Psychometrika

, Volume 79, Issue 4, pp 569–584 | Cite as

Testing for Measurement Invariance with Respect to an Ordinal Variable

Article

Abstract

Researchers are often interested in testing for measurement invariance with respect to an ordinal auxiliary variable such as age group, income class, or school grade. In a factor-analytic context, these tests are traditionally carried out via a likelihood ratio test statistic comparing a model where parameters differ across groups to a model where parameters are equal across groups. This test neglects the fact that the auxiliary variable is ordinal, and it is also known to be overly sensitive at large sample sizes. In this paper, we propose test statistics that explicitly account for the ordinality of the auxiliary variable, resulting in higher power against “monotonic” violations of measurement invariance and lower power against “non-monotonic” ones. The statistics are derived from a family of tests based on stochastic processes that have recently received attention in the psychometric literature. The statistics are illustrated via an application involving real data, and their performance is studied via simulation.

Key words

measurement invariance stochastic process factor analysis ordinal data 

Notes

Acknowledgements

This work was supported by National Science Foundation grant SES-1061334.

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Copyright information

© The Psychometric Society 2013

Authors and Affiliations

  1. 1.Department of Psychological SciencesUniversity of MissouriColumbiaUSA
  2. 2.Auburn UniversityAuburnUSA
  3. 3.Universität InnsbruckInnsbruckAustria

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