Exploring joint maximum likelihood estimation for cognitive diagnosis models

Chia Yi Chiu, Hans Friedrich Koehn, Yi Zheng, Robert Henson

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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.

Original languageEnglish (US)
Title of host publicationQuantitative Psychology Research - The 79th Annual Meeting of the Psychometric Society, 2014
EditorsL. Andries van der Ark, Wen-Chung Wang, Jeffrey A. Douglas, Daniel M. Bolt, Sy-Miin Chow
PublisherSpringer New York LLC
Pages263-277
Number of pages15
ISBN (Print)9783319199764
DOIs
StatePublished - Jan 1 2015
Event79th Annual International Meeting of the Psychometric Society, IMPS 2014 - Madison, United States
Duration: Jul 21 2014Jul 25 2014

Publication series

NameSpringer Proceedings in Mathematics and Statistics
Volume140
ISSN (Print)2194-1009
ISSN (Electronic)2194-1017

Other

Other79th Annual International Meeting of the Psychometric Society, IMPS 2014
CountryUnited States
CityMadison
Period7/21/147/25/14

Fingerprint

Maximum Likelihood Estimation
Expectation Maximization
Markov Chain Monte Carlo
CPU Time
Estimation Algorithms
Model
Consistent Estimator
Resolve
Likelihood
Simulation Study
Iteration
Estimator
Alternatives
Estimate

Keywords

  • Cognitive diagnosis
  • Consistency
  • Joint maximum likelihood estimation
  • Nonparametric classification

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Chiu, C. Y., Koehn, H. F., Zheng, Y., & Henson, R. (2015). Exploring joint maximum likelihood estimation for cognitive diagnosis models. In L. A. van der Ark, W-C. Wang, J. A. Douglas, D. M. Bolt, & S-M. Chow (Eds.), Quantitative Psychology Research - The 79th Annual Meeting of the Psychometric Society, 2014 (pp. 263-277). (Springer Proceedings in Mathematics and Statistics; Vol. 140). Springer New York LLC. https://doi.org/10.1007/978-3-319-19977-1_19

Exploring joint maximum likelihood estimation for cognitive diagnosis models. / Chiu, Chia Yi; Koehn, Hans Friedrich; Zheng, Yi; Henson, Robert.

Quantitative Psychology Research - The 79th Annual Meeting of the Psychometric Society, 2014. ed. / L. Andries van der Ark; Wen-Chung Wang; Jeffrey A. Douglas; Daniel M. Bolt; Sy-Miin Chow. Springer New York LLC, 2015. p. 263-277 (Springer Proceedings in Mathematics and Statistics; Vol. 140).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Chiu, CY, Koehn, HF, Zheng, Y & Henson, R 2015, Exploring joint maximum likelihood estimation for cognitive diagnosis models. in LA van der Ark, W-C Wang, JA Douglas, DM Bolt & S-M Chow (eds), Quantitative Psychology Research - The 79th Annual Meeting of the Psychometric Society, 2014. Springer Proceedings in Mathematics and Statistics, vol. 140, Springer New York LLC, pp. 263-277, 79th Annual International Meeting of the Psychometric Society, IMPS 2014, Madison, United States, 7/21/14. https://doi.org/10.1007/978-3-319-19977-1_19
Chiu CY, Koehn HF, Zheng Y, Henson R. Exploring joint maximum likelihood estimation for cognitive diagnosis models. In van der Ark LA, Wang W-C, Douglas JA, Bolt DM, Chow S-M, editors, Quantitative Psychology Research - The 79th Annual Meeting of the Psychometric Society, 2014. Springer New York LLC. 2015. p. 263-277. (Springer Proceedings in Mathematics and Statistics). https://doi.org/10.1007/978-3-319-19977-1_19
Chiu, Chia Yi ; Koehn, Hans Friedrich ; Zheng, Yi ; Henson, Robert. / Exploring joint maximum likelihood estimation for cognitive diagnosis models. Quantitative Psychology Research - The 79th Annual Meeting of the Psychometric Society, 2014. editor / L. Andries van der Ark ; Wen-Chung Wang ; Jeffrey A. Douglas ; Daniel M. Bolt ; Sy-Miin Chow. Springer New York LLC, 2015. pp. 263-277 (Springer Proceedings in Mathematics and Statistics).
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