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Generalized Measurement Invariance Tests with Application to Factor Analysis

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  • Edgar C. Merkle

    ()

  • Achim Zeileis

    ()

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.

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File URL: http://eeecon.uibk.ac.at/wopec2/repec/inn/wpaper/2011-09.pdf
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Bibliographic Info

Paper provided by Faculty of Economics and Statistics, University of Innsbruck in its series Working Papers with number 2011-09.

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Length: 26 pages
Date of creation: Apr 2011
Date of revision:
Handle: RePEc:inn:wpaper:2011-09

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Keywords: measurement invariance; parameter stability; factor analysis; structural equation models;

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  1. Zeileis, Achim & Leisch, Friedrich & Hornik, Kurt & Kleiber, Christian, 2001. "Strucchange: An R package for testing for structural change in linear regression models," Technical Reports 2001,26, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
  2. Achim Zeileis & Kurt Hornik, 2007. "Generalized M-fluctuation tests for parameter instability," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, Netherlands Society for Statistics and Operations Research, vol. 61(4), pages 488-508.
  3. Carolin Strobl & Julia Kopf & Achim Zeileis, 2011. "A new method for detecting differential item functioning in the Rasch model," Working Papers, Faculty of Economics and Statistics, University of Innsbruck 2011-01, Faculty of Economics and Statistics, University of Innsbruck.
  4. Ploberger, Werner & Kramer, Walter, 1992. "The CUSUM Test with OLS Residuals," Econometrica, Econometric Society, Econometric Society, vol. 60(2), pages 271-85, March.
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