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Tests of Measurement Invariance Without Subgroups: A Generalization of Classical Methods

Published online by Cambridge University Press:  01 January 2025

Edgar C. Merkle  and
Achim Zeileis
Edgar C. Merkle*
Affiliation:
University of Missouri
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: [email protected]
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Abstract

The issue of measurement invariance commonly arises in factor-analytic contexts, with methods for assessment including likelihood ratio tests, Lagrange multiplier tests, and Wald tests. These tests all require advance definition of the number of groups, group membership, and offending model parameters. In this paper, we study tests of measurement invariance based on stochastic processes of casewise derivatives of the likelihood function. These tests can be viewed as generalizations of the Lagrange multiplier test, and they are especially useful for: (i) identifying subgroups of individuals that violate measurement invariance along a continuous auxiliary variable without prespecified thresholds, and (ii) identifying specific parameters impacted by measurement invariance violations. The tests are presented and illustrated in detail, including an application to a study of stereotype threat and simulations examining the tests’ abilities in controlled conditions.

Keywords

measurement invarianceparameter stabilityfactor analysisstructural equation models
Type
Original Paper
Information
Psychometrika , Volume 78 , Issue 1 , January 2013 , pp. 59 - 82
Copyright
Copyright © The Psychometric Society

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