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Testing Manifest Monotonicity Using Order-Constrained Statistical Inference

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 ofMethodology and Statistics, Faculty of Social Sciences, Utrecht Univeristy, PO Box 80140, 3508 TC Utrecht, The Netherlands. E-mail: j.tijmstra@uu.nl
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Abstract

Most dichotomous item response models share the assumption of latent monotonicity, which states that the probability of a positive response to an item is a nondecreasing function of a latent variable intended to be measured. Latent monotonicity cannot be evaluated directly, but it implies manifest monotonicity across a variety of observed scores, such as the restscore, a single item score, and in some cases the total score. In this study, we show that manifest monotonicity can be tested by means of the order-constrained statistical inference framework. We propose a procedure that uses this framework to determine whether manifest monotonicity should be rejected for specific items. This approach provides a likelihood ratio test for which the p-value can be approximated through simulation. A simulation study is presented that evaluates the Type I error rate and power of the test, and the procedure is applied to empirical data.

Keywords

item response theorylatent monotonicitymanifest monotonicitymonotone homogeneity modelorder-constrained statistical inference

Information

Type
Original Paper
Information
Psychometrika , Volume 78 , Issue 1 , January 2013 , pp. 83 - 97
Copyright
Copyright © The Psychometric Society

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