On nonequivalence of several procedures of structural equation modeling

Psychometrika

Volumn 70, Issue 4, 2005, Pages 791-798

  Yuan, K E Hai ^a   Chan, Wai ^b  

^a UNIVERSITY OF NOTRE DAME   (United States)

^b CHINESE UNIVERSITY OF HONG KONG   (Hong Kong)

Author keywords

Generalized least squares; Incorrect model; Incremental fit index; Maximum likelihood; Noncentrality parameter

Indexed keywords

EID: 33646391227     PISSN: 00333123     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11336-001-0930-9     Document Type: Article

References (32)

1. Anderson, T.W. (1973). Asymptotically efficient estimation of covariance matrices with linear structure. Annals of Statistics, 1, 135-141.
2. Bentler, P.M. (1990). Comparative fit indexes in structural models. Psychological Bulletin, 107, 238-246.
3. Bentler, P.M. (1995). EQS structural equations program manual. Encino, CA: Multivariate Software.
4. Bentler, P.M., & Dijkstra, T.K. (1985). Efficient estimation via linearization in structural models. In P.R. Krishnaiah (Ed.), Multivariate analysis VI (pp. 9-42). Amsterdam: North-Holland.
5. Bishop, Y.M.M., Fienberg, S.E., & Holland, P.W. (1975). Discrete multivariate analysis: Theory and practice. Cambridge, MA: MIT Press.
6. Browne, M.W. (1974). Generalized least-squares estimators in the analysis of covariance structures. South African Statistical Journal, 8, 1-24.
7. Browne, M. W. (1984). Asymptotic distribution-free methods for the analysis of covariance structures. British Journal of Mathematical and Statistical Psychology, 37, 62-83.
8. Holzinger, K.J., & Swineford, F. (1939). A study in factor analysis: The stability of a bi-factor solution. University of Chicago: Supplementary Educational Monographs, No. 48.
9. Hu, L.T., & Bentler, P.M. (1998). Fit indices in covariance structure modeling: Sensitivity to underparameterized model misspecification. Psychological Methods, 3, 424-4-53.
10. Hu, L.T., & Bentler, P.M. (1999). Cutoff criteria for fit indexes in covariance structure analysis: Conventional criteria versus new alternatives. Structural Equation Modeling, 6, 1-55.
11. Jöreskog, K.G. (1969). A general approach to confirmatory maximum likelihood factor analysis. Psychometrika, 34, 183-202.
12. Jöreskog, K.G., & Goldberger, A.S. (1972). Factor analysis by generalized least squares. Psychometrika, 37, 243-260.
13. La Du, T.J., & Tanaka, J.S. (1989). The influence of sample size, estimation method, and model specification on goodness-of-fit assessments in structural equation models. Journal of Applied Psychology, 74, 625-636.
14. Lee, S.-Y., & Jennrich, R.I. (1979). A study of algorithms for covariance structure analysis with specific comparisons using factor analysis. Psychometrika, 44, 99-114.
15. Magnus, J.R., & Neudecker, H. (1999). Matrix differential calculus with applications in statistics and econometrics. New York: Wiley.
16. McDonald, R.P., & Ho, R.M. (2002). Principles and practice in reporting structural equation analyses. Psychological Methods, 7, 64-82.
17. McDonald, R.P., & Marsh, H.W. (1990). Choosing a multivariate model: Noncentrality and goodness of fit. Psychological Bulletin, 107, 247-255.
18. Pitman, E.J.G. (1948). Lecture notes on nonparumetric statistical inference. Columbia University.
19. Satorra, A. (1989). Alternative test criteria in covariance structure analysis: A unified approach. Psychometrika, 54, 131-151.
20. Satorra, A., & Saris, W.E. (1985). Power of the likelihood ratio test in covariance structure analysis. Psychometrika, 50, 83-90.
21. Satorra, A., Saris, W.E., & de Pijper W.M. (1991). A comparison of several approximations to the power function of the likelihood ratio test in covariance structure analysis. Statistica Neerlandica, 45, 173-185.
22. Shapiro, A. (1983). Asymptotic distribution theory in the analysis of covariance structures (A unified approach). South African Statistical Journal, 17, 33-81.
23. Shapiro, A. (1985). Asymptotic equivalence of minimum discrepancy function estimators to GLS estimators. South African Statistical Journal, 19, 73-81.
24. Steiger, J.H., Shapiro, A., & Browne, M.W. (1985). On the multivariate asymptotic distribution of sequential chi-square statistics. Psychometrika, 50, 253-264.
25. Stroud, T.W.F. (1972). Fixed alternatives and Wald's formulation of the noncentral asymptotic behavior of the likelihood ratio statistic. Annals of Mathematical Statistics, 43, 447-454.
26. Sugawara, H.M., & MacCallum, R.C. (1993). Effect of estimation method on incremental fit indexes for covariance structure models. Applied Psychological Measurement, 17, 365-377.
27. Swain, A.J. (1975). A class of factor analysis estimation procedures with common asymptotic sampling properties. Psychometrika, 40, 315-335.
28. Tanaka, J.S. (1987). "How big is big enough?": Sample size and goodness of fit in structural equation models with latent variables. Child Development. 58, 134-146.
29. Weng, L.-J., & Cheng, C.-P. (1997). Why might relative fit indices differ between estimators'? Structural Equation Modeling, 4, 121-128.
30. Yuan, K.-H., & Hayashi, H. (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.
31. Yuan, K.-H., & Hayashi, K. (2004). Standard errors with misspecified covariance structure models. Unpublished manuscript.
32. Yuan, K.-H., & Marshall, L. L. (2004). A new measure of misfit for covariance structure models. Behaviormetrika, 31, 67-90.