Abstract
Although latent attributes that follow a hierarchical structure are anticipated in many areas of educational and psychological assessment, current psychometric models are limited in their capacity to objectively evaluate the presence of such attribute hierarchies. This paper introduces the Hierarchical Diagnostic Classification Model (HDCM), which adapts the Log-linear Cognitive Diagnosis Model to cases where attribute hierarchies are present. The utility of the HDCM is demonstrated through simulation and by an empirical example. Simulation study results show the HDCM is efficiently estimated and can accurately test for the presence of an attribute hierarchy statistically, a feature not possible when using more commonly used DCMs. Empirically, the HDCM is used to test for the presence of a suspected attribute hierarchy in a test of English grammar, confirming the data is more adequately represented by hierarchical attribute structure when compared to a crossed, or nonhierarchical structure.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Bradshaw, L.P., & Templin, J. (2013). Combining scaling and classification: a psychometric model for scaling ability and diagnosing misconceptions. Psychometrika. doi:10.1007/S11336-013-9350-4.
Buck, G., & Tatsuoka, K.K. (1998). Application of the rule-space procedure to language testing: examining attributes of a free response listening test. Language Testing, 15, 119–157.
Choi, H.-J. (2010). A model that combines diagnostic classification assessment with mixture item response theory models. Unpublished doctoral dissertation, University of Georgia, Athens, Georgia.
Croon, M. (1990). Latent class analysis with ordered latent classes. British Journal of Mathematical & Statistical Psychology, 43, 171–192.
Cui, Y., & Leighton, J.P. (2009). The hierarchy consistency index: evaluating person fit for cognitive diagnostic assessment. Journal of Educational Measurement, 46, 429–449.
de la Torre, J. (2011). The generalized DINA model framework. Psychometrika, 76, 179–199.
Gierl, M. J., Cui, Y., & Hunka, S. (2007a). Using connectionist models to evaluate examinees’ response patterns on tests. Paper presented at the annual meeting of the National Council on Measurement in Education, Chicago, IL.
Gierl, M.J., Leighton, J.P., & Hunka, S.M. (2007b). Using the attribute hierarchy method to make diagnostic inferences about respondents’ cognitive skills. In J.P. Leighton & M.J. Gierl (Eds.), Cognitive diagnostic assessment for education: theory and applications (pp. 242–274). Cambridge: Cambridge University Press.
Gierl, M.J., Cui, Y., & Zhou, J. (2009). Reliability of attribute-based scoring in cognitive diagnostic assessment. Journal of Educational Measurement, 46, 293–313.
Haertel, E.H. (1989). Using restricted latent class models to map the skill structure of achievement items. Journal of Educational Measurement, 26, 333–352.
Hartz, S. (2002). A Bayesian framework for the unified model for assessing cognitive abilities: blending theory with practicality. Unpublished doctoral dissertation, University of Illinois at Urbana-Champaign.
Henson, R., & Templin, J. (2005). Hierarchical log-linear modeling of the joint skill distribution. Unpublished manuscript.
Henson, R., & Templin, J. (2007). Large-scale language assessment using cognitive diagnosis models. Paper presented at the annual meeting of the National Council for Measurement in Education in Chicago, Illinois.
Henson, R., Templin, J., & Willse, J. (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.
Lazarsfeld, P.F., & Henry, N.W. (1968). Latent structure analysis. Boston: Houghton Mifflin.
Leighton, J.P. & Gierl, M.J. (Eds.) (2007). Cognitive diagnostic assessment for education: theory and applications. Cambridge: Cambridge University Press.
Leighton, J.P., Gierl, M.J., & Hunka, S.M. (2004). The attribute hierarchy model for cognitive assessment: a variation on Tatsuoka’s rule-space approach. Journal of Educational Measurement, 41, 205–237.
Leighton, J.P., Cui, Y., & Corr, M.K. (2009). Testing expert-based and student-based cognitive models: an application of the attribute hierarchy method and hierarchy consistency index. Applied Measurement in Education, 22, 229–254.
Lindsay, B., Clogg, C.C., & Grego, J. (1991). Semiparametric estimation in the Rasch model and related exponential response models, including a simple latent class model for item analysis. Journal of the American Statistical Association, 86, 96–107.
Maris, E. (1999). Estimating multiple classification latent class models. Psychometrika, 64, 197–212.
Maydeu-Olivares, A., & Joe, H. (2005). Limited- and full-information estimation and goodness-of-fit testing in 2n contingency tables: a unified framework. Journal of the American Statistical Association, 100, 1009–1020.
Muthén, L.K., & Muthén, B.O. (2013). Mplus user’s guide (Version 6.1) [Computer software and manual]. Los Angeles: Muthén & Muthén.
Roussos, L., DiBello, L., Stout, W., Hartz, S., Henson, R., & Templin, J. (2007). The fusion model skills diagnosis system. In J. Leighton & M. Gierl (Eds.), Cognitive diagnostic assessment in education (pp. 275–318). New York: Cambridge University Press.
Rupp, A., Templin, J., & Henson, R. (2010). Diagnostic measurement: theory, methods, and applications. New York: Guilford.
Shapiro, A. (1985). Asymptotic distribution of test statistics in the analysis of moment structures under inequality constraints. Biometrika, 72, 133–144.
Stoel, R.D., Garre, F.G., Dolan, C., & van den Wittenboer, G. (2006). On the likelihood ratio test in structural equation modeling when parameters are subject to boundary constraints. Psychological Methods, 11, 439–455.
Tatsuoka, K.K. (1983). Rule space: an approach for dealing with misconceptions based on item response theory. Journal of Educational Measurement, 20, 345–354.
Tatsuoka, K.K. (1990). Toward an integration of item-response theory and cognitive error diagnosis. In N. Fredrickson, R.L. Glaser, A.M. Lesgold, & M.G. Shafto (Eds.), Diagnostic monitoring of skills and knowledge acquisition (pp. 453–488). Hillsdale: Erlbaum.
Tatsuoka, K.K. (1993). Item construction and psychometric models appropriate for constructed responses. In R.E. Bennett & W.C. Ward (Eds.), Construction versus choice in cognitive measurement (pp. 107–133). Hillsdale: Erlbaum.
Tatsuoka, K.K. (1995). Architecture of knowledge structures and cognitive diagnosis: a statistical pattern recognition and classification approach. In P.D. Nichols, S.F. Chipman, & R.L. Brennan (Eds.), Cognitively diagnostic assessment (pp. 327–359). Hillsdale: Erlbaum.
Tatsuoka, K.K. (2009). Cognitive assessment: an introduction to the rule space method. New York: Routledge.
Templin, J. (2006). CDM user’s guide. Unpublished manuscript.
Templin, J., & Bradshaw, L. (2013). Measuring the reliability of diagnostic classification model examinee estimates. Journal of Classification, 30, 251–275.
Templin, J., & Henson, R. (2006). Measurement of psychological disorders using cognitive diagnosis models. Psychological Methods, 11(3), 287–305.
Templin, J., & Hoffman, L. (2013). Obtaining diagnostic classification model estimates using Mplus. Educational Measurement: Issues and Practice, 32(2), 37–50.
Templin, J., Rupp, A., Henson, R., Jang, E., & Ahmed, M. (2008). Nominal response diagnostic models. Paper presented at the annual meeting of the National Council on Measurement in Education in New York, NY.
Verbeke, G., & Molenberghs, G. (2000). Linear mixed models for longitudinal data. New York: Springer.
von Davier, M. (2005). A general diagnostic model applied to language testing data (ETS Research Report RR-05-16).
von Davier, M., & Yamamoto, K. (2004). A class of models for cognitive diagnosis. Paper presented at the 4th Spearman Conference in Philadelphia, PA.
Xu, X., & von Davier, M. (2008). Fitting the structured general diagnostic model to NAEP data (RR-08-27). Princeton: Educational Testing Service.
Acknowledgements
This research was supported by the National Science Foundation under grants DRL-0822064, SES-0750859, and SES-1030337. The opinions expressed are those of the authors and do not necessarily reflect the views of NSF.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Templin, J., Bradshaw, L. Hierarchical Diagnostic Classification Models: A Family of Models for Estimating and Testing Attribute Hierarchies. Psychometrika 79, 317–339 (2014). https://doi.org/10.1007/s11336-013-9362-0
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11336-013-9362-0