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An Inequality for Correlations in Unidimensional Monotone Latent Variable Models for Binary Variables

Published online by Cambridge University Press:  01 January 2025

Jules L. Ellis
Jules L. Ellis*
Affiliation:
Radboud University Nijmegen
*
Requests for reprints should be sent to Jules L. Ellis, School of Psychology and Artificial Intelligence, Radboud University Nijmegen, P.O. Box 9104, 6500 HE Nijmegen, The Netherlands. E-mail: j.ellis@psych.ru.nl
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Abstract

It is shown that a unidimensional monotone latent variable model for binary items implies a restriction on the relative sizes of item correlations: The negative logarithm of the correlations satisfies the triangle inequality. This inequality is not implied by the condition that the correlations are nonnegative, the criterion that coefficient H exceeds 0.30, or manifest monotonicity. The inequality implies both a lower bound and an upper bound for each correlation between two items, based on the correlations of those two items with every possible third item. It is discussed how this can be used in Mokken’s (A theory and procedure of scale-analysis, Mouton, The Hague, 1971) scale analysis.

Keywords

nonparametric IRTconditional associationpartial correlationmonotonicityMokken scale analysis

Information

Type
Original Paper
Information
Psychometrika , Volume 79 , Issue 2 , April 2014, pp. 303 - 316
Copyright
Copyright © 2013 The Psychometric Society

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