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Estimating Item Parameters and Latent Ability when Responses are Scored in Two or More Nominal Categories

Published online by Cambridge University Press:  01 January 2025

R. Darrell Bock
R. Darrell Bock*
Affiliation:
University of Chicago
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Abstract

A multivariate logistic latent trait model for items scored in two or more nominal categories is proposed. Statistical methods based on the model provide 1) estimation of two item parameters for each response alternative of each multiple choice item and 2) recovery of information from “wrong” responses when estimating latent ability. An application to a large sample of data for twenty vocabulary items shows excellent fit of the model according to a chi-square criterion. Item and test information curves are compared for estimation of ability assuming multiple category and dichotomous scoring of these items. Multiple scoring proves substantially more precise for subjects of less than median ability, and about equally precise for subjects above the median.

Keywords

Public PolicyStatistical TheoryMultiple ChoiceResponse AlternativeLatent Trait

Information

Type
Original Paper
Information
Psychometrika , Volume 37 , Issue 1 , March 1972 , pp. 29 - 51
Copyright
Copyright © 1972 The Psychometric Society

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Footnotes

*

Preparation of this paper was supported in part by N.S.F. Grant GS-2900.

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