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Using the Conditional Grade-Of-Membership Model to Assess Judgment Accuracy

Published online by Cambridge University Press:  01 January 2025

Bruce Cooil  and
Sajeev Varki
Bruce Cooil*
Affiliation:
Owen Graduate School of Management, Vanderbilt University
Sajeev Varki
Affiliation:
College of Business Administration, University of Rhode Island
*
Requests for reprints should be sent to Bruce Cooil, OGSM, Vanderbilt University, 401 21st Avenue South, Nashville, TN 37203. E-Mail: bruce.cooil@owen.vanderbilt.edu
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Abstract

Consider the case where J instruments are used to classify each of I objects relative to K nominal categories. The conditional grade-of-membership (GoM) model provides a method of estimating the classification probabilities of each instrument (or “judge”) when the objects being classified consist of both pure types that lie exclusively in one of K nominal categories, and mixtures that lie in more than one category. Classification probabilities are identifiable whenever the sample of GoM vectors includes pure types from each category. When additional, relatively mild, assumptions are made about judgment accuracy, the identifiable correct classification probabilities are the greatest lower bounds among all solutions that might correspond to the observed multinomial process, even when the unobserved GoM vectors do not include pure types from each category. Estimation using the conditional GoM model is illustrated on a simulated data set. Further simulations show that the estimates of the classification probabilities are relatively accurate, even when the sample contains only a small percentage of approximately pure objects.

Keywords

nominal classificationincidental parametersextreme profilesmixtures

Information

Type
Article
Information
Psychometrika , Volume 68 , Issue 3 , September 2003 , pp. 453 - 471
Copyright
Copyright © 2003 The Psychometric Society

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Footnotes

The authors thank Max A. Woodbury, Kenneth G. Manton and H. Dennis Tolley for their help and four anonymous Psychometrika reviewers (including an associate editor) for their beneficial expository and technical suggestions. This work was supported by the Dean's Fund for Summer Research, Owen Graduate School of Management, Vanderbilt University.

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