Abstract
The associations between the items of a test based on the cognitive diagnosis framework and the skills required to solve them are documented in the Q-matrix. If the items have skill profiles that allow for the identification of all possible proficiency classes among examinees, then the Q-matrix of the test is said to be complete. An incomplete Q-matrix causes examinees to be assigned to proficiency classes to which they do not belong. Thus, completeness of the Q-matrix is an integral requirement of any cognitively diagnostic test. However, completeness of the Q-matrix is often difficult to establish, especially, for tests with a large number of items involving multiple skills. As an additional complication, completeness is not an intrinsic property of the Q-matrix, but can only be assessed in reference to a specific diagnostic classification model (DCM) supposed to underlie the data—that is, the Q-matrix of a given test can be complete for one model but incomplete for another. For different types of DCMs, conditions of Q-completeness are studied. Rules are derived to determine the completeness of a given Q-matrix.
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References
Chiu, C.-Y., Douglas, J. A., & Li, X. (2009). Cluster analysis for cognitive diagnosis: Theory and applications. Psychometrika, 74, 633–665.
Chiu, C.-Y., & Köhn, H.-F. (2015). Consistency of cluster analysis for cognitive diagnosis: The DINO model and the DINA model revisited. Applied Psychological Measurement, 39, 465–479.
de la Torre, J. (2011). The generalized DINA model framework. Psychometrika, 76, 179–199.
DiBello, L. V., Roussos, L. A., & Stout, W. F. (2007). Review of cognitively diagnostic assessment and a summary of psychometric models. In C. R. Rao, & S. Sinharay (Eds.), Handbook of statistics. Psychometrics (Vol. 26, pp. 979–1030). Amsterdam: Elsevier.
Haberman, S. J., & von Davier, M. (2007). Some notes on models for cognitively based skill diagnosis. In C. R. Rao, & S. Sinharay (Eds.), Handbook of statistics. Psychometrics (Vol. 26, pp. 1031–1038). Amsterdam: Elsevier.
Henson, R. A., Templin, J. L., & Willse, J. T. (2009). Defining a family of cognitive diagnosis models using log-linear models with latent variables. Psychometrika, 74, 191–210.
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.
Leighton, J., & Gierl, M. (2007) Cognitive diagnostic assessment for education: Theory and applications. Cambridge: Cambridge University Press.
Macready, G. B., & Dayton, C. M. (1977). The use of probabilistic models in the assessment of mastery. Journal of Educational Statistics, 33, 379–416.
Rupp, A. A., Templin, J. L., & Henson, R. A. (2010). Diagnostic measurement. Theory, methods, and applications. New York: Guilford.
Tatsuoka, K. K. (1985). A probabilistic model for diagnosing misconception in the pattern classification approach. Journal of Educational Statistics, 12, 55–73.
Templin, J. L., & Henson, R. A. (2006). Measurement of psychological disorders using cognitive diagnosis models. Psychological Methods, 11, 287–305.
von Davier, M. (2005, September). A general diagnostic model applied to language testing data (Research Rep. No. RR-05-16). Princeton: Educational Testing Service.
von Davier, M. (2008). A general diagnostic model applied to language testing data. British Journal of Mathematical and Statistical Psychology, 61, 287–301.
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Köhn, HF., Chiu, CY. (2016). Conditions of Completeness of the Q-Matrix of Tests for Cognitive Diagnosis. In: van der Ark, L., Bolt, D., Wang, WC., Douglas, J., Wiberg, M. (eds) Quantitative Psychology Research. Springer Proceedings in Mathematics & Statistics, vol 167. Springer, Cham. https://doi.org/10.1007/978-3-319-38759-8_19
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DOI: https://doi.org/10.1007/978-3-319-38759-8_19
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