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Evaluating Measurement Invariance in Categorical Data Latent Variable Models with the EPC-Interest

Published online by Cambridge University Press:  04 January 2017

Daniel L. Oberski*
Department of Methodology and Statistics, Tilburg University, Room P 1107, PO Box 90153, 5000 LE Tilburg, The Netherlands
Jeroen K. Vermunt
Department of Methodology and Statistics, Tilburg University, Room P 1114, PO Box 90153, 5000 LE Tilburg, The Netherlands, e-mail:
Guy B. D. Moors
Department of Methodology and Statistics, Tilburg University, Room P 1110, PO Box 90153, 5000 LE Tilburg, The Netherlands, e-mail:
e-mail: (corresponding author)


Many variables crucial to the social sciences are not directly observed but instead are latent and measured indirectly. When an external variable of interest affects this measurement, estimates of its relationship with the latent variable will then be biased. Such violations of “measurement invariance” may, for example, confound true differences across countries in postmaterialism with measurement differences. To deal with this problem, researchers commonly aim at “partial measurement invariance” that is, to account for those differences that may be present and important. To evaluate this importance directly through sensitivity analysis, the “EPC-interest” was recently introduced for continuous data. However, latent variable models in the social sciences often use categorical data. The current paper therefore extends the EPC-interest to latent variable models for categorical data and demonstrates its use in example analyses of U.S. Senate votes as well as respondent rankings of postmaterialism values in the World Values Study.

Copyright © The Author 2015. Published by Oxford University Press on behalf of the Society for Political Methodology 

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Authors' note: The authors are grateful to two anonymous reviewers, the editor, Katrijn van Deun, Lianne Ippel, Eldad Davidov, Zsuzsa Bakk, Verena Schmittmann, and participants of EAM2014 for their comments. Replication materials for this article can be obtained from, Harvard Dataverse, V1. Supplementary materials for this article are available on the Political Analysis Web site.


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