Fitting structural equation models using estimating equations: A model segregation approach

British Journal of Mathematical and Statistical Psychology

Volumn 55, Issue 1, 2002, Pages 41-62

  Yuan, Ke Hai ^b   Chan, Wai ^a  

^a CHINESE UNIVERSITY OF HONG KONG   (Hong Kong)

^b UNIVERSITY OF NOTRE DAME   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ARTICLE; BEHAVIORAL SCIENCE; HUMAN; METHODOLOGY; PSYCHOLOGICAL MODEL;

BEHAVIORAL SCIENCES; HUMANS; MODELS, PSYCHOLOGICAL;

EID: 0036584029     PISSN: 00071102     EISSN: None     Source Type: Journal    
DOI: 10.1348/000711002159699     Document Type: Article

References (43)

1. Anderson, J. C., & Gerbing, D. W. (1984). The effects of sampling error on convergence, improper solutions and goodness-of-fit indices for maximum likelihood confirmatory factor analysis. Psychometrika, 49, 155-173.
2. Anderson, J. C., & Gerbing, D. W. (1988). Structural equation modeling in practice: A review and recommended two-step approach. Psychological Bulletin, 103, 411-423.
3. Bentler, P. M. (1994). A testing model for covariance structure analysis. In T. W. Anderson, K. T. Fang, & I Olkin (Eds.), Multivariate analysis and its applications (pp. 123-135). Hayward, CA: Institute of Mathematical Statistics.
4. Bentler, P. M. (1995). EQS structural equations program manual. Encino, CA: Multivariate Software.
5. Bentler, P. M., & Dijkstra, T. (1985). Efficient estimation via linearization in structural models. In P. R. Krishnaiah (Ed.), Multivariate analysis VI (pp. 9-42). Amsterdam: North-Holland.
6. Bollen, K. A. (1989). Structural equations with latent variables. New York: Wiley.
7. Box, G. E. P. (1954). Some theorems on quadratic forms applied in the study of analysis of variance problems: I. Effect of inequality of variance in the one-way classification. Annals of Mathematical Statistics, 25, 290-302.
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). Asymptotic distribution-free methods for the analysis of covariance structures. British Journal of Mathematical and Statistical Psychology, 37, 62-83.
10. Casella, G., & Berger, R. L. (1990). Statistical inference. Belmont, CA: Wadsworth.
11. Curran, P. S., 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.
12. Godambe, V. P. (1960). An optimal property of regular maximum likelihood estimation. Annals of Mathematical Statistics, 31, 1208-1212.
13. Godambe, V. P., & Kale, B. K. (1991). Estimating functions: An overview. In V. P. Godambe (Ed.), Estimating functions (pp. 3-20). Oxford: Oxford University Press.
14. Gong, G., & Samaniego, F. J. (1981). Pseudo maximum likelihood estimation: Theory and applications. Annals of Statistics, 9, 861-869.
15. Holzinger, K. J., & Swineford, F. (1939). A study in factor analysis: The stability of a bi-factor solution. University of Chicago: Supplementary Educational Monographs 48.
16. Hu, L. T., Bentler, P. M., & Kano, Y. (1992). Can test statistics in covariance structure analysis be trusted? Psychological Bulletin, 112, 351-362.
17. Jöreskog, K. G. (1967). Some contributions to maximum likelihood factor analysis. Psychometrika, 32, 443-482.
18. Jöreskog, K. G. (1969). A general approach to confirmatory maximum likelihood factor analysis. Psychometrika, 34, 183-202.
19. Jöreskog, K. G., & Sörbom, D. (1993). LISREL 8 user's reference guide. Chicago: Scientific Software International.
20. Kale, B. K. (1985). Theory of unbiased statistical estimation functions. Lecture notes, Department of Statistics, Iowa State University.
21. Kano, Y., Berkane, M., & Bentler, P. M. (1993). Statistical inference based on pseudo-maximum likelihood estimators in elliptical populations. Journal of the American Statistical Association, 88, 135-143.
22. Lawley, D. N., & Maxwell, A. E. (1971). Factor analysis as a statistical method (2nd ed.). New York: American Elsevier.
23. Liang, K. Y., and Zeger, S. L. (1995). Inference based on estimating functions in the presence of nuisance parameters, Statistical Science, 10, 158-173.
24. Magnus, J. R., & Neudecker, H. (1999). Matrix differential calculus with applications in statistics and econometrics. New York: Wiley.
25. Mardia, K. V. (1970). Measures of multivariate skewness and kurtosis with applications. Biometrika, 57, 519-530.
26. Mardia, K. V. (1974). Applications of some measures of multivariate skewness and kurtosis in testing normality and robustness studies. Sankhyā B, 36, 115-128.
27. Marshall, L. L. (1999). Effect of men's subtle and overt psychological abuse on low income women. Violence and Victims, 14, 69-88.
28. Martin, J. K., & McDonald, R. P. (1975). Bayesian estimation in unrestricted factor analysis: A treatment for Heywood cases. Psychometrika, 40, 505-517.
29. Parke, W. R. (1986). Pseudo maximum likelihood estimation: The asymptotic distribution. Annals of Statistics, 14, 355-357.
30. Pierce, D. A. (1982). The asymptotic effect of substituting estimators for parameters in certain types of statistics. Annals of Statistics, 10, 475-478.
31. Satorra, A. (1992). Asymptotic robust inferences in the analysis of mean and covariance structures. In P. V. Marsden (Ed.), Sociological methodology 1992 (pp. 249-278). Oxford: Basil Blackwell.
32. Satorra, A., & Bentler, P. M. (1988). Scaling corrections for chi-square statistics in covariance structure analysis. In American Statistical Association 1988 Proceedings of Business and Economics Sections (pp. 308-313). Alexandria, VA: American Statistical Association.
33. Satorra, A., & Bentler, P. M. (1994). Corrections to test statistics and standard errors in covariance structure analysis. In A. von Eye and C. C. Clogg (Eds.), Latent variables analysis: Applications for developmental research (pp. 399-419). Thousand Oaks, CA: Sage.
34. Satterthwaite, F. E. (1941). Synthesis of variance. Psychometrika, 6, 309-316.
35. Small, C., & McLeish, D. L. (1988). The theory and applications of statistical inference functions, Lecture Notes in Statistics 44. Berlin: Springer-Verlag.
36. Tyler, D. E. (1983). Robustness and efficiency properties of scatter matrices. Biometrika, 70, 411-420.
37. van Driel, O. P. (1978). On various causes of improper solutions of maximum likelihood factor analysis. Psychometrika, 43, 225-243.
38. Yuan, K.-H., & Bentler, P. M. (1997a). Mean and covariance structure analysis: Theoretical and practical improvements. Journal of the American Statistical Association, 92, 767-774.
39. Yuan, K.-H., & Bentler, P. M. (1997b). Improving parameter tests in covariance structure analysis. Computational Statistics & Data Analysis, 26, 177-198.
40. Yuan, K.-H., & Bentler, P. M. (1998a). Structural equation modeling with robust covariances. In A. F. Raftery (Ed.), Sociological methodology 1998 (pp. 363-396). Boston: Blackwell.
41. Yuan, K.-H., & Bentler, P. M. (1998b). Robust mean and covariance structure analysis. British Journal of Mathematical and Statistical Psychology, 51, 63-88.
42. Yuan, K.-H., & Bentler, P. M. (2000). Robust mean and covariance structure analysis through iteratively reweighted least squares. Psychometrika, 65, 43-58.
43. Yuan, K. H., & Jennrich, R. I. (2000). Estimating equations with nuisance parameters: Theory and applications. Annals of the Institute of Statistical Mathematics, 52, 343-350.