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Local Homogeneity in Latent Trait Models. A Characterization of the Homogeneous Monotone IRT Model

Published online by Cambridge University Press:  01 January 2025

Jules L. Ellis  and
Arnold L. van den Wollenberg
Jules L. Ellis*
Affiliation:
University of Nijmegen
Arnold L. van den Wollenberg
Affiliation:
University of Nijmegen
*
Requests for reprints should be sent to Jules L. Ellis, University of Nijmegen, Department of Mathematical Psychology, Montessorilaan 3, PO Box 9104, 6500 HE Nijmegen, THE NETHERLANDS.
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Abstract

The stochastic subject formulation of latent trait models contends that, within a given subject, the event of obtaining a certain response pattern may be probabilistic. Ordinary latent trait models do not imply that these within-subject probabilities are identical to the conditional probabilities specified by the model. The latter condition is called local homogeneity. It is shown that local homogeneity is equivalent to subpopulation invariance of the model. In case of the monotone IRT model, local homogeneity implies absence of item bias, absence of item specific traits, and the possibility to join overlapping subtests. The following characterization theorem is proved: the homogeneous monotone IRT model holds for a finite or countable item pool if and only if the pool is experimentally independent and pairwise nonnegative association holds in every positive subpopulation.

Keywords

stochastic subjectunidimensionalitylocal independenceexperimental independencelocal homogeneitymonotonicitysubpopulation invariancepairwise determinationnonnegative association
Type
Original Paper
Information
Psychometrika , Volume 58 , Issue 3 , September 1993 , pp. 417 - 429
Copyright
Copyright © 1993 The Psychometric Society

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Footnotes

This research was supported by the Dutch Interuniversity Graduate School of Psychometrics and Sociometrics. The authors wish to thank two reviewers for their thorough comments.

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