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Continuous and Discrete Latent Structure Models for Item Response Data

Published online by Cambridge University Press:  01 January 2025

Edward H. Haertel
Edward H. Haertel*
Affiliation:
Standford University
*
Requests for reprints should be sent to Edward Haertel, School of Education, Stanford University, Stanford, California 94305-3096.
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Abstract

Relations are examined between latent trait and latent class models for item response data. Conditions are given for the two-latent class and two-parameter normal ogive models to agree, and relations between their item parameters are presented. Generalizations are then made to continuous models with more than one latent trait and discrete models with more than two latent classes, and methods are presented for relating latent class models to factor models for dichotomized variables. Results are illustrated using data from the Law School Admission Test, previously analyzed by several authors.

Keywords

latent structurelatent classlatent traititem analysisdichotomous factor analysisLaw School Admission Test (LSAT)
Type
Original Paper
Information
Psychometrika , Volume 55 , Issue 3 , September 1990 , pp. 477 - 494
Copyright
Copyright © 1990 The Psychometric Society

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Footnotes

I thank Lee J. Cronbach for his careful reading of this manuscript. His numerous constructive suggestions improved the clarity of the presentation, adn helped me to clarify my own thinking on critical points. I also thank Ingram Olkin, David E. Wiley, anonymous reviewers, and the Editor for constructive suggestions. Finally, I thank the Law School Admission Council/Law School Admission Services, and especially Ms. Deborah L. Palser, for locating and permitting me to inspect copies of the LSAT items used in the illustrative data.

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