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Score-Based Tests of Measurement Invariance: Use in Practice

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  • Ting Wang

    ()

  • Edgar C. Merkle

    ()

  • Achim Zeileis

    ()

Abstract

In this paper, we consider a family of recently-proposed measurement invariance tests that are based on the scores of a fitted model. This family can be used to test for measurement invariance w.r.t. a continuous auxiliary variable, without pre-specification of subgroups. Moreover, the family can be used when one wishes to test for measurement invariance w.r.t. an ordinal auxiliary variable, yielding test statistics that are sensitive to violations that are monotonically related to the ordinal variable (and less sensitive to non-monotonic violations). The paper is specifically aimed at potential users of the tests who may wish to know (i) how the tests can be employed for their data, and (ii) whether the tests can accurately identify specific models parameters that violate measurement invariance (possibly in the presence of model misspecification). After providing an overview of the tests, we illustrate their general use via the R packages lavaan and strucchange. We then describe two novel simulations that provide evidence of the tests' practical abilities. As a whole, the paper provides researchers with the tools and knowledge needed to apply these tests to general measurement invariance scenarios.

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File URL: http://eeecon.uibk.ac.at/wopec2/repec/inn/wpaper/2013-33.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 2013-33.

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Length: 26 pages
Date of creation: Oct 2013
Date of revision:
Handle: RePEc:inn:wpaper:2013-33

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

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  1. 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.
  2. 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.
  3. 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.
  4. Edgar C. Merkle & Jinyan Fan & Achim Zeileis, 2012. "Testing for Measurement Invariance with Respect to an Ordinal Variable," Working Papers 2012-24, Faculty of Economics and Statistics, University of Innsbruck.
  5. Bruce E. Hansen, 1995. "Approximate Asymptotic P-Values for Structural Change Tests," Boston College Working Papers in Economics 297., Boston College Department of Economics.
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