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Separability of Item and Person Parameters in Response Time Models

Published online by Cambridge University Press:  01 January 2025

Gerard J. P. Van Breukelen
Gerard J. P. Van Breukelen*
Affiliation:
Maastricht University, The Netherlands
*
Please send requests for reprints to Gerard J.P. Van Breukelen, Department of Methodology and Statistics, Maastricht University, P.O. Box 616, 6200 MD Maastricht, THE NETHERLANDS.
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Abstract

This paper discusses two forms of separability of item and person parameters in the context of response time (RT) models. The first is “separate sufficiency”: the existence of sufficient statistics for the item (person) parameters that do not depend on the person (item) parameters. The second is “ranking independence”: the likelihood of the item (person) ranking with respect to RTs does not depend on the person (item) parameters. For each form a theorem stating sufficient conditions, is proved. The two forms of separability are shown to include several (special cases of) models from psychometric and biometric literature. Ranking independence imposes no restrictions on the general distribution form, but on its parametrization. An estimation procedure based upon ranks and pseudolikelihood theory is discussed, as well as the relation of ranking independence to the concept of double monotonicity.

Keywords

response timesseparate sufficiencyranking independenceexponential familyscale parameterlocation parameteraccelerated life modelproportional hazards modelproportional odds modelpseudolikelihooddouble monotonicity
Type
Original Paper
Information
Psychometrika , Volume 62 , Issue 4 , December 1997 , pp. 525 - 544
Copyright
Copyright © 1997 The Psychometric Society

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Footnotes

I am indebted to Wim van der Linden for bringing Thissen's (1983) paper to my notice, and to Martijn Berger, Frans Tan, and the anonymous reviewers for their constructive comments on earlier drafts of this paper.

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