Tests of Measurement Invariance Without Subgroups: A Generalization of Classical Methods

Psychometrika

Volumn 78, Issue 1, 2013, Pages 59-82

  Merkle, Edgar C ^a   Zeileis, Achim ^b  

^a UNIVERSITY OF MISSOURI   (United States)

^b UNIVERSITY OF INNSBRUCK   (Austria)

Author keywords

factor analysis; measurement invariance; parameter stability; structural equation models

Indexed keywords

HUMAN; PROCEDURES; PSYCHOMETRY; STATISTICS;

HUMANS; PSYCHOMETRICS; STATISTICS AS TOPIC;

EID: 84872346023     PISSN: 00333123     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11336-012-9302-4     Document Type: Article

References (46)

1. Andrews, D. W. K. (1993). Tests for parameter instability and structural change with unknown change point. Econometrica, 61, 821-856.
2. Bauer, D. J., & Curran, P. J. (2004). The integration of continuous and discrete latent variable models: potential problems and promising opportunities. Psychological Methods, 9, 3-29.
3. Bauer, D. J., & Hussong, A. M. (2009). Psychometric approaches for developing commensurate measures across independent studies: traditional and new models. Psychological Methods, 14, 101-125.
4. Boker, S., Neale, M., Maes, H., Wilde, M., Spiegel, M., Brick, T., et al. (2011). OpenMx: an open source extended structural equation modeling framework. Psychometrika, 76(2), 306-317.
5. Bollen, K. A. (1989). Structural equations with latent variables. New York: Wiley.
6. Borsboom, D. (2006). When does measurement invariance matter? Medical Care, 44(11), S176-S181.
7. Breiman, L., Friedman, J. H., Olshen, R. A., & Stone, C. J. (1984). Classification and regression trees. Belmont: Wadsworth.
8. Brown, R. L., Durbin, J., & Evans, J. M. (1975). Techniques for testing the constancy of regression relationships over time. Journal of the Royal Statistical Society. Series B, 37, 149-163.
9. Dolan, C. V., & van der Maas, H. L. J. (1998). Fitting multivariate normal finite mixtures subject to structural equation modeling. Psychometrika, 63, 227-253.
10. Ferguson, T. S. (1996). A course in large sample theory. London: Chapman & Hall.
11. Ferrer, E., Balluerka, N., & Widaman, K. F. (2008). Factorial invariance and the specification of second-order latent growth models. Methodology, 4, 22-36.
12. Hansen, B. E. (1992). Testing for parameter instability in linear models. Journal of Policy Modeling, 14, 517-533.
13. Hansen, B. E. (1997). Approximate asymptotic p values for structural-change tests. Journal of Business & Economic Statistics, 15, 60-67.
14. Hjort, N. L., & Koning, A. (2002). Tests for constancy of model parameters over time. Nonparametric Statistics, 14, 113-132.
15. Horn, J. L., & McArdle, J. J. (1992). A practical and theoretical guide to measurement invariance in aging research. Experimental Aging Research, 18, 117-144.
16. Jöreskog, K. G. (1971). Simultaneous factor analysis in several populations. Psychometrika, 36, 409-426.
17. Lubke, G. H., & Muthén, B. (2005). Investigating population heterogeneity with factor mixture models. Psychological Methods, 10, 21-39.
18. MacCallum, R. C., Zhang, S., Preacher, K. J., & Rucker, D. D. (2002). On the practice of dichotomization of quantitative variables. Psychological Methods, 7, 19-40.
19. McArdle, J. J. (2009). Latent variable modeling of differences and changes with longitudinal data. Annual Review of Psychology, 60, 577-605.
20. McDonald, R. P. (1999). Test theory: a unified treatment. Mahwah: Erlbaum.
21. Mellenbergh, G. J. (1989). Item bias and item response theory. International Journal of Educational Research, 13, 127-143.
22. Meredith, W. (1993). Measurement invariance, factor analysis, and factorial invariance. Psychometrika, 58, 525-543.
23. Merkle, E. C., & Shaffer, V. A. (2011). Binary recursive partitioning methods with application to psychology. British Journal of Mathematical & Statistical Psychology, 64(1), 161-181.
24. Millsap, R. E. (2005). Four unresolved problems in studies of factorial invariance. In A. Maydeu-Olivares & J. J. McArdle (Eds.), Contemporary psychometrics (pp. 153-171). Mahwah: Erlbaum.
25. Millsap, R. E. (2011). Statistical approaches to measurement invariance. New York: Routledge.
26. Molenaar, D., Dolan, C. V., Wicherts, J. M., & van der Mass, H. L. J. (2010). Modeling differentiation of cognitive abilities within the higher-order factor model using moderated factor analysis. Intelligence, 38, 611-624.
27. Neale, M. C., Aggen, S. H., Maes, H. H., Kubarych, T. S., & Schmitt, J. E. (2006). Methodological issues in the assessment of substance use phenotypes. Addictive Behaviors, 31, 1010-1034.
28. Nyblom, J. (1989). Testing for the constancy of parameters over time. Journal of the American Statistical Association, 84, 223-230.
29. Ploberger, W., & Krämer, W. (1992). The CUSUM test with OLS residuals. Econometrica, 60(2), 271-285.
30. Purcell, S. (2002). Variance components models for gene-environment interaction in twin analysis. Twin Research, 5, 554-571.
31. R Development Core Team (2012). R: a language and environment for statistical computing [Computer software manual]. URL http://www. R-project. org/. Vienna, Austria (ISBN 3-900051-07-0).
32. Rosseel, Y. (2012). lavaan: an R package for structural equation modeling. Journal of Statistical Software, 48(2), 1-36. URL: http://www. jstatsoft. org/v48/i02/.
33. Sánchez, G. (2009). PATHMOX approach: segmentation trees in partial least squares path modeling. Unpublished doctoral dissertation. Universitat Politécnica de Catalunya.
34. Satorra, A. (1989). Alternative test criteria in covariance structure analysis: a unified approach. Psychometrika, 54, 131-151.
35. Shorack, G. R., & Wellner, J. A. (1986). Empirical processes with applications to statistics. New York: Wiley.
36. Stark, S., Chernyshenko, O. S., & Drasgow, F. (2006). Detecting differential item functioning with confirmatory factor analysis and item response theory: Toward a unified strategy. Journal of Applied Psychology, 91, 1292-1306.
37. Strobl, C., Kopf, J., & Zeileis, A. (2010). A new method for detecting differential item functioning in the Rasch model (Technical Report No. 92). Department of Statistics, Ludwig-Maximilians-Universität München. URL http://epub. ub. uni-muenchen. de/11915/.
38. Strobl, C., Malley, J., & Tutz, G. (2009). An introduction to recursive partitioning: rationale, application, and characteristics of classification and regression trees, bagging, and random forests. Psychological Methods, 14, 323-348.
39. Wicherts, J. M., Dolan, C. V., & Hessen, D. J. (2005). Stereotype threat and group differences in test performance: a question of measurement invariance. Journal of Personality and Social Psychology, 89(5), 696-716.
40. Wothke, W. (2000). Longitudinal and multi-group modeling with missing data. In T. D. Little, K. U. Schnabel, & J. Baumert (Eds.), Modeling longitudinal and multilevel data: practical issues, applied approaches, and specific examples. Mahwah: Erlbaum.
41. Zeileis, A. (2005). A unified approach to structural change tests based on ML scores, F statistics, and OLS residuals. Econometric Reviews, 24(4), 445-466.
42. Zeileis, A. (2006). Implementing a class of structural change tests: an econometric computing approach. Computational Statistics & Data Analysis, 50(11), 2987-3008.
43. Zeileis, A., & Hornik, K. (2007). Generalized M-fluctuation tests for parameter instability. Statistica Neerlandica, 61, 488-508.
44. Zeileis, A., Hothorn, T., & Hornik, K. (2008). Model-based recursive partitioning. Journal of Computational and Graphical Statistics, 17, 492-514.
45. Zeileis, A., Leisch, F., Hornik, K., & Kleiber, C. (2002). strucchange: an R package for testing for structural change in linear regression models. Journal of Statistical Software, 7(2), 1-38. URL http://www. jstatsoft. org/v07/i02/.
46. Zeileis, A., Shah, A., & Patnaik, I. (2010). Testing, monitoring, and dating structural changes in exchange rate regimes. Computational Statistics & Data Analysis, 54, 1696-1706.