Test of linear trend in eigenvalues of a covariance matrix with application to data analysis

British Journal of Mathematical and Statistical Psychology

Volumn 49, Issue 2, 1996, Pages 299-312

  Bentler, R M ^a   Yuan, Ke Hai ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0038895135     PISSN: 00071102     EISSN: None     Source Type: Journal    
DOI: 10.1111/j.2044-8317.1996.tb01090.x     Document Type: Article

References (30)

1. Anderson, T. W. (1963). Asymptotic theory for principal component analysis. Annals of Mathematical Statistics, 34, 122-148.
2. Anderson, T. W. (1984). An Introduction to Multivariate Statistical Analysis. New York: Wiley.
3. 2 approximations. Journal of the Royal Statistical Society, Series B, 16, 296-298.
4. Bentler, P. M. & Yuan, K.-H. (1993a). On the relative increase in eigenvalues with linear trend: Application to principal components analysis. Technical Report, University of California, Los Angeles.
5. Bentler, P. M. & Yuan, K.-H. (1993b). Tests for linear trend in the eigenvalues of the correlation matrix with application to data analysis. Technical Report, University of California, Los Angeles.
6. Box, G. E. P., Hunter, W. G., MacGregor, J. F., & Erjavac, J. (1973). Some problems associated with the analysis of multiresponse data. Technometrics, 15, 33-51.
7. Cattell, R. B. (1966). The scree test for the number of factors. Multivariate Behavioral Research, 1, 245-276.
8. Cattell, R. B. (1978). The Scientific Use of Factor Analysis in Behavioral and Life Science. New York: Plenum.
9. Cattell, R. B. & Jaspers, J. (1967). A general plasmode (No. 30-10-5-2) for factor analytic exercises and research. Multivariate Behavioral Research Monographs, No. 67-3.
10. Cattell, R. B. & Vogelmann, S. (1977). A comprehensive trial of the scree and KG criteria for determining the number of factors. Multivariate Behavioral Research, 12, 289-325.
11. Comrey, A. L. & Lee, H. B. (1992). A First Course in Factor Analysis. Hillsdale, NJ: Erlbaum.
12. Cordeiro, G. M. (1987). On the corrections to the likelihood ratio statistics. Biometrika, 74, 265-274.
13. Devlin, S. J., Gnanadesikan, R., & Kettering, J. R. (1981). Robust estimation of dispersion matrices and principal components. Journal of the American Statistical Association, 76, 354-362.
14. Gorsuch, R. L. (1983). Factor Analysis. Hillsdale, NJ: Erlbaum.
15. Harman, H. H. (1976). Modern Factor Analysis. Chicago: University of Chicago Press.
16. Holzinger, K. J. & Harman, H. H. (1941). Factor Analysis. Chicago: University of Chicago Press.
17. Holzinger, K. J. & Swineford, E (1939). A Study in Factor Analysis: The Stability of a Bi-Factor Solution. Supplementary Educational Monographs, 48. Chicago: University of Chicago, Department of Education.
18. Horn, J. L. & Engstrom, R. (1979). Cattell's scree test in relation to Bartlett's chi-square test and other observations on the number of factors problem. Multivariate Behavioral Research, 14, 283-300.
19. Hotelling, H. (1933). Analysis of a complex of statistical variables into principal components. Journal of Educational Psychology, 24, 417-441.
20. Jackson, J. E. (1991). A User's Guide to Principal Components. New York: Wiley.
21. James, A. T. (1969). Test of equality of the latent roots of the covariance matrix. In P. K. Krishnaiah (Ed.), Multivariate Analysis, vol. 2, pp. 205-218. New York: Academic Press.
22. Jöreskog, K. G. (1979). Analyzing psychological data by structural analysis of covariance matrices. In J. Magidson (Ed.), Advances in Factor Analysis and Structural Equation Models, pp. 45-100. Lanham, MD: University Press of America.
23. Kaiser, H. F. (1958). The varimax criterion for analytic rotation in factor analysis. Psychometrika, 23, 187-200.
24. Lawley, D. N. (1956). Test of significance for the latent roots of covariance and correlation matrices. Biometrika, 43, 128-136.
25. Lord, F. M. (1956). A study of speed factor in tests and academic grades. Psychometrika, 21, 31-50.
26. Muirhead, R. J. (1982). Aspects of Multivariate Statistical Theory. New York: Wiley.
27. Neuhaus, J. O. & Wrigley, C. (1954). The quartimax method: An analytical approach to orthogonal simple structure. British Journal of Statistical Psychology, 7, 81-91.
28. Wakaki, H., Eguchi, S., & Fujikoshi, Y. (1990). A class of tests for a general covariance structure. Journal of Multivariate Analysis, 32, 313-325.
29. Wernimont, G. (1967). Evaluating laboratory performance of spectrophotometers. Annals of Chemistry, 39, 554-562.
30. Yuan, K.-K. & Bentler, P. M. (1994). Test of linear trend in eigenvalues of A: covariance matrices with applications in common principal components analysis. Communications in Statistics - Theory and Method, 23, 3141-3156.