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On Compensation in Multidimensional Response Modeling

Published online by Cambridge University Press:  01 January 2025

Wim J. van der Linden*
Affiliation:
CTB/McGraw-Hill
*
Requests for reprints should be sent to Wim J. van der Linden, CTB/McGraw-Hill, 20 Ryan Ranch Road, Monterey, CA 93940, USA. E-mail: wim_vanderlinden@ctb.com

Abstract

The issue of compensation in multidimensional response modeling is addressed. We show that multidimensional response models are compensatory in their ability parameters if and only if they are monotone. In addition, a minimal set of assumptions is presented under which the MLEs of the ability parameters are also compensatory. In a recent series of articles, beginning with Hooker, Finkelman, and Schwartzman (2009) in this journal, the second type of compensation was presented as a paradoxical result for certain multidimensional response models, leading to occasional unfairness in maximum-likelihood test scoring. First, it is indicated that the compensation is not unique and holds generally for any multiparameter likelihood with monotone score functions. Second, we analyze why, in spite of its generality, the compensation may give the impression of a paradox or unfairness.

Type
Original Paper
Copyright
Copyright © 2011 The Psychometric Society

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