Score-Based Tests of Measurement Invariance: Use in Practice
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.
|Date of creation:||Oct 2013|
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- Achim Zeileis & Friedrich Leisch & Kurt Hornik & Christian Kleiber, .
"strucchange: An R Package for Testing for Structural Change in Linear Regression Models,"
Journal of Statistical Software,
American Statistical Association, vol. 7(i02).
- 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.
- 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.
- Edgar Merkle & Jinyan Fan & Achim Zeileis, 2014.
"Testing for Measurement Invariance with Respect to an Ordinal Variable,"
Springer, vol. 79(4), pages 569-584, October.
- 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.
- Albert Satorra, 1989. "Alternative test criteria in covariance structure analysis: A unified approach," Psychometrika, Springer, vol. 54(1), pages 131-151, March.
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"Approximate Asymptotic P Values for Structural-Change Tests,"
Journal of Business & Economic Statistics,
American Statistical Association, vol. 15(1), pages 60-67, January.
- Tom Doan, . "RATS programs to replicate Hansen's examples of Andrews-Ploberger test," Statistical Software Components RTZ00087, Boston College Department of Economics.
- Bruce E. Hansen, 1995. "Approximate Asymptotic P-Values for Structural Change Tests," Boston College Working Papers in Economics 297., Boston College Department of Economics.
- 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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