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Estimating Latent Distributions

Published online by Cambridge University Press:  01 January 2025

Robert J. Mislevy
Robert J. Mislevy*
Affiliation:
National Opinion Research Center
*
Requests for reprints should be addressed to Dr. Robert Mislevy, Educational Testing Service, Princeton, N.J. 08540
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Abstract

Consider vectors of item responses obtained from a sample of subjects from a population in which ability θ is distributed with density g (θ‖α), where the α are unknown parameters. Assuming the responses depend on θ through a fully specified item response model, this paper presents maximum likelihood equations for the estimation of the population parameters directly from the observed responses; i.e., without estimating an ability parameter for each subject. Also provided are asymptotic standard errors and tests of fit, computing approximations, and details of four special cases: a non-parametric approximation, a normal solution, a resolution of normal components, and a beta-binomial solution.

Keywords

latent distributionsmaximum likelihoodEM algorithmempirical Bayes estimationGaussian resolutionbeta-binomial modelitem response theory
Type
Original Paper
Information
Psychometrika , Volume 49 , Issue 3 , September 1984 , pp. 359 - 381
Copyright
Copyright © 1984 The Psychometric Society

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Footnotes

The author would like to thank R. Darrell Bock for his comments, suggestions, and encouragement during the course of this work.

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