122032064 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. http://dx.doi.org/10.1111/j.1745-3984.2010.00119.x Google Scholar
Schrepp, M. (2005). About the connection between knowledge structures and latent class models. Methodology, 1, 93–103. http://dx.doi.org/10.1027/1614-2241.1.3.93 Google Scholar
Spoto, A., Stefanutti, L., & Vidotto, G. (2012). On the unidentifiability of a certain class of skill multi map based probabilistic knowledge structures. Journal of Mathematical Psychology, 56, 248–255. http://dx.doi.org/10.1016/j.jmp.2012.05.001 Google Scholar
Stefanutti, L., Heller, J., Anselmi, P., & Robusto, E. (2012). Assessing local identifiability of probabilistic knowledge structures. Behavior Research Methods, 44, 1197–1211. http://dx.doi.org/10.3758/s13428-012-0187-z CrossRefGoogle ScholarPubMed
Stefanutti, L., & Robusto, E. (2009). Recovering a probabilistic knowledge structure by constraining its parameter space. Psychometrika, 74, 83–96. http://dx.doi.org/10.1007/s11336-008-9095-7 CrossRefGoogle Scholar