Testing for Measurement Invariance with Respect to an Ordinal Variable
AbstractResearchers 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.
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Bibliographic InfoPaper provided by Faculty of Economics and Statistics, University of Innsbruck in its series Working Papers with number 2012-24.
Date of creation: Oct 2012
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measurement invariance; ordinal variable; parameter stability; factor analysis; structural equation models;
Find related papers by JEL classification:
- C30 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - General
- C38 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Classification Methdos; Cluster Analysis; Principal Components; Factor Analysis
- C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
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- Zeileis, Achim, 2006. "Implementing a class of structural change tests: An econometric computing approach," Computational Statistics & Data Analysis, Elsevier, vol. 50(11), pages 2987-3008, July.
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- 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.
- 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, University of Innsbruck.
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