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Testing for Measurement Invariance with Respect to an Ordinal Variable

Published online by Cambridge University Press:  01 January 2025

Edgar C. Merkle ,
Jinyan Fan  and
Achim Zeileis
Edgar C. Merkle*
Affiliation:
University of Missouri
Jinyan Fan
Affiliation:
Auburn University
Achim Zeileis
Affiliation:
Universität Innsbruck
*
Requests for reprints should be sent to Edgar C. Merkle, Department of Psychological Sciences, University of Missouri, Columbia, MO 65211, USA. E-mail: merklee@missouri.edu
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Abstract

Researchers are often interested in testing for measurement invariance with respect to an ordinal auxiliary variable such as age group, income class, or school grade. In a factor-analytic context, these tests are traditionally carried out via a likelihood ratio test statistic comparing a model where parameters differ across groups to a model where parameters are equal across groups. This test neglects the fact that the auxiliary variable is ordinal, and it is also known to be overly sensitive at large sample sizes. In this paper, we propose test statistics that explicitly account for the ordinality of the auxiliary variable, resulting in higher power against “monotonic” violations of measurement invariance and lower power against “non-monotonic” ones. The statistics are derived from a family of tests based on stochastic processes that have recently received attention in the psychometric literature. The statistics are illustrated via an application involving real data, and their performance is studied via simulation.

Keywords

measurement invariancestochastic processfactor analysisordinal data
Type
Original Paper
Information
Psychometrika , Volume 79 , Issue 4 , October 2014 , pp. 569 - 584
Copyright
Copyright © 2013 The Psychometric Society

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