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Test Theory without an Answer Key

Published online by Cambridge University Press:  01 January 2025

William H. Batchelder  and
A. Kimball Romney
William H. Batchelder*
Affiliation:
University of California, Irvine
A. Kimball Romney
Affiliation:
University of California, Irvine
*
Requests for reprints should be sent to W. H. Batehelder, School of Social Sciences, University of California, Irvine, CA 92717.
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Abstract

A general model is presented for homogeneous, dichotomous items when the answer key is not known a priori. The model is structurally related to the two-class latent structure model with the roles of respondents and items interchanged. For very small sets of respondents, iterative maximum likelihood estimates of the parameters can be obtained by existing methods. For other situations, new estimation methods are developed and assessed with Monte Carlo data. The answer key can be accurately reconstructed with relatively small sets of respondents. The model is useful when a researcher wants to study objectively the knowledge possessed by members of a culturally coherent group that the researcher is not a member of.

Keywords

test theorydichotomous responsessignal detectionlatent class modelparameter estimationinformation pooling
Type
Original Paper
Information
Psychometrika , Volume 53 , Issue 1 , March 1988 , pp. 71 - 92
Copyright
Copyright © 1988 The Psychometric Society

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Footnotes

This research was supported by NSF Grant No. SES-8320173 to the authors. We gratefully acknowledge comments and suggestions from John Boyd, Tarow Indow, and Kathy Maher as well as the editor and several anonymous referees.

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