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Joint Maximum Likelihood Estimation for Diagnostic Classification Models

Published online by Cambridge University Press:  01 January 2025

Chia-Yi Chiu ,
Hans-Friedrich Köhn ,
Yi Zheng  and
Robert Henson
Chia-Yi Chiu*
Affiliation:
Rutgers, The State University of New Jersey
Hans-Friedrich Köhn
Affiliation:
University of Illinois at Urbana-Champaign
Yi Zheng
Affiliation:
Arizona State University
Robert Henson
Affiliation:
University of North Carolina
*
Correspondence should be made to Chia-Yi Chiu, Rutgers, The State University of New Jersey, New Brunswick, NJ, USA. Email: chia-yi.chiu@gse.rutgers.edu
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Abstract

Joint maximum likelihood estimation (JMLE) is developed for diagnostic classification models (DCMs). JMLE has been barely used in Psychometrics because JMLE parameter estimators typically lack statistical consistency. The JMLE procedure presented here resolves the consistency issue by incorporating an external, statistically consistent estimator of examinees’ proficiency class membership into the joint likelihood function, which subsequently allows for the construction of item parameter estimators that also have the consistency property. Consistency of the JMLE parameter estimators is established within the framework of general DCMs: The JMLE parameter estimators are derived for the Loglinear Cognitive Diagnosis Model (LCDM). Two consistency theorems are proven for the LCDM. Using the framework of general DCMs makes the results and proofs also applicable to DCMs that can be expressed as submodels of the LCDM. Simulation studies are reported for evaluating the performance of JMLE when used with tests of varying length and different numbers of attributes. As a practical application, JMLE is also used with “real world” educational data collected with a language proficiency test.

Keywords

cognitive diagnosisjoint maximum likelihood estimationnonparametric classificationstatistical consistency
Type
Article
Information
Psychometrika , Volume 81 , Issue 4 , December 2016 , pp. 1069 - 1092
Copyright
Copyright © 2016 The Psychometric Society

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