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Higher-Order Latent Trait Models for Cognitive Diagnosis

Published online by Cambridge University Press:  01 January 2025

Jimmy de la Torre  and
Jeffrey A. Douglas
Jimmy de la Torre*
Affiliation:
Rutgers, The State University of New Jersey
Jeffrey A. Douglas
Affiliation:
University of Illinois
*
Correspondence should be sent to Jimmy de la Torre, Department of Educational Psychology, Rutgers, The State University of New Jersey, 10 Seminary Place, New Brunswick, NJ 08901, USA. E-Mail: jdelator@rci.rutgers.edu
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Abstract

Higher-order latent traits are proposed for specifying the joint distribution of binary attributes in models for cognitive diagnosis. This approach results in a parsimonious model for the joint distribution of a high-dimensional attribute vector that is natural in many situations when specific cognitive information is sought but a less informative item response model would be a reasonable alternative. This approach stems from viewing the attributes as the specific knowledge required for examination performance, and modeling these attributes as arising from a broadly-defined latent trait resembling the ϑ of item response models. In this way a relatively simple model for the joint distribution of the attributes results, which is based on a plausible model for the relationship between general aptitude and specific knowledge. Markov chain Monte Carlo algorithms for parameter estimation are given for selected response distributions, and simulation results are presented to examine the performance of the algorithm as well as the sensitivity of classification to model misspecification. An analysis of fraction subtraction data is provided as an example.

Keywords

cognitive diagnosisitem response theorylatent class modelMarkov chain Monte Carlo
Type
Theory and Methods
Information
Psychometrika , Volume 69 , Issue 3 , September 2004 , pp. 333 - 353
Copyright
Copyright © 2004 The Psychometric Society

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Footnotes

This research was funded by National Institute of Health grant R01 CA81068. We would like to thank William Stout and Sarah Hartz for many useful discussions, three anonymous reviewers for helpful comments and suggestions, and Kikumi Tatsuoka and Curtis Tatsuoka for generously sharing data.

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