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Testing the Conditional Independence and Monotonicity Assumptions of Item Response Theory

Published online by Cambridge University Press:  01 January 2025

Paul R. Rosenbaum
Paul R. Rosenbaum*
Affiliation:
Research Statistics Group, Educational Testing Service
*
Requests for reprints should be sent to Paul R. Rosenbaum, Research Statistics Group, 2 I-T, Educational Testing Service, Princeton, N.J. 08541
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Abstract

When item characteristic curves are nondecreasing functions of a latent variable, the conditional or local independence of item responses given the latent variable implies nonnegative conditional covariances between all monotone increasing functions of a set of item responses given any function of the remaining item responses. This general result provides a basis for testing the conditional independence assumption without first specifying a parametric form for the nondecreasing item characteristic curves. The proposed tests are simple, have known asymptotic null distributions, and possess certain optimal properties. In an example, the conditional independence hypothesis is rejected for all possible forms of monotone item characteristic curves.

Keywords

Latent trait modelsAssociation of random variablesDiscrete dataContingency tables
Type
Original Paper
Information
Psychometrika , Volume 49 , Issue 3 , September 1984 , pp. 425 - 435
Copyright
Copyright © 1984 The Psychometric Society

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Footnotes

The author acknowledges Paul W. Holland for valuable conversations on the subject of this paper; Henry Braun and Fred Lord for comments at a presentation on this subject which led to improvements in the paper; Carl H. Haag for permission to use the data in §4; Bruce Kaplan for assistance with computing; and two referees for helpful suggestions.

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