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A Constrained Metropolis–Hastings Robbins–Monro Algorithm for Q Matrix Estimation in DINA Models

Published online by Cambridge University Press:  01 January 2025

Chen-Wei Liu Open the ORCID record for Chen-Wei Liu [Opens in a new window] ,
Björn Andersson Open the ORCID record for Björn Andersson [Opens in a new window]  and
Anders Skrondal
Chen-Wei Liu*
Affiliation:
National Taiwan Normal University
Björn Andersson
Affiliation:
University of Oslo
Anders Skrondal
Affiliation:
Norwegian Institute of Public Health University of Oslo University of California, Berkeley
*
Correspondence should be made to Chen-Wei Liu, Department of Educational Psychology and Counseling, National Taiwan Normal University, 162, Section 1, Heping E. Road, 10610, Taipei, Taiwan. Email: cwliu@ntnu.edu.tw
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Abstract

In diagnostic classification models (DCMs), the Q matrix encodes in which attributes are required for each item. The Q matrix is usually predetermined by the researcher but may in practice be misspecified which yields incorrect statistical inference. Instead of using a predetermined Q matrix, it is possible to estimate it simultaneously with the item and structural parameters of the DCM. Unfortunately, current methods are computationally intensive when there are many attributes and items. In addition, the identification constraints necessary for DCMs are not always enforced in the estimation algorithms which can lead to non-identified models being considered. We address these problems by simultaneously estimating the item, structural and Q matrix parameters of the Deterministic Input Noisy “And” gate model using a constrained Metropolis–Hastings Robbins–Monro algorithm. Simulations show that the new method is computationally efficient and can outperform previously proposed Bayesian Markov chain Monte-Carlo algorithms in terms of Q matrix recovery, and item and structural parameter estimation. We also illustrate our approach using Tatsuoka’s fraction–subtraction data and Certificate of Proficiency in English data.

Keywords

Diagnostic classification modelsQ matrixstochastic algorithm
Type
Theory and Methods
Information
Psychometrika , Volume 85 , Issue 2 , June 2020 , pp. 322 - 357
Copyright
Copyright © 2020 The Psychometric Society, corrected publication 2024

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