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Two-Group Classification in Latent Trait Theory: Scores with Monotone Likelihood Ratio

Published online by Cambridge University Press:  01 January 2025

D. A. Grayson
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Abstract

This paper deals with two-group classification when a unidimensional latent trait, θ, is appropriate for explaining the data, X. It is shown that if X has monotone likelihood ratio then optimal allocation rules can be based on its magnitude when allocation must be made to one of two groups related to θ. These groups may relate to θ probabilistically via a non-decreasing function p(θ), or may be defined by all subjects above or below a selected value on θ.

In the case where the data arise from dichotomous items, then only the assumption that the items have nondecreasing item characteristic functions is enough to ensure that the unweighted sum of responses (the number-right score or raw score) possesses this fundamental monotone likelihood ratio property.

Keywords

monotone likelihood ratiolatent traittwo-group classificationnumber-right score
Type
Original Paper
Information
Psychometrika , Volume 53 , Issue 3 , September 1988 , pp. 383 - 392
Copyright
Copyright © 1988 The Psychometric Society

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References

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