Hostname: page-component-7b7567c8c-2n9c9 Total loading time: 0 Render date: 2026-11-15T18:30:33.820Z Has data issue: false hasContentIssue false
  • English
  • Français

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,
Jeroen K. Vermunt and
Guy B. D. Moors
Daniel L. Oberski*
Affiliation:
Department of Methodology and Statistics, Tilburg University, Room P 1107, PO Box 90153, 5000 LE Tilburg, The Netherlands
Jeroen K. Vermunt
Affiliation:
Department of Methodology and Statistics, Tilburg University, Room P 1114, PO Box 90153, 5000 LE Tilburg, The Netherlands, e-mail: j.k.vermunt@tilburguniversity.edu
Guy B. D. Moors
Affiliation:
Department of Methodology and Statistics, Tilburg University, Room P 1110, PO Box 90153, 5000 LE Tilburg, The Netherlands, e-mail: g.b.d.moors@tilburguniversity.edu
*
e-mail: d.oberski@tilburguniversity.edu (corresponding author)
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the 'Save PDF' action button.

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.

Information

Type
Articles
Information
Political Analysis , Volume 23 , Issue 4 , Autumn 2015, pp. 550 - 563
Copyright
Copyright © The Author 2015. Published by Oxford University Press on behalf of the Society for Political Methodology 

Footnotes

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 http://dx.doi.org/10.7910/DVN/I7Y3G2, Harvard Dataverse, V1. Supplementary materials for this article are available on the Political Analysis Web site.

References

Arel-Bundock, Vincent 2013. WDI: World Development Indicators (World Bank). R package version 2.4. http://CRAN. R-project.org/package=WDI (accessed August 1, 2014).Google Scholar
Benjamini, Yoav, and Hochberg, Yosef. 1995. Controlling the false discovery rate: A practical and powerful approach to multiple testing. Journal of the Royal Statistical Society. Series B (Methodological) 57:289–300.Google Scholar
Bentler, P. M., and Chou, C. P. 1993. Some new covariance structure model improvement statistics. In Testing structural equation models, eds. Jöreskog, K. G. and Scott, J. Long, W, 199–235. Thousand Oaks, CA: Sage.Google Scholar
Böckenholt, U. 2002. Comparison and choice: Analyzing discrete preference data by latent class scaling models. In Applied latent class analysis, eds. Hagenaars, Jacques A. P. and McCutcheon, Allan L., 163–82. Cambridge, UK: Cambridge University Press.Google Scholar
Bollen, Kenneth A. 2002. Latent variables in psychology and the social sciences. Annual Review of Psychology 53:605–34.Google Scholar
Byrne, B. M., Shavelson, R. J., and Muthén, Bengt 1989. Testing for the equivalence of factor covariance and mean structures: The issue of partial measurement invariance. Psychological Bulletin 105:456.Google Scholar
Chen, F. F. 2007. Sensitivity of goodness of fit indexes to lack of measurement invariance. Structural Equation Modeling 14:464–504.Google Scholar
Cheung, G. W., and Rensvold, R. B. 2002. Evaluating goodness-of-fit indexes for testing measurement invariance. Structural Equation Modeling 9:233–55.Google Scholar
Croon, Marcel 1989. Latent class models for the analysis of rankings. In New developments in psychological choice modelling, eds. De Soete, G., Feger, H., and Klauer, K. C., 99–121. North-Holland: Elsevier Science Publishers.Google Scholar
Hancock, Gregory R., Stapleton, Laura M., and Arnold-Berkovits, Ilona. 2009. The tenuousness of invariance tests within multisample covariance and mean structure models. In Structural equation modeling in educational research: Concepts and applications, eds. Teo, T. and Khine, M. S., 137–74. Rotterdam, The Netherlands: Sense Publishers.Google Scholar
Holland, Paul W., and Wainer, Howard. 1993. Differential item functioning. New York: Routledge.Google Scholar
Hu, L., and Bentler, P. M. 1998. Fit indices in covariance structure modeling: Sensitivity to underparameterized model misspecification. Psychological Methods 3:424.CrossRefGoogle Scholar
Inglehart, Ronald. 1981. Post-materialism in an environment of insecurity. American Political Science Review 75:880–900.Google Scholar
Inglehart, Ronald, and Welzel, Christian. 2010. Changing mass priorities: The link between modernization and democracy. Perspectives on Politics 8:551–67.Google Scholar
Inglehart, Ronald, Norris, Pippa, Welzel, Christian. 2002. Gender equality and democracy. Comparative Sociology 1:321–45.Google Scholar
Kankaraš, Miloš, Moors, Guy, and Vermunt, Jeroen K. 2010. Testing for measurement invariance with latent class analysis. In Cross-cultural analysis: Methods and applications, eds. Davidov, Eldad, Schmidt, Peter, and Billiet, Jaak, 359–84. New York: Taylor & Francis.Google Scholar
Luce, R. Duncan 1959. Individual choice behavior: A theoretical analysis. New York: John Wiley and Sons.Google Scholar
Magnus, J. R., and Vasnev, A. L. 2007. Local sensitivity and diagnostic tests. Econometrics Journal 10:166–92.Google Scholar
McCutcheon, Allan L. 1985. A latent class analysis of tolerance for nonconformity in the American public. Public Opinion Quarterly 49:474–88.Google Scholar
Mellenbergh, G. J. 1989. Item bias and item response theory. International Journal of Educational Research 13:127–43.Google Scholar
Meredith, W. 1993. Measurement invariance, factor analysis, and factorial invariance. Psychometrika 58:525–43.CrossRefGoogle Scholar
Moors, Guy, and Vermunt, Jeroen. 2007. Heterogeneity in post-materialist value priorities: Evidence from a latent class discrete choice approach. European Sociological Review 23:631–48.Google Scholar
Oberski, Daniel 2015. Replication Data for: “Evaluating measurement invariance in categorical data latent variable models with the EPC-interest.” http://dx.doi.org/10.7910/DVN/I7Y3G2 (accessed July 1, 2015).Google Scholar
Oberski, D. L. 2014. Evaluating sensitivity of parameters of interest to measurement invariance in latent variable models. Political Analysis 22:45–60.Google Scholar
Poole, Keith, Lewis, James Lo, Jeffrey, and Carroll, Royce. 2012. oc: OC Roll Call Analysis Software. http://cran.r-project.org/web/packages/oc/index.html (accessed August 1, 2014).Google Scholar
Poole, Keith T., and Rosenthal, Howard. 1985. A spatial model for legislative roll call analysis. American Journal of Political Science 29(2): 357–84.Google Scholar
Poole, Keith T., Lewis, Jeffrey B., Lo, James, and Carroll, Royce. 2011. Scaling roll call votes with w-nominate in R. Journal of Statistical Software 42(14).Google Scholar
R Core Team. 2012. R: A language and environment for statistical computing. Vienna, Austria: R Foundation for Statistical Computing. ISBN 3-900051-07-0. http://www.R-project.org/(accessed August 1, 2014).Google Scholar
Rabe-Hesketh, Sophia, Skrondal, Andrew, and Pickles, Andrew. 2004. Generalized multilevel structural equation modeling. Psychometrika 69:167–90.Google Scholar
Saris, W. E., Satorra, A., and Sörbom, D. 1987. The detection and correction of specification errors in structural equation models. Sociological Methodology 17:105–29.CrossRefGoogle Scholar
Saris, W. E., Satorra, A., and Van der Veld, W. M. 2009. Testing structural equation models or detection of misspecifications? Structural Equation Modeling 16:561–82.Google Scholar
Satorra, A. 1989. Alternative test criteria in covariance structure analysis: A unified approach. Psychometrika 54:131–51.Google Scholar
Schmitt, N., and Kuljanin, G. 2008. Measurement invariance: Review of practice and implications. Human Resource Management Review18:210–22.Google Scholar
Steenkamp, J. B. E. M., and Baumgartner, H. 1998. Assessing measurement invariance in cross-national consumer research. Journal of Consumer Research 25:78–107.Google Scholar
Vandenberg, R. J., and Lance, C. E. 2000. A review and synthesis of the measurement invariance literature: Suggestions, practices, and recommendations for organizational research. Organizational Research Methods 3:4–70.Google Scholar
Vermunt, J. K., and Magidson, J. 2004. Factor analysis with categorical indicators: A comparison between traditional and latent class approaches. In New developments in categorical data analysis for the social and behavioral sciences, eds. Andries van der Ark, L., Croon, Marcel A., and Sijtsma, Klaas, 41–63. Mahwah: Erblaum.Google Scholar
Vermunt, J. K., and Magidson, J. 2013. Technical guide for Latent GOLD 5.0: Basic, advanced, and syntax. Belmont, MA: Statistical Innovations Inc.Google Scholar
Supplementary material: PDF

Oberski et al. supplementary material

Appendix

Download Oberski et al. supplementary material(PDF)
PDF 207.5 KB