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Generalized Measurement Invariance Tests with Application to Factor Analysis

Edgar C. Merkle () and Achim Zeileis ()

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

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 construct 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: (1) isolating specific parameters affected by measurement invariance violations, and (2) identifying subgroups of individuals that violated measurement invariance based on a continuous auxiliary variable. The tests are presented and illustrated in detail, along with simulations examining the tests' abilities in controlled conditions.

Keywords: measurement invariance; 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: 2011-04
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