Invariant Ordering of Item-Total Regressions |
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| Authors: | Jesper Tijmstra David J Hessen Peter G M van der Heijden Klaas Sijtsma |
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| Institution: | 1.Department of Methodology and Statistics, Faculty of Social Sciences,Utrecht University,Utrecht,The Netherlands;2.Department of Methodology and Statistics, School of Social and Behavioral Sciences,Tilburg University,Tilburg,The Netherlands |
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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. |
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