Testing for Measurement Invariance with Respect to an Ordinal Variable

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...

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Veröffentlicht in:Psychometrika 2014-10, Vol.79 (4), p.569-584
Hauptverfasser: Merkle, Edgar C., Fan, Jinyan, Zeileis, Achim
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Fan, Jinyan
Zeileis, Achim
description 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.
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subjects Adolescent
Adult
Assessment
Behavioral Science and Psychology
Child
Ethnicity
Factor Analysis
Factor Analysis, Statistical
High Stakes Tests
Humanities
Humans
Hypotheses
Lagrange multiplier
Law
Measurement Techniques
Psychology
Psychometrics
Psychometrics - methods
Quantitative psychology
Random variables
Research Design - statistics & numerical data
Researchers
Statistical Theory and Methods
Statistics
Statistics as Topic - methods
Statistics for Social Sciences
Testing and Evaluation
Violations
Young Adult
title Testing for Measurement Invariance with Respect to an Ordinal Variable
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