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|
|Date of revision:|
|Contact details of provider:|| Postal: Universitätsstraße 15, A - 6020 Innsbruck|
Web page: http://www.uibk.ac.at/fakultaeten/volkswirtschaft_und_statistik/index.html.en
More information through EDIRC
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Albert Satorra, 1989. "Alternative test criteria in covariance structure analysis: A unified approach," Psychometrika, Springer;The Psychometric Society, vol. 54(1), pages 131-151, March.
- 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.
- 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.
- Rosseel, Yves, 2012. "lavaan: An R Package for Structural Equation Modeling," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 48(i02).
- Hansen, Bruce E, 1997.
"Approximate Asymptotic P Values for Structural-Change Tests,"
Journal of Business & Economic Statistics,
American Statistical Association, vol. 15(1), pages 60-67, January.
- Bruce E. Hansen, 1995. "Approximate Asymptotic P-Values for Structural Change Tests," Boston College Working Papers in Economics 297., Boston College Department of Economics.
- Tom Doan, . "RATS programs to replicate Hansen's examples of Andrews-Ploberger test," Statistical Software Components RTZ00087, Boston College Department of Economics.
- Edgar C. Merkle & Jinyan Fan & Achim Zeileis, 2012.
"Testing for Measurement Invariance with Respect to an Ordinal Variable,"
2012-24, 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," Psychometrika, Springer;The Psychometric Society, vol. 79(4), pages 569-584, October.
When requesting a correction, please mention this item's handle: RePEc:inn:wpaper:2013-33. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Janette Walde)
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.