On equivariance and invariance of standard errors in three exploratory factor models

Psychometrika

Volumn 65, Issue 1, 2000, Pages 121-133

  Yuan, Ke Hai ^a   Bentler, Peter M ^b  

^a UNIVERSITY OF NORTH TEXAS   (United States)

^b UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Augmented information matrix; Canonical rotation; Maximum likelihood; Scale equivariance; Standard error; Varimax rotation

Indexed keywords

EID: 0034147062     PISSN: 00333123     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF02294189     Document Type: Article

References (23)

1. Aitchison, J., & Silvey, S. D. (1958). Maximum likelihood estimation of parameters subject to restraints. Annals of Mathematical Statistics, 29, 813-828.
2. Archer, C. O., & Jennrich, R. I. (1973). Standard errors for orthogonally rotated factor loadings. Psychometrika, 38, 581-592.
3. Bentler, P. M. (1976). Multistructure statistical model applied to factor analysis. Multivariate Behavioral Research, 11, 3-25.
4. Browne, M. W. (1982). Covariance structures. In D. M. Hawkins (Ed.), Topics in applied multivariate analysis (pp. 72-141). Cambridge: Cambridge University Press.
5. Browne, M. W., & Arminger, G. (1995). Specification and estimation of mean and covariance structure models. In G. Arminger, C. C. Clogg, & M. E. Sobel (Eds.), Handbook of statistical modeling for the social and behavioral sciences (pp. 185-249). New York: Plenum.
6. Cudeck, R. (1989). Analysis of correlation matrices using covariance structure models. Psychological Bulletin, 105, 317-327.
7. Cudeck, R., & O'Dell, L. L. (1994). Applications of standard error estimates in unrestricted factor analysis: Significance tests for factor loadings and correlations. Psychological Bulletin, 115, 475-487.
8. Jennrich, R. I. (1973). Standard errors for obliquely rotated factor loadings. Psychometrika, 38, 593-604.
9. Jennrich, R. I. (1974). Simplified formulae for standard errors in maximum-likelihood factor analysis. British Journal of Mathematical and Statistical Psychology, 27, 122-131.
10. Jennrich, R. I., &Thayer, D. T. (1973). A note on Lawley's formulas for standard errors in maximum likelihood factor analysis. Psychometrika, 38, 571-580.
11. Kaiser, H. F. (1958). The varimax criterion for analytic rotation in factor analysis. Psychometrika, 23, 187-200.
12. Krane, W. R., & McDonald, R. P. (1978). Scale invariance and the factor analysis of correlation matrices. British Journal of Mathematical and Statistical Psychology, 31, 218-228.
13. Lawley, D. N., & Maxwell, A. E. (1971). Factor analysis as a statistical method (2nd ed.). New York: American Elsevier.
14. Lee, S. Y. & Bentler, P. M. (1980), Some asymptotic properties of constrained generalized least squares estimation in covariance structures. South African Statistical Journal, 14, 121-136.
15. Lehmann, E. L., & Casella, G. (1998). Theory of point estimation. New York: Springer-Verlag.
16. Magnus, J. R., & Neudecker, H. (1988). Matrix differential calculus with applications in statistics and econometrics. New York: Wiley.
17. Maxwell, A. E. (1959). Statistical methods in factor analysis. Psychological Bulletin, 56, 228-235.
18. McDonald, R. P., Parker, P. M., & Ishizuka, T. (1993). A scale-invariant treatment for recursive path models. Psychometrika, 58, 431-443.
19. Norusis, M. J. (1996). SPSS professional statistics, Chicago: SPSS.
20. Ogasawara, H. (1996). Standard errors for rotated factor loadings by normalized orthomax method. Japanese Journal of Behaviormetrics, 23, 122-129.
21. Ogasawara, H. (1998a). Standard errors of several indices for unrotated and rotated factors. Economic Review, 49, 21-69 (Otaru University of Commerce)
22. Ogasawara, H. (1998b). Standard errors for rotation matrices with an application to promax solution. British Journal of Mathematical and Statistical Psychology, 51, 163-178.
23. Swaminathan, H., & Algina, J. (1978). Scale freeness in factor analysis. Psychometrika, 43, 581-583.