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Invariant Ordering of Item-Total Regressions

Published online by Cambridge University Press:  01 January 2025

Jesper Tijmstra ,
David J. Hessen ,
Peter G. M. van der Heijden  and
Klaas Sijtsma
Jesper Tijmstra*
Affiliation:
Utrecht University
David J. Hessen
Affiliation:
Utrecht University
Peter G. M. van der Heijden
Affiliation:
Utrecht University
Klaas Sijtsma
Affiliation:
Tilburg University
*
Requests for reprints should be sent to Jesper Tijmstra, Department of Methodology and Statistics, Faculty of Social Sciences, Utrecht University, PO Box 80140, 3508 TC Utrecht, The Netherlands. E-mail: j.tijmstra@uu.nl
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Abstract

A new observable consequence of the property of invariant item ordering is presented, which holds under Mokken’s double monotonicity model for dichotomous data. The observable consequence is an invariant ordering of the item-total regressions. Kendall’s measure of concordance W and a weighted version of this measure are proposed as measures for this property. Karabatsos and Sheu proposed a Bayesian procedure (Appl. Psychol. Meas. 28:110–125, 2004), which can be used to determine whether the property of an invariant ordering of the item-total regressions should be rejected for a set of items. An example is presented to illustrate the application of the procedures to empirical data.

Keywords

double monotonicity Mokken modelinvariant item orderinginvariant ordering of item-total regressionsKendall’s Wmanifest invariant item orderingnonparametric item response theory
Type
Original Paper
Information
Psychometrika , Volume 76 , Issue 2 , April 2011 , pp. 217 - 227
Copyright
Copyright © 2011 The Psychometric Society

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