Examining identification issues in factor analysis

Structural Equation Modeling

Volumn 13, Issue 4, 2006, Pages 631-645

  Hayashi, Kentaro ^a   Marcoulides, George A ^b  

^a UNIVERSITY OF HAWAII   (United States)

^b CALIFORNIA STATE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EXPLORATORY FACTOR ANALYSIS; MATHEMATICAL COMPLEXITY;

MULTIVARIANT ANALYSIS;

FACTOR ANALYSIS;

EID: 33750300199     PISSN: 10705511     EISSN: None     Source Type: Journal    
DOI: 10.1207/s15328007sem1304_7     Document Type: Article

References (28)

1. Albert, A. A. (1944a). The matrices of factor analysis. Proceedings of the National Academy of Science, USA, 30, 90-95.
2. Albert, A. A. (1944b). The minimum rank of a correlation matrix. Proceedings of the National Academy of Science, USA, 30, 144-146.
3. Anderson, T. W., & Rubin, H. (1956). Statistical inference in factor analysis. In J. Neyman (Ed.), Proceedings of the Third Berkeley Symposium on Mathematical Statistics and Probability (Vol. 5, pp. 111-150). Berkeley: University of California.
4. Bekker, P. A., & de Leeuw, J. (1987). The rank of reduced dispersion matrices. Psychometrika, 52, 125-135.
5. Bekker, P. A., Merckens, A., & Wansbeek, T. J. (1994). Identification, equivalent models and computer algebra. Boston: Academic Press.
6. Bekker, P. A., & ten Berge, J. M. F. (1997). Generic global identification in factor analysis. Linear Algebra and Its Applications, 264, 255-263.
7. Bentler, P. M. (1995). EQS structural equations program manual. Encino, CA: Multivariate Software.
8. Bollen, K. A., & Jöreskog, K. G. (1985). Uniqueness does not imply identification: A note on confirmatory factor analysis. Sociological Methods and Research, 14, 155-163.
9. Fisher, F. M. (1966). The identification problem in econometrics. New York: McGraw-Hill.
10. Guttman, L. (1958). To what extent can communalities reduce rank? Psychometrika, 23, 297-308.
11. Ihara, M., & Kano, Y. (1986). A new estimator of the uniqueness in factor analysis. Psychometrika, 51, 563-566.
12. Kano, Y. (1997). Exploratory factor analysis with a common factor with two indicators. Behavior-metrika, 24, 129-145.
13. Lawley, D. N., & Maxwell, A. E. (1971). Factor analysis as a statistical method (2nd ed). London: Butterworth.
14. Ledermann, W. (1937). On the rank of reduced correlation matrices in multiple factor analysis. Psychometrika, 2, 85-93.
15. Magnus, J. R., & Neudecker, H. (1999). Matrix differential calculus with applications in statistics and econometrics (rev. ed.). New York: Wiley.
16. Marcoulides, G. A., & Hershberger, S. L. (1997). Multivariate analysis: A first course. Mahwah, NJ: Lawrence Erlbaum Associates, Inc.
17. Raykov, T., & Marcoulides, G. A. (1999). On desirability of parsimony in structural equation model selection. Structural Equation Modeling, 6, 292-301.
18. Sato, M. (1992). A study of identification problem and substitute use of principal component analysis in factor analysis. Hiroshima Mathematical Journal, 22, 479-524.
19. Sato, M. (2004). On the identification problem of the factor analysis model: A review and an application for an estimation of air pollution source profiles and amounts. In Factor analysis centennial symposium at Osaka (pp. 179-184).
20. Shapiro, A. (1985). Identifiability of factor analysis: Some results and open problems. Linear Algebra and Its Applications, 70, 1-7.
21. Shapiro, A. (1989). Erratum of "Identifiability of factor analysis: Some results and open problems." Linear Algebra and Its Applications, 125, 149.
22. Solow, D. (2002). How to read and do proofs: An introduction to mathematical thought processes (3rd ed.). New York: Wiley.
23. Spearman, C. E. (1904). General intelligence objectively determined and measured. American Journal of Psychology, 5, 201-293.
24. ten Berge, J. M. F. (2004). Factor analysis, reliability and unidimensionality. Factor analysis centennial symposium at Osaka (pp. 55-69).
25. Tumura, Y., & Sato, M. (1980). On the identification in factor analysis. TRU Mathematics, 16, 121-131.
26. van Driel, O. P. (1978). On various causes of improper solutions in maximum likelihood factor analysis. Psychometrika, 43, 225-243.
27. Williams, J. S. (1981). A note on the uniqueness of minimum rank solutions in factor analysis. Psychometrika, 46, 109-110.
28. Yanai, H., Shigemasu, K., Maekawa, S., & Ichikawa, M. (1990). Factor analysis: Its theory and methods. Tokyo, Japan: Asakura-shoten (in Japanese).