Is the ML chi-square ever robust to nonnormality? A cautionary note with missing data

Structural Equation Modeling

Volumn 15, Issue 1, 2008, Pages 1-22

  Savalei, Victoria ^a  

^a UNIVERSITY OF BRITISH COLUMBIA   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

ASYMPTOTIC DISTRIBUTIONS; CONFIRMATORY FACTOR ANALYSIS; EXOGENOUS VARIABLES; MODEL TESTING; NON-NORMAL DATA; NON-NORMALITY; STRUCTURAL EQUATION MODELING; TESTING METHOD;

TESTING;

FACTOR ANALYSIS;

EID: 41149165338     PISSN: 10705511     EISSN: None     Source Type: Journal    
DOI: 10.1080/10705510701758091     Document Type: Article

References (48)

1. Allison, P. D. (1987). Estimation of linear models with, incomplete data. In C. C. Clogg (Ed.), Sociological methodology, 1987 (pp. 71-103). San Francisco: Jossey-Bass.
2. Amemiya, Y., & Anderson, T. W. (1990). Asymptotic chi-square tests for a large class of factor analysis models. The Annals of Statistics, 18, 1453-1463.
3. Arbuckle, J. L. (1996). Full information estimation in the presence of incomplete data. In G. A. Marcoulides & R. E. Schumacker (Eds.), Advanced structural equation modeling (pp. 243-277). Mahwah, NJ: Lawrence Erlbaum Associates, Inc.
4. Arminger, G., & Sobel, M. (1990). Pseudo-maximum likelihood estimation of mean and covariance structures with missing data. Journal of the American Statistical Association, 85, 195-203.
5. Bentler, P. M. (2007). EQS 6 structural equations program manual. Encino, CA: Multivariate Software.
6. Bentler, P. M., & Yuan, K.-H. (1999). Structural equation modeling with small samples: Test statistics. Multivariate Behavioral Research, 34, 181-197.
7. Bentler, P. M., & Weeks, D. G. (1980). Linear structural, equations with latent variables. Psychometrika, 45, 289-308.
8. Browne, M. W. (1974). Generalized least squares estimators in the analysis of covariance structures. South African Statistical Journal, 8, 1-24.
9. Browne, M. W. (1984). Asymptotically distribution free methods for the analysis of covariance structures. British Journal of Mathematical and Statistical Psychology, 37, 62-83.
10. Browne, M. W. (1987). Robustness of statistic inference in factor analysis and related models. Biometrika, 74, 375-384.
11. Browne, M. W. (1990). Asymptotic robustness of normal theory methods for the analysis of latent curves. In W. Fuller & P. Brown (Eds.). Statistical analysis of measurement error models and applications (pp. 211-225). Providence, RI: American Mathematical Society.
12. Browne, M. W., & Shapiro, A. (1988). Robustness of normal theory methods in the analysis of linear latent variate models. British Journal of Mathematical and Statistical Psychology, 41, 193-208.
13. Curran, P. J., West, S. G., & Finch, J. F. (1996). The robustness of test statistics to nonnormality and specification error in confirmatory factor analysis. Psychological Methods, 1, 16-29.
14. Enders, C. K. (2001a). The impact of nonnormality on full information maximum-likelihood estimation for structural equation models with missing data. Psychological Methods, 6, 352-370.
15. Enders, C. K. (2001b). A primer on maximum likelihood algorithms available for use with missing data. Structural Equation Modeling, 8, 128-141.
16. Enders, C. K., & Bandalos, D. L. (2001). The relative performance of full information maximum likelihood estimation for missing data in structural equation models. Structural Equation Modeling, 8, 430-457.
17. Fleishman, A. I. (1978). A method for simulating non-normal distributions. Psychometrika, 43, 521-532.
18. Gold, M. S., Bentler, P. M., & Kim, K. H. (2003). A comparison of maximum-likelihood and asymptotically distribution-free methods of treating incomplete nonnormal data. Structural Equation Modeling, 10, 48-82.
19. Henly, S. J. (1993). Robustness of some estimators for the analysis of covariance structures. British Journal of Mathematical and Statistical Psychology, 46, 313-338.
20. Hu, L., Bentler, P. M., & Kano, Y. (1992). Can test statistics in covariance structure analysis be trusted? Psychological Bulletin, 112, 351-362.
21. Jöreskog, K. G. (1977). Structural equation models in the social sciences: Specification, estimation, and testing. In P. R. Krishnaiah (Ed.), Applications of statistics (pp. 265-287). Amsterdam: North-Holland.
22. Kendall, M. G., & Stuart, A. (1977). The advanced theory of statistics. London: Griffin.
23. Kim, K. H., & Bentler, P. M. (2002). Tests of homogeneity of means and covariance matrices for multivariate incomplete data. Psychometrika, 67, 609-624.
24. Little, R. J. A., & Rubin, D. B. (2002). Statistical analysis with missing data. New York: Wiley.
25. Mardia, K. V. (1970). Measures of multivariate skewness and kurtosis with applications, Biometrika, 57, 519-530.
26. Magnus, J. R., & Neudecker, H. (1999). Matrix differential calculus with applications in statistics and econometrics (rev. ed.). Chichester, UK: Wiley.
27. Mooijaart, A. (1985). Factor analysis for nonnormal variables. Psychometrika, 50, 323-342.
28. Mooijaart, A., & Bentler, P. M. (1991). Robustness of normal theory test statistics in structural equation models. Statistica Neerlandica, 45, 159-171.
29. Muthen, B., Kaplan, D., & Hollis, M. (1987). On structural equation modeling with data that are not missing completely at random. Psychometrika, 52, 431-462.
30. Powell, D. A., & Schafer, W. D. (2001). The robustness of the likelihood ratio chi-square test for structural equation models: a meta-analysis. Journal of Educational and Behavioral Statistics, 26, 105-132.
31. Rubin, D. B. (1976). Inference and missing data (with discussion). Biometrika, 63, 581-592.
32. Satorra, A. (1989). Alternative test criteria in covariance structure analysis: A unified approach. Psychometrika, 54, 131-151.
33. Satorra, A. (2001). Goodness of fit testing of structural equation models with, multiple group data and nonnormality. In R. Cudeck, S. H. C. du Toit, & D. Sörbom (Eds.), Structural equation modeling: Present and future (pp. 231-258). Lincolnwood, IL: Scientific Software International.
34. Satorra, A. (2002). Asymptotic robustness in multiple group linear-latent variable models. Econometric Theory, 18, 297-312.
35. Satorra, A., & Bentler, P. M. (1990). Model conditions for asymptotic robustness in the analysis of linear relations. Computational Statistics and Data Analysis, 10, 235-249.
36. 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 variables analysis: Applications for developmental research (pp. 399-419). Thousand Oaks, CA: Sage.
37. Savalei, V. (2005). On asymptotic robustness of NT methods with missing data (UCLA Statistics Preprint 430). Los Angeles: University of California.
38. Savalei, V., & Bentler, P. M. (2005). A statistically justified pairwise ML method for incomplete nonnormal data: A comparison with direct ML and pairwise ADF. Structural Equation Modeling, 12, 183-214.
39. Seber, G. A. F., & Lee, A. J. (2003). Linear regression analysis. Hoboken, NJ: Wiley.
40. Shapiro, A. (1985). Asymptotic equivalence of minimum discrepancy function estimators to GLS estimators. South African Statistical Journal, 17, 33-81.
41. Shapiro, A. (1986). Asymptotic theory of overparameterized structural models. Journal of the American Statistical Association, 81, 142-149.
42. Shapiro, A. (1987). Robustness properties of the MDF analysis of moment structures. South African Statistical Journal, 21, 39-62.
43. Vale, S. G., & Maurelli, V. A. (1983). Simulating multivariate nonnormal distributions. Psychometrika, 48, 465-471.
44. Yuan, K.-H., & Bentler, P. M. (1997). Mean and covariance structure analysis: Theoretical and practical improvements. Journal of the American Statistical Association, 92, 161-114.
45. Yuan, K.-H., & Bentler, P. M. (1998). Normal theory based test statistics in structural equation modeling. British Journal of Mathematical and Statistical Psychology, 51, 289-309.
46. Yuan, K.-H., & Bentler, P. M. (1999a). F tests for mean and covariance structure analysis. Journal of Educational and Behavioral Statistics, 24, 225-243.
47. Yuan, K.-H., & Bentler, P. M. (1999b). On normal theory and associated test statistics in covariance structure analysis under two classes of nonnormal distributions. Statistica Sinica, 9, 831-853.
48. Yuan, K.-H., & Bentler, P. M. (2000). Three likelihood-based methods for mean and covariance structure analysis with nonnormal missing data. Sociological Methodology, 30, 165-200.