The performance of robust test statistics with categorical data

British Journal of Mathematical and Statistical Psychology

Volumn 66, Issue 2, 2013, Pages 201-223

  Savalei, Victoria ^a   Rhemtulla, Mijke ^b  

^a UNIVERSITY OF BRITISH COLUMBIA   (Canada)

^b UNIVERSITY OF KANSAS   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ARTICLE; FACTORIAL ANALYSIS; HUMAN; PSYCHOLOGIC TEST; PSYCHOMETRY; REGRESSION ANALYSIS; SAMPLE SIZE; STATISTICAL MODEL; STATISTICS;

FACTOR ANALYSIS, STATISTICAL; HUMANS; LEAST-SQUARES ANALYSIS; MODELS, STATISTICAL; PSYCHOLOGICAL TESTS; PSYCHOMETRICS; SAMPLE SIZE;

EID: 84876022167     PISSN: 00071102     EISSN: 20448317     Source Type: Journal    
DOI: 10.1111/j.2044-8317.2012.02049.x     Document Type: Article

References (34)

1. Asparouhov, T., & Muthén, B. O. (2010). Simple second order chi-square correction. Mplus Technical Appendix Retrieved from http://www.statmodel.com/download/WLSMV_new_chi21.pdf
2. Babakus, E., Ferguson, C. E. J., & Jöreskog, K. G. (1987). The sensitivity of confirmatory maximum likelihood factor analysis to violations of measurement scale and distributional assumptions. Journal of Marketing Research, 24, 222-228. doi:10.2307/3151512
3. Beauducel, A., & Herzberg, P. Y. (2006). On the performance of maximum likelihood versus means and variance adjusted weighted least squares estimation in CFA. Structural Equation Modeling, 13, 186-203. doi: 10.1207/s15328007sem1302_2
4. Bentler, P. M. (2008). EQS structural equation modeling software Encino, CA : Multivariate Software.
5. Bradley, J. V. (1978). Robustness? British Journal of Mathematical and Statistical Psychology, 31, 144-152. doi:10.1111/j.2044-8317.1978.tb00581.x
6. Chen, F., Bollen, K., Paxton, P., Curran, P. J., & Kirby, J. (2001). Improper solutions in structural equation models: Causes, consequences, and strategies. Sociological Methods and Research, 29, 468-508. doi: 10.1177/0049124101029004003
7. Christoffersson, A. (1975). Factor analysis of dichotomized variables. Psychometrika, 40, 5-32. doi: 10.1007/BF02291477
8. DiStefano, C. (2002). The impact of categorization with confirmatory factor analysis. Structural Equation Modeling, 9, 327-346. doi: 10.1207/S15328007SEM0903_2
9. Dolan, C. V. (1994). Factor analysis of variables with 2, 3, 5 and 7 response categories: A comparison of categorical variable estimators using simulated data. British Journal of Mathematical and Statistical Psychology, 47, 309-326. doi: 10.1111/j.2044-8317.1994.tb01039.x
10. Flora, D., & Curran, P. (2004). An empirical evaluation of alternative methods of estimation for confirmatory factor analysis with ordinal data. Psychological Methods, 9, 466-491. doi: 10.1037/1082-989X.9.4.466
11. Forero, C. G., Maydeu-Olivares, A., & Gallardo-Pujol, D. (2009). Factor analysis with ordinal indicators: A Monte Carlo study comparing DWLS and ULS estimation. Structural Equation Modeling, 16, 625-641. doi: 10.1080/10705510903203573
12. Hoogland, J. J., & Boomsma, A. (1998). Robustness studies in covariance structure modeling: An overview and a meta-analysis. Sociological Methods Research, 26, 329-367. doi:10.1177/0049124198026003003
13. Jöreskog, K. G. (1994). On the estimation of polychoric correlations and their asymptotic covariance matrix. Psychometrika, 59, 381-390. doi: 10.1007/BF02296131
14. Lee, S.-Y., Poon, W.-Y., & Bentler, P. M. (1990). A three-stage estimation procedure for structural equation models with polytomous variables. Psychometrika, 55, 45-51. doi: 10.1007/BF02294742
15. Lee, S.-Y., Poon, W.-Y., & Bentler, P. M. (1995). A two-stage estimation of structural equation models with continuous and polytomous variables. British Journal of Mathematical and Statistical Psychology, 48, 339-358. doi: 10.1111/j.2044-8317.1995.tb01067.x
16. Lei, P.-W. (2009). Evaluating estimation methods for ordinal data in structural equation modeling. Quality and Quantity, 43, 495-507. doi: 10.1007/s11135-007-9133-z
17. Maydeu-Olivares, A. (2001). Limited information estimation and testing of Thurstonian models for paired comparison data under multiple judgment sampling. Psychometrika, 66, 209-227. doi: 10.1007/BF02294836
18. n contingency tables: A unified framework. Journal of the American Statistical Association, 100, 1009-1020. doi: 10.1198/016214504000002069
19. Muthén, B. (1978). Contributions to factor analysis of dichotomous variables. Psychometrika, 43, 551-560. doi: 10.1007/BF02293813
20. Muthén, B. (1984). A general structural equation model with dichotomous, ordered categorical, and continuous latent variable indicators. Psychometrika, 49, 115-132. doi: 10.1007/BF02294210
21. Muthén, B. O. (1993). Goodness of fit with categorical and other nonnormal variables. In K. A. Bollen & J. S. Long (Eds.), Testing structural equation models (pp. 205-234). Newbury Park, CA : Sage.
22. Muthén, B. O., du Toit, S. H. C., & Spisic, D. (1997). Robust inference using weighted least squares and quadratic estimating equations in latent variable modeling with categorical and continuous outcomes Unpublished manuscript.
23. Muthén, L. K., & Muthén, B. O. (2010). Mplus user's guide (6th ed.). Los Angeles : Muthén & Muthén.
24. Nussbeck, F. W., Eid, M., & Lischetzke, T. (2006). Analysing multitrait-multimethod data with structural equation models for ordinal variables applying the WLSMV estimator: What sample size is needed for valid results? British Journal of Mathematical and Statistical Psychology, 59, 195-213. doi: 10.1348/000711005X67490
25. Olsson, U. (1979). On the robustness of factor analysis against crude classification of the observations. Multivariate Behavioral Research, 14, 485-500. doi: 10.1207/s15327906mbr1404_7
26. Potthast, M. J. (1993). Confirmatory factor analysis of ordered categorical variables with large models. British Journal of Mathematical and Statistical Psychology, 46, 273-286. doi: 10.1111/j.2044-8317.1993.tb01016.x
27. Rhemtulla, M., Brosseau-Liard, P., & Savalei, V. May (2012). When can categorical variables be treated as continuous? A comparison of robust continuous and categorical SEM estimation methods under suboptimal conditions Manuscript submitted for publication.
28. Rigdon, E. E., & Ferguson, C. E. (1991). The performance of the polychoric correlation coefficient and selected fitting functions in confirmatory factor analysis with ordinal data. Journal of Marketing Research, 28, 491-497. doi: 10.2307/3172790
29. Savalei, V. (2010). Small sample statistics for incomplete nonnormal data: Extensions of complete data formulae and a Monte Carlo comparison. Structural Equation Modeling, 17, 245-268. doi: 10.1080/10705511003659375
30. Savalei, V., & Kolenikov, S. (2008). Constrained vs. unconstrained estimation in structural equation modeling. Psychological Methods, 13, 150-170. doi: 10.1037/1082-989X.13.2.150
31. Satorra, A., & Bentler, P. M. (1994). Corrections to test statistics and standard errors in covariance structure analysis. In A. von Eye & C. C. Clogg (Eds.), Latent variable analysis: Applications to developmental research (pp. 399-419). Thousand Oaks, CA : Sage.
32. Yang-Wallentin, F., Jöreskog, K., & Luo, H. (2010). Confirmatory factor analysis of ordinal variables with misspecified models. Structural Equation Modeling, 17, 392-423. doi: 10.1080/10705511.2010.489003
33. Yuan, K.-H., & Bentler, P. M. (1998). Normal theory based test statistics in structural equation modelling. British Journal of Mathematical and Statistical Psychology, 51, 289-309. doi: 10.1111/j.2044-8317.1998.tb00682.x
34. Yuan, K.-H., & Hayashi, K. (2003). Bootstrap approach to inference and power analysis based on three test statistics for covariance structure models. British Journal of Mathematical and Statistical Psychology, 56, 93-110. doi: 10.1348/000711003321645368