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Defining a Family of Cognitive Diagnosis Models Using Log-Linear Models with Latent Variables

Published online by Cambridge University Press:  01 January 2025

Robert A. Henson ,
Jonathan L. Templin  and
John T. Willse
Robert A. Henson*
Affiliation:
The University of North Carolina at Greensboro
Jonathan L. Templin
Affiliation:
University of Georgia
John T. Willse
Affiliation:
The University of North Carolina at Greensboro
*
Requests for reprints should be sent to Robert A. Henson, The University of North Carolina at Greensboro, Greensboro, USA. E-mail: rahenson@uncg.edu
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Abstract

This paper uses log-linear models with latent variables (Hagenaars, in Loglinear Models with Latent Variables, 1993) to define a family of cognitive diagnosis models. In doing so, the relationship between many common models is explicitly defined and discussed. In addition, because the log-linear model with latent variables is a general model for cognitive diagnosis, new alternatives to modeling the functional relationship between attribute mastery and the probability of a correct response are discussed.

Keywords

cognitive diagnosis modelslog-linear latent class modelslatent class models
Type
Theory and Methods
Information
Psychometrika , Volume 74 , Issue 2 , June 2009 , pp. 191 - 210
Copyright
Copyright © 2008 The Psychometric Society

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References

Agresti, A. (1990). Categorical data analysis, New York: Wiley.Google Scholar
Akaike, H. (1974). A new look at the statistical model identification. IEEE Transactions on Automatic Control, 19(6), 716–723.CrossRefGoogle Scholar
de la Torre, J., Douglas, J.A. (2004). Higher order latent trait models for cognitive diagnosis. Psychometrika, 69, 333–353.CrossRefGoogle Scholar
DiBello, L., Stout, W., Roussos, L. (2007). Cognitive diagnosis Part I. In Rao, C.R., Sinharay, S. (Eds.), Psychometrics, Amsterdam: Elsevier.Google Scholar
Embretson, S. (1985). Studying intelligence with test theory models. In Current topics in human intelligence (Vol. 1, pp. 98–140).Google Scholar
Fischer, G., Forman, A. (1982). Some Applications of Logistic Latent Trait Models with Linear Constraints on the Parameters. Applied Psychological Measurement, 6(4), 397–416.CrossRefGoogle Scholar
Fu, J. (2005). A polytomous extension of the fusion model and its Bayesian parameter estimation. Unpublished doctoral dissertation.Google Scholar
Gelman, A., Carlin, J., Stern, H., Rubin, D. (1995). Bayesian data analysis, London: Chapman & Hall.CrossRefGoogle Scholar
Gelman, A., Meng, X., Stern, H. (1996). Posterior predictive assessment of model fitness via realized discrepancies. Statistica Sinica, 6, 733–807.Google Scholar
Haberman, S.J. (1974). Loglinear models for frequency tables derived by indirect observation: Maximum likelihood equations. Annals of Statistics, 2, 911–924.CrossRefGoogle Scholar
Haberman, S.J. (1979). New developments, New York: Academic Press.Google Scholar
Haertel, E.H. (1989). Using restricted latent class models to map the skill structure of achievement items. Journal of Educational Measurement, 26, 333–352.CrossRefGoogle Scholar
Hagenaars, J. (1993). Loglinear models with latent variables, Thousand Oaks: Sage.CrossRefGoogle Scholar
Hartz, S. (2002) A Bayesian framework for the unified model for assessing cognitive abilities: Blending theory with practicality. Unpublished doctoral dissertation.Google Scholar
Jang, E. (2005) A validity narrative: Effects of reading skills diagnosis on teaching and learning in the context of NG TOEFL. Unpublished doctoral dissertation, University of Illinois at Urbana-Champaign.Google Scholar
Janssen, R., DeBoeck, P. (1997). Psychometric modeling of componentially designed synonym tasks. Applied Psychological Measurement, 21, 37–50.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.CrossRefGoogle Scholar
Lynch, S., Western, B. (2004). Bayesian posterior predictive checks for complex models. Sociological Methods and Research, 32, 302–335.CrossRefGoogle Scholar
Macready, G.B., Dayton, C.M. (1977). The use of probabilistic models in the assessment of mastery. Journal of Education Statistics, 33, 379–416.Google Scholar
Muthén, L.K., Muthén, B.O. (1998–2006). Mplus user’s guide, (4th ed.). Los Angeles: Muthén & Muthén.Google Scholar
Rindskopf, D. (1983). Ageneral framework for using latent class analysis to test hierarchical and non hierarchical learning models. Psychometrika, 48, 85–97.CrossRefGoogle Scholar
Schwarz, G. (1978). Estimating the dimension of a model. Annals of Statistics, 6(2), 461–464.CrossRefGoogle Scholar
Tatsuoka, K.K. (1990). Toward an integration of item-response theory and cognitive error diagnosis. In N. Frederiksen, R. Glaser, A. Lesgold, & M. Shafto (Eds.), Diagnostic monitoring of skill and knowledge acquisition. Hillsdale: Erlbaum.Google Scholar
Templin, J. (2004). Generalized linear mixed proficiency models for cognitive diagnosis. Unpublished doctoral dissertation, University of Illinois at Urbana-Champaign.Google Scholar
Templin, J., Henson, R. (2006). Measurement of psychological disorders using cognitive diagnosis models. Psychological Methods, 11(3), 287–305.CrossRefGoogle ScholarPubMed
Templin, J., Henson, R., & Douglas, J. (2006). General theory and estimation of cognitive diagnosis models: Using Mplus to derive model estimates. 2007 National Council on Measurement in Education training session, Chicago, Illinois.Google Scholar
Templin, J., Henson, R., & Douglas, J. (2008). General theory and estimation of cognitive diagnosis models as constrained latent class models. Manuscript under review.Google Scholar
Templin, J., Henson, R., Templin, S., & Roussos, L. (in press). Robustness of hierarchical modeling of attribute correlation in cognitive diagnosis models. Applied Psychological Measurement.Google Scholar
Vermunt, J.K., Magidson, J. (2005). Technical guide for latent GOLD choice 4.0: Basic and advanced, Belmont: Statistical Innovations.Google Scholar
von Davier, M. (2005). A general diagnostic model applied to language testing data (ETS Research Report RR-05-16).CrossRefGoogle Scholar