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Bridging Parametric and Nonparametric Methods in Cognitive Diagnosis

Published online by Cambridge University Press:  01 January 2025

Chenchen Ma ,
Jimmy de la Torre  and
Gongjun Xu Open the ORCID record for Gongjun Xu [Opens in a new window]
Chenchen Ma
Affiliation:
University of Michigan
Jimmy de la Torre
Affiliation:
University of Hong Kong
Gongjun Xu*
Affiliation:
University of Michigan
*
Correspondence should be made to Gongjun Xu, Department of Statistics, University of Michigan, 1085 South University, Ann Arbor 48108, USA. Email: gongjun@umich.edu
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Abstract

A number of parametric and nonparametric methods for estimating cognitive diagnosis models (CDMs) have been developed and applied in a wide range of contexts. However, in the literature, a wide chasm exists between these two families of methods, and their relationship to each other is not well understood. In this paper, we propose a unified estimation framework to bridge the divide between parametric and nonparametric methods in cognitive diagnosis to better understand their relationship. We also develop iterative joint estimation algorithms and establish consistency properties within the proposed framework. Lastly, we present comprehensive simulation results to compare different methods and provide practical recommendations on the appropriate use of the proposed framework in various CDM contexts.

Keywords

cognitive diagnosislikelihood estimationnonparametric estimation
Type
Theory and Methods
Information
Psychometrika , Volume 88 , Issue 1 , March 2023 , pp. 51 - 75
Copyright
Copyright © 2022 The Author(s) under exclusive licence to The Psychometric Society

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Footnotes

Supplementary Information The online version contains supplementary material available at https://doi.org/10.1007/s11336-022-09878-2.

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