Generalized Measurement Invariance Tests with Application to Factor Analysis
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.
|Date of creation:||Apr 2011|
|Date of revision:|
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- Zeileis, Achim & Leisch, Friedrich & Hornik, Kurt & Kleiber, Christian, 2001.
"Strucchange: An R package for testing for structural change in linear regression models,"
2001,26, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
- Zeileis, Achim & Leisch, Friedrich & Hornik, Kurt & Kleiber, Christian, 2002. "strucchange: An R Package for Testing for Structural Change in Linear Regression Models," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 7(i02).
- Carolin Strobl & Julia Kopf & Achim Zeileis, 2011. "A new method for detecting differential item functioning in the Rasch model," Working Papers 2011-01, Faculty of Economics and Statistics, University of Innsbruck.
- Ploberger, Werner & Kramer, Walter, 1992. "The CUSUM Test with OLS Residuals," Econometrica, Econometric Society, vol. 60(2), pages 271-85, March.
- Achim Zeileis & Kurt Hornik, 2007. "Generalized M-fluctuation tests for parameter instability," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 61(4), pages 488-508.
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