IDEAS home Printed from https://ideas.repec.org/p/inn/wpaper/2013-33.html
   My bibliography  Save this paper

Score-Based Tests of Measurement Invariance: Use in Practice

Author

Listed:
  • 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.

Suggested Citation

  • Ting Wang & Edgar C. Merkle & Achim Zeileis, 2013. "Score-Based Tests of Measurement Invariance: Use in Practice," Working Papers 2013-33, Faculty of Economics and Statistics, Universität Innsbruck.
    • Handle: RePEc:inn:wpaper:2013-33
    as

    Download full text from publisher

    File URL: https://www2.uibk.ac.at/downloads/c4041030/wpaper/2013-33.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. 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).
    4. 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, Universität Innsbruck.
    5. 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, November.
    6. Rosseel, Yves, 2012. "lavaan: An R Package for Structural Equation Modeling," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 48(i02).
    7. 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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Edgar Merkle & Achim Zeileis, 2013. "Tests of Measurement Invariance Without Subgroups: A Generalization of Classical Methods," Psychometrika, Springer;The Psychometric Society, vol. 78(1), pages 59-82, January.
    2. 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.
    3. Ting Wang & Carolin Strobl & Achim Zeileis & Edgar C. Merkle, 2018. "Score-Based Tests of Differential Item Functioning via Pairwise Maximum Likelihood Estimation," Psychometrika, Springer;The Psychometric Society, vol. 83(1), pages 132-155, March.
    4. K. B. S. Huth & L. J. Waldorp & J. Luigjes & A. E. Goudriaan & R. J. Holst & M. Marsman, 2022. "A Note on the Structural Change Test in Highly Parameterized Psychometric Models," Psychometrika, Springer;The Psychometric Society, vol. 87(3), pages 1064-1080, September.
    5. Ting Wang & Carolin Strobl & Achim Zeileis & Edgar C. Merkle, 2016. "Score-Based Tests of Differential Item Functioning in the Two-Parameter Model," Working Papers 2016-05, Faculty of Economics and Statistics, Universität Innsbruck.
    6. Edgar C. Merkle & Achim Zeileis, 2011. "Generalized Measurement Invariance Tests with Application to Factor Analysis," Working Papers 2011-09, Faculty of Economics and Statistics, Universität Innsbruck.
    7. Payton J. Jones & Patrick Mair & Thorsten Simon & Achim Zeileis, 2020. "Network Trees: A Method for Recursively Partitioning Covariance Structures," Psychometrika, Springer;The Psychometric Society, vol. 85(4), pages 926-945, December.
    8. Jones, Payton J. & Mair, Patrick & Simon, Thorsten & Zeileis, Achim, 2019. "Network Model Trees," OSF Preprints ha4cw, Center for Open Science.
    9. Gutiérrez-Vargas, Álvaro A. & Meulders, Michel & Vandebroek, Martina, 2023. "Modeling preference heterogeneity using model-based decision trees," Journal of choice modelling, Elsevier, vol. 46(C).
    10. Ting Wang & Benjamin Graves & Yves Rosseel & Edgar C. Merkle, 2022. "Computation and application of generalized linear mixed model derivatives using lme4," Psychometrika, Springer;The Psychometric Society, vol. 87(3), pages 1173-1193, September.
    11. Grün, Bettina & Kosmidis, Ioannis & Zeileis, Achim, 2012. "Extended Beta Regression in R: Shaken, Stirred, Mixed, and Partitioned," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 48(i11).
    12. Yang, Yang & Liu, Qing & Chang, Chia-Hsun, 2023. "China-Europe freight transportation under the first wave of COVID-19 pandemic and government restriction measures," Research in Transportation Economics, Elsevier, vol. 97(C).
    13. Kleiber Christian & Zeileis Achim, 2013. "Reproducible Econometric Simulations," Journal of Econometric Methods, De Gruyter, vol. 2(1), pages 89-99, July.
    14. John M. Fry & Baoying Lai & Mark Rhodes, 2011. "The interdependence of Coffee spot and futures market," Working Papers 2011.1, International Network for Economic Research - INFER.
    15. Sandip Sinharay & Peter W. van Rijn, 2020. "Assessing Fit of the Lognormal Model for Response Times," Journal of Educational and Behavioral Statistics, , vol. 45(5), pages 534-568, October.
    16. Thomas Windberger & Achim Zeileis, 2011. "Structural Breaks in Inflation Dynamics within the European Monetary Union," Working Papers 2011-12, Faculty of Economics and Statistics, Universität Innsbruck.
    17. Russell P. Robins & Geoffrey Peter Smith, 2020. "Selection bias and pseudo discoveries on the constancy of stock return anomalies," Review of Quantitative Finance and Accounting, Springer, vol. 55(4), pages 1407-1426, November.
    18. Achim Zeileis & Torsten Hothorn, 2013. "A toolbox of permutation tests for structural change," Statistical Papers, Springer, vol. 54(4), pages 931-954, November.
    19. Matsypura, Dmytro & Pauwels, Laurent L., 2016. "Does portfolio margining make borrowing more attractive?," International Review of Financial Analysis, Elsevier, vol. 43(C), pages 128-134.
    20. Albert Satorra, 2015. "A Comment on a Paper by H. Wu and M. W. Browne (2014)," Psychometrika, Springer;The Psychometric Society, vol. 80(3), pages 613-618, September.

    More about this item

    Keywords

    measurement invariance; parameter stability; ordinal variable; factor analysis; structural equation models;
    All these keywords.

    JEL classification:

    • C30 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - General
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • C87 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs - - - Econometric Software

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. 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.

    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 CitEc recognized a bibliographic reference but did not link an item in RePEc 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 RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Janette Walde (email available below). General contact details of provider: https://edirc.repec.org/data/fuibkat.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.