Skip to main content
SpringerLink
Log in
Book cover

Quantitative Psychology Research pp 263–277Cite as

Exploring Joint Maximum Likelihood Estimation for Cognitive Diagnosis Models

  • Conference paper

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 140))

Abstract

Current methods for fitting cognitive diagnosis models (CDMs) to educational data typically rely on expectation maximization (EM) or Markov chain Monte Carlo (MCMC) for estimating the item parameters and examinees’ proficiency class memberships. However, for advanced, more complex CDMs like the reduced reparameterized unified model (Reduced RUM) and the (saturated) loglinear cognitive diagnosis model (LCDM), EM and Markov chain Monte Carlo (MCMC) have the reputation of often consuming excessive CPU times. Joint maximum likelihood estimation (JMLE) is proposed as an alternative to EM and MCMC. The maximization of the joint likelihood is typically accomplished in a few iterations, thereby drastically reducing the CPU times usually needed for fitting advanced CDMs like the Reduced RUM or the (saturated) LCDM. As another attractive feature, the JMLE algorithm presented here resolves the traditional issue of JMLE estimators—their lack of statistical consistency—by using an external, statistically consistent estimator to obtain initial estimates of examinees’ class memberships as starting values. It can be proven that under this condition the JMLE item parameter estimators are also statistically consistent. The computational performance of the proposed JMLE algorithm is evaluated in two comprehensive simulation studies.

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

References

  • Baker, F. B., & Kim, S.-H. (2004). Item response theory: Parameter estimation techniques (2nd ed.). New York: Marcel Dekker.

    Google Scholar 

  • Birnbaum, A. (1968). Some latent trait models and their use in inferring an examinee’s ability. In F. M. Load & M. R. Novick (Eds.), Statistical theories of mental test scores (pp. 397–479). Reading, MA: Addison-Wesley.

    Google Scholar 

  • Chiu, C.-Y., & Douglas, J. A. (2013). A nonparametric approach to cognitive diagnosis by proximity to ideal response profiles. Journal of Classification, 30, 225–250.

    Article  MathSciNet  Google Scholar 

  • Chiu, C.-Y., Douglas, J. A., & Li, X. (2009). Cluster analysis for cognitive diagnosis: Theory and applications. Psychometrika, 74, 633–665.

    Article  MathSciNet  MATH  Google Scholar 

  • Chiu, C.-Y., Zheng, Y., & Henson, R. (2013) Joint maximum likelihood estimation for cognitive diagnostic models in conjunction with proximity to ideal response patterns. Psychometrika (Manuscript under revision).

    Google Scholar 

  • de la Torre, J. (2011). The generalized DINA model framework. Psychometrika, 76, 179–199.

    Article  MathSciNet  MATH  Google Scholar 

  • 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.

    Chapter  Google Scholar 

  • Embretson, S. E., & Reise, S. P. (2000). Item response theory for psychologists. Mahwah, NJ: Erlbaum.

    Google Scholar 

  • Feng, Y., Habing, B. T., & Huebner, A. (2014). Parameter estimation of the reduced RUM using the EM algorithm. Applied Psychological Measurement, 38, 137–150.

    Article  Google Scholar 

  • 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.

    Chapter  Google Scholar 

  • Hartz, S. M. (2002). A Bayesian framework for the unified model for assessing cognitive abilities: Blending theory with practicality. (Doctoral dissertation) Available from ProQuest Dissertations and Theses database (UMI No. 3044108).

    Google Scholar 

  • Hartz, S. M., & Roussos, L. A. (2008, October). The fusion model for skill diagnosis: Blending theory with practicality (Research report No. RR-08-71). Princeton, NJ: Educational Testing Service.

    Google Scholar 

  • Henson, R., & Douglas, J. (2005). Test construction for cognitive diagnosis. Applied Psychological Measurement, 29, 262–277.

    Article  MathSciNet  Google Scholar 

  • Henson, R., Roussos, L. A., Douglas, J., & He, X. (2008). Cognitive diagnostic attribute-level discrimination indices. Applied Psychological Measurement, 32, 275–288.

    Article  MathSciNet  Google Scholar 

  • Henson, R., Templin, J. L., & Douglas, J. (2007). Using efficient model based sum-scores for conducting skills diagnoses. Journal of Educational Measurement, 44, 361–376.

    Article  Google Scholar 

  • Henson, R. A., & Templin, J. (2007, April). Large-scale language assessment using cognitive diagnosis models. Paper presented at the Annual Meeting of the National Council on Measurement in Education, Chicago, IL.

    Google Scholar 

  • 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.

    Article  MathSciNet  MATH  Google 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.

    Article  MathSciNet  Google Scholar 

  • Kim, Y.-H. (2011). Diagnosing EAP writing ability using the reduced reparameterized unified model. Language Testing, 28, 509–541.

    Article  Google Scholar 

  • Leighton, J., & Gierl, M. (2007) Cognitive diagnostic assessment for education: Theory and applications. Cambridge, UK: Cambridge University Press.

    Book  Google Scholar 

  • Liu, Y., Douglas, J. A., & Henson, R. A. (2009). Testing person fit in cognitive diagnosis. Applied Psychological Measurement, 33, 579–598.

    Article  Google Scholar 

  • Lunn, D., Spiegelhalter, D., Thomas, A., & Best, N. (2009). The BUGS project: Evolution, critique, and future directions. Statistics in Medicine, 28, 3049–3067.

    Article  MathSciNet  Google Scholar 

  • Macready, G. B., & Dayton, C. M. (1977). The use of probabilistic models in the assessment of mastery. Journal of Educational Statistics, 33, 379–416.

    Google Scholar 

  • Maris, E. (1999). Estimating multiple classification latent class models. Psychometrika, 64, 187–212.

    Article  MathSciNet  MATH  Google Scholar 

  • Neyman, J., & Scott, E. L. (1948). Consistent estimates based on partially consistent observations. Econometrica, 16, 1–32.

    Article  MathSciNet  Google Scholar 

  • Robitzsch, A., Kiefer, T., George, A. C., & Uenlue, A. (2014). CDM: Cognitive diagnosis modeling. R package version 3.1-14. Retrieved from the Comprehensive R Archive Network [CRAN] website http://CRAN.R-project.org/package=CDM

  • Rupp, A. A., & Templin, J. L., & Henson, R. A. (2010). Diagnostic measurement: Theory, methods, and applications. New York: Guilford.

    Google Scholar 

  • Tatsuoka, K. K. (1985). A probabilistic model for diagnosing misconception in the pattern classification approach. Journal of Educational Statistics, 12, 55–73.

    Google Scholar 

  • Templin, J., & Bradshaw, L. (2014). Hierarchical diagnostic classification models: A family of models for estimating and testing attribute hierarchies. Psychometrika, 79, 317–339.

    Article  MathSciNet  MATH  Google Scholar 

  • Templin, J. L., & Henson, R. A. (2006). Measurement of psychological disorders using cognitive diagnosis models. Psychological Methods, 11, 287–305.

    Article  Google Scholar 

  • Templin, J. L., Henson, R. A., Templin, S. E., & Roussos, L. A. (2008). Robustness of hierarchical modeling of skill association in cognitive diagnosis models. Applied Psychological Measurement, 32, 559–574.

    Article  MathSciNet  Google Scholar 

  • von Davier, M. (2005, September). A general diagnostic model applied to language testing data (Research report No. RR-05-16). Princeton, NJ: Educational Testing Service.

    Google Scholar 

  • von Davier, M. (2008). A general diagnostic model applied to language testing data. British Journal of Mathematical and Statistical Psychology, 61, 287–301.

    Article  MathSciNet  Google Scholar 

  • Wang, S., & Douglas, J. (2015). Consistency of nonparametric classification in cognitive diagnosis. Psychometrika, 80, 85–100.

    Article  MathSciNet  Google Scholar 

  • Zheng, Y., & Chiu, C.-Y. (2014). NPCD: Nonparametric methods for cognitive diagnosis. R package version 1.0-5. Retrieved from the Comprehensive R Archive Network [CRAN] website http://CRAN.R-project.org/package=NPCD

Download references

Author information

Authors and Affiliations

  1. Rutgers, The State University of New Jersey, New Brunswick, NJ, USA

    Chia-Yi Chiu

  2. University of Illinois at Urbana-Champaign, Champaign, IL, USA

    Hans-Friedrich Köhn

  3. Arizona State University, Tempe, AZ, USA

    Yi Zheng

  4. University of North Carolina, Greensboro, NC, USA

    Robert Henson

Authors
  1. Chia-Yi Chiu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Hans-Friedrich Köhn
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yi Zheng
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Robert Henson
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Chia-Yi Chiu .

Editor information

Editors and Affiliations

  1. University of Amsterdam, Amsterdam, The Netherlands

    L. Andries van der Ark

  2. University of Wisconsin, Madison, Wisconsin, USA

    Daniel M. Bolt

  3. The Hong Kong Institute of Education, Hong Kong, Hong Kong SAR

    Wen-Chung Wang

  4. University of Illinois, Champaign, Illinois, USA

    Jeffrey A. Douglas

  5. The Penn State University, University Park, Pennsylvania, USA

    Sy-Miin Chow

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer International Publishing Switzerland

About this paper

Cite this paper

Chiu, CY., Köhn, HF., Zheng, Y., Henson, R. (2015). Exploring Joint Maximum Likelihood Estimation for Cognitive Diagnosis Models. In: van der Ark, L., Bolt, D., Wang, WC., Douglas, J., Chow, SM. (eds) Quantitative Psychology Research. Springer Proceedings in Mathematics & Statistics, vol 140. Springer, Cham. https://doi.org/10.1007/978-3-319-19977-1_19

Download citation

Publish with us

Policies and ethics

Search

Navigation