Hostname: page-component-7dd5485656-dk7s8 Total loading time: 0 Render date: 2025-10-31T02:18:45.185Z Has data issue: false hasContentIssue false
  • English
  • Français

Hierarchical Diagnostic Classification Models Morphing into Unidimensional ‘Diagnostic’ Classification Models—A Commentary

Published online by Cambridge University Press:  01 January 2025

Matthias von Davier  and
Shelby J. Haberman
Matthias von Davier*
Affiliation:
Educational Testing Service
Shelby J. Haberman
Affiliation:
Educational Testing Service
*
Requests for reprints should be sent to Matthias von Davier, Educational Testing Service, Princeton, NJ, USA. E-mail: mvondavier@ets.org
Get access Rights & Permissions [Opens in a new window]

Abstract

This commentary addresses the modeling and final analytical path taken, as well as the terminology used, in the paper “Hierarchical diagnostic classification models: a family of models for estimating and testing attribute hierarchies” by Templin and Bradshaw (Psychometrika, doi:10.1007/s11336-013-9362-0, 2013). It raises several issues concerning use of cognitive diagnostic models that either assume attribute hierarchies or assume a certain form of attribute interactions. The issues raised are illustrated with examples, and references are provided for further examination.

Keywords

latent structure modellatent class analysisdiagnostic modelsGuttman scalinghierarchical models

Information

Type
Original Paper
Information
Psychometrika , Volume 79 , Issue 2 , April 2014 , pp. 340 - 346
Copyright
Copyright © 2013 The Psychometric Society

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

DeCarlo, L.T. (2011). On the analysis of fraction subtraction data: the DINA model, classification, latent class sizes, and the Q-matrix. Applied Psychological Measurement, 35, 8–26CrossRefGoogle Scholar
de Leeuw, J., Verhelst, N. (1986). Maximum likelihood estimation in generalized Rasch models. Journal of Educational Statistics, 11, 183–196CrossRefGoogle Scholar
Follmann, D. (1988). Consistent estimation in the Rasch model based on nonparametric margins. Psychometrika, 53, 553–562CrossRefGoogle Scholar
Formann, A.K. (1989). Constrained latent class models: some further applications. British Journal of Mathematical & Statistical Psychology, 42, 37–54CrossRefGoogle Scholar
Guttman, L. et al. (1950). The basis for scalogram analysis. In Stouffer, S.A. et al. (Eds.), Measurement and prediction, New York: WileyGoogle Scholar
Haberman, S.J. (1977). Maximum likelihood estimates in exponential response models. The Annals of Statistics, 5, 815–841CrossRefGoogle Scholar
Haberman, S.J., von Davier, M. (2006). Some notes on models for cognitively based attribute diagnosis. In Rao, C.R., Sinharay, S. (Eds.), Psychometrics, Amsterdam: Elsevier 10311038CrossRefGoogle Scholar
Haberman, S.J., von Davier, M., & Lee, Y. (2008). Comparison of multidimensional item response models: Multivariate normal ability distributions versus multivariate polytomous ability distributions (Research Report 08-45). Princeton, NJ: Educational Testing Service. Google Scholar
Henson, R., Templin, J., Willse, J. (2009). Defining a family of cognitive diagnosis models using log linear models with latent variables. Psychometrika, 74, 191–210CrossRefGoogle Scholar
Hermelin, M., Nyberg, K. (2012). Multidimensional linear distinguishing attacks and Boolean functions. Cryptography and Communications, 4(1), 4764CrossRefGoogle Scholar
Hox, J. (2002). Multilevel analysis: techniques and applications, Mahwah: ErlbaumCrossRefGoogle Scholar
Junker, B.W., Sijtsma, K. (2001). Cognitive assessment models with few assumptions, and connections with nonparametric item response theory. Applied Psychological Measurement, 25(3), 258272CrossRefGoogle Scholar
Kreft, I., de Leeuw, J. (1998). Introducing multilevel modeling, London: SageCrossRefGoogle Scholar
Lazarsfeld, P.F. et al. (1950). The logical and mathematical foundations of latent structure analysis. In Stouffer, S.A. et al. (Eds.), Measurement and prediction, Princeton: Princeton University Press 362472Google Scholar
Lazarsfeld, P.F., Henry, N.W. (1968). Latent structure analysis, Boston: Houghton MifflinGoogle Scholar
Leighton, J.P., Gierl, M.J. (2007). Cognitive diagnostic assessment for education. Theory and applications, Cambridge: Cambridge University PressCrossRefGoogle Scholar
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, 96–107CrossRefGoogle Scholar
Maris, E. (1999). Estimating multiple classification latent class models. Psychometrika, 64, 187–212CrossRefGoogle Scholar
Raudenbush, S.W., Bryk, A.S. (2001). Hierarchical linear models: applications and data analysis methods, (2nd ed.). Thousand Oaks: SageGoogle Scholar
Rojas, G., & de la Torre, J. (2012). Choosing between general and specific cognitive diagnosis models when the sample size is small. Unpublished manuscript, Rutgers University, New Brunswick, NJ. Google Scholar
Rupp, A., Templin, J., Henson, R. (2010). Diagnostic measurement: theory, methods, and applications, New York: GuilfordGoogle Scholar
Schwarz, G.E. (1978). Estimating the dimension of a model. The Annals of Statistics, 6(2), 461464CrossRefGoogle Scholar
Templin, J.L., Bradshaw, L. (2013). Hierarchical diagnostic classification models: a family of models for estimating and testing attribute hierarchies. Psychometrika,Google Scholar
Tsai, S.C. (1996). Lower bounds on representing Boolean functions as polynomials in Z m. SIAM Journal on Discrete Mathematics, 9, 96–101CrossRefGoogle Scholar
van der Linden, W. (2012). On compensation in multidimensional response modeling. Psychometrika, 77(1), 2130CrossRefGoogle Scholar
Vermunt, J.K. (2003). Multilevel latent class models. Sociological Methodology, 33(1), 213239CrossRefGoogle Scholar
von Davier, M. (2005). A general diagnostic model applied to language testing data (Research Report 05-16). Princeton, NJ: Educational Testing Service. Google Scholar
von Davier, M. (2007). Hierarchical general diagnostic models (Research Report 07-19). Princeton, NJ: Educational Testing Service. Google Scholar
von Davier, M. (2009). Some notes on the reinvention of latent structure models as diagnostic classification models. Measurement, 7(1), 6774Google Scholar
von Davier, M. (2010). Hierarchical mixtures of diagnostic models. Psychological Test and Assessment Modeling, 52(1), 828 Retrieved from http://www.psychologie-aktuell.com/fileadmin/download/ptam/1-2010/02_vonDavier.pdfGoogle Scholar
von Davier, M. (2011). Equivalency of the DINA model and a constrained general diagnostic model (Research Report 11-37). Princeton, NJ: Educational Testing Service. Retrieved from http://www.ets.org/Media/Research/pdf/RR-11-37.pdf. Google Scholar
von Davier, M. (2013). The DINA model as a constrained general diagnostic model—two variants of a model equivalency. British Journal of Mathematical & Statistical Psychology,Google Scholar
von Davier, M., Rost, J. (1995). Polytomous mixed Rasch models. In Fischer, G.H., Molenaar, I.W. (Eds.), Rasch models—foundations, recent developments and applications, New York: Springer 371379Google Scholar
von Davier, M., Xu, X., & Yamamoto, K. (2011, July). Why diagnostic models are latent class models—or the other way around? Paper presented at the many faces of latent class analysis symposium, 75th international meeting of the Psychometric Society, Hong Kong, China. Google Scholar