Assessing the Dimensionality of the Latent Attribute Space in Cognitive Diagnosis Through Testing for Conditional Independence
Cognitive diagnosis seeks to assess an examinee’s mastery of a set of cognitive skills called (latent) attributes. The entire set of attributes characterizing a particular ability domain is often referred to as the latent attribute space. The correct specification of the latent attribute space is essential in cognitive diagnosis because misspecifications of the latent attribute space result in inaccurate parameter estimates, and ultimately, in the incorrect assessment of examinees’ ability. Misspecifications of the latent attribute space typically lead to violations of conditional independence. In this article, the Mantel-Haenszel statistic (Lim & Drasgow in J Classif, 2019) is implemented to detect possible misspecifications of the latent attribute space by checking for conditional independence of the items of a test with parametric cognitive diagnosis models. The performance of the Mantel-Haenszel statistic is evaluated in simulation studies based on its Type-I-error rate and power.
KeywordsCognitive diagnosis model Dimensionality Mantel-haenszel statistic
- Lim, Y. S., & Drasgow, F. (2019). Conditional independence and dimensionality of nonparametric cognitive diagnostic models: A test for model fit. Journal of,. Classification.Google Scholar
- Mantel, N., & Haenszel, W. (1959). Statistical aspects of the analysis of data from retrospective studies of disease. Journal of National Cancer Institute, 22, 719–748.Google Scholar
- Robitzsch, A., Kiefer, T., George, A. C., & Uenlue, A. (2015). CDM: Cognitive diagnostic modeling. R package version 3.4–21.Google Scholar
- Rupp, A., Templin, J., & Henson, R. (2010). Diagnostic assessment: Theory, methods, and applications. New York: Guilford.Google Scholar