On a test of dimensionality in redundancy analysis

Psychometrika

Volumn 70, Issue 2, 2005, Pages 271-281

  Takane, Yoshio ^a   Hwang, Heungsun ^b  

^a MCGILL UNIVERSITY   (Canada)

^b HEC MONTRÉAL   (Canada)

Author keywords

Parallel analysis; PCA of instrumental variables; Permutation tests; Reduced rank regression

Indexed keywords

EID: 24344489534     PISSN: 00333123     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11336-003-1089-x     Document Type: Review

References (16)

1. Anderson, T.W. (1951). Estimating linear restrictions on regression coefficients for multivariate normal distributions. Annals of Mathematical Statistics, 22, 327-351.
2. Bartlett, M.S. (1951). The goodness of fit of a single hypothetical discriminant function in the case of several groups. Annals of Eugenics, 16, 199-214.
3. ter Braak, C.J.F., & Šmilauer, P. (1998). CANOCO Reference Manual and User's Guide to Canoco for Windows: Software for Canonical Community Ordination (version 4). Ithaka, N. Y.: Microcomputer Power.
4. Horn, J.L. (1965). A rationale and the test of the number of factors in factor analysis. Psychometrika, 30, 179-185.
5. Lambert, Z.V., Wildt, A.R., & Durand, R.M. (1988). Redundancy analysis: An alternative to canonical correlation and multivariate multiple regression in exploring interset association. Psychological Bulletin, 104, 282-289.
6. 2. Quarterly Journal of Mathematics, 14, 220-224.
7. Lazraq, A., & Cléroux, R. (1988). Un algorithme pas à pas de sélection de variables en régression linéaire multivariée [A stepwise variable selection algorithm in multivariate linear regression]. Statistique et Analyse des donnes, 13, 39-58.
8. Lazraq, A., & Cléroux, R. (2002). Testing the significance of the successive components in redundancy analysis. Psychometrika, 67, 411-419.
9. Legendre, P., & Legendre, L. (1998). Numerical Ecology. Second English edition. Oxford: Elsevier.
10. Legendre, P., & ter Braak, C.J.F. (in preparation). Partial canonical analysis, variation partitioning, and tests of significance of eigenvalues in redundancy analysis.
11. Rao, C.R. (1964). The use and interpretation of principal component analysis in applied research. Sankhya, A, 26, 329-358.
12. Reinsel, G.C., & Velu, R.P. (1998). Multivariate Reduced-rank Regression. New York: Springer.
13. Takane, Y., & Hwang, H. (2002). Generalized constrained canonical correlation analysis. Multivariate Behavioral Research, 37, 163-195.
14. Takane, Y., van der Heijden, P.G.M., & Browne, M.W. (2003). On likelihood ratio tests for dimensionality selection. In T. Higuchi, Y. Iba, M. Ishiguro. (Eds.), Proceedings of Science of Modeling: The 30th Anniversary Meeting of the Information Criterion (AIC), (pp. 348-349).
15. van den Wollenberg, A.L. (1977). Redundancy analysis: An alternative for canonical correlation analysis. Psychometrika, 42, 207-219.
16. Wilks, S.S. (1938). The large-sample distriution of the likelihood ratio for testing composite hypotheses. Annals of Mathematical Statistics, 9, 60-62.