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Testing for Measurement Invariance with Respect to an Ordinal Variable

Edgar C. Merkle (), Jinyan Fan () and Achim Zeileis ()

Working Papers from Faculty of Economics and Statistics, University of Innsbruck

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 invariance; ordinal variable; parameter stability; factor analysis; structural equation models (search for similar items in EconPapers)
JEL-codes: C30 C38 C52 (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-ecm
Date: 2012-10
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Journal Article: Testing for Measurement Invariance with Respect to an Ordinal Variable (2014) Downloads
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