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When are Item Response Models Consistent with Observed Data?

Published online by Cambridge University Press:  01 January 2025

Paul W. Holland
Paul W. Holland*
Affiliation:
Educational Testing Service
*
Requests for reprints should be sent to Paul W. Holland, Division of Measurement, Statistics, and Data Analysis Research, Educational Testing Service, Princeton, New Jersey 08541.
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Abstract

The problem of deciding whether a set of mental test data is consistent with any one of a large class of item response models is considered. The “classical” assumption of locla independence is weakened to a new condition, local nonnegative dependence (LND). Necessary and sufficient conditions are derived for a LND item response model to fit a set of data. This leads to a condition that a set of data must satisfy if it is to be representable by any item response model that assumes both local independence and monotone item characteristic curves. An example is given to show that LND is strictly weaker than local independence. Thus rejection of LND models implies rejection of all item response models that assume local independence for a given set of data.

Keywords

latent-trait modelslocal independenceitem-characteristic curves
Type
Original Paper
Information
Psychometrika , Volume 46 , Issue 1 , March 1981 , pp. 79 - 92
Copyright
Copyright © 1981 The Psychometric Society

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Footnotes

This research was supported in part by Grant NIE-G-78-0157 to ETS from the NIE, by the Program Statistics Research Project, and by TOEFL Program Research. I would like to thank Dr. Douglas Jones of ETS for stimulating discussions during the early stages of this research, Dr. Frederick Lord of ETS for his encouragement of this work and comments on earlier drafts of this paper and Professor Robert Berk of Rutgers University for pointing out that conditions (a), (b) and (c) of Theorem 2 were also sufficient for LND and Monotonicity. Dr. Donald Alderman of ETS provided financial support for the development of a computer program to apply these results to data from the TOEFL program.

References

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