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Consistency of Nonparametric Classification in Cognitive Diagnosis

Published online by Cambridge University Press:  01 January 2025

Shiyu Wang  and
Jeff Douglas
Shiyu Wang
Affiliation:
University of Illinois at Urbana-Champaign
Jeff Douglas*
Affiliation:
University of Illinois at Urbana-Champaign
*
Requests for reprints should be sent to Jeff Douglas, University of Illinois at Urbana-Champaign, Champaign, IL, USA. E-mail: jeffdoug@uiuc.edu
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Abstract

Latent class models for cognitive diagnosis have been developed to classify examinees into one of the 2K attribute profiles arising from a K-dimensional vector of binary skill indicators. These models recognize that response patterns tend to deviate from the ideal responses that would arise if skills and items generated item responses through a purely deterministic conjunctive process. An alternative to employing these latent class models is to minimize the distance between observed item response patterns and ideal response patterns, in a nonparametric fashion that utilizes no stochastic terms for these deviations. Theorems are presented that show the consistency of this approach, when the true model is one of several common latent class models for cognitive diagnosis. Consistency of classification is independent of sample size, because no model parameters need to be estimated. Simultaneous consistency for a large group of subjects can also be shown given some conditions on how sample size and test length grow with one another.

Keywords

cognitive diagnosisnonparametric classificationlarge sample theory
Type
Original Paper
Information
Psychometrika , Volume 80 , Issue 1 , March 2015 , pp. 85 - 100
Copyright
Copyright © 2013 The Psychometric Society

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