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Part and Bipartial Canonical Correlation Analysis

Published online by Cambridge University Press:  01 January 2025

Neil H. Timm  and
James E. Carlson
Neil H. Timm*
Affiliation:
University of Pittsburgh
James E. Carlson
Affiliation:
University of Pittsburgh
*
Requests for reprints should be sent to Nell H. Timm, School of Education, University of Pittsburgh, Pittsburgh, Pa 15260.
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Abstract

Extending the definitions of part and bipartial correlation to sets of variates, the notion of part and bipartial canonical correlation analysis are developed and illustrated.

Keywords

multivariate analysis
Type
Original Paper
Information
Psychometrika , Volume 41 , Issue 2 , June 1976 , pp. 159 - 176
Copyright
Copyright © 1976 The Psychometric Society

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References

Reference Note

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Bartlett, M. S. The goodness of fit of a single hypothetical discriminant function in the case of several groups. Annals of Eugenics, 1951, 16, 199–214.CrossRefGoogle ScholarPubMed
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Fisher, R. A. The frequency distribution of the values of the correlation coefficient in samples from an indefinitely large population. Biometrika, 1915, 10, 507–521.Google Scholar
Fisher, R. A. The distribution of the partial correlation coefficient. Metron, 1924, 3, 329–332.Google Scholar
Galton, F. Natural inheritance. London-Macmillan, 1889.Google Scholar
Heck, D. L. Charts of some upper percentage points of the distribution of the largest characteristic root. Annals of Mathematical Statistics, 1960, 31, 625–642.CrossRefGoogle Scholar
Hotelling, H. The most predictable criterion. Journal of Educational Psychology, 1935, 26, 139–142.CrossRefGoogle Scholar
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McNemar, Q. Psychological statistics, 4th Ed., New York: John Wiley, 1969.Google Scholar
Miller, J. K. In defense of the general canonical correlation index: Reply to Nicewander and Wood. Psychological Bulletin, 1975, 82, 207–209.CrossRefGoogle Scholar
Morrison, D. F. Multivariate statistical methods, 1967, New York: McGraw Hill.Google Scholar
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Pearson, K. Mathematical contributions to the theory of evolution III. Regression, heredity and panmixia. Philosophical Transactions of the Royal Society of London, Series A, 1886, 187, 253–318.Google Scholar
Pearson, K. Mathematical contributions to the theory of evolution V. On the reconstruction of the stature of prehistoric races. Philosophical Transactions of the Royal Society of London, Series A, 1898, 192, 169–244.Google Scholar
Rao, B. R. Partial canonical correlations. Trabajos de Estadistica y de Investigacion operativa, 1969, 20, 211–219.CrossRefGoogle Scholar
Rao, C. R. Advanced statistical methods in biometric research, 1952, New York: John Wiley.Google Scholar
Rao, C. R. Linear statistical inference and its applications, 2nd Ed., New York: John Wiley, 1973.CrossRefGoogle Scholar
Roy, S. N. On a heuristic method of test construction and its use in multivariate analysis. Annals of Mathematical Statistics, 1953, 24, 220–238.CrossRefGoogle Scholar
Roy, S. N. Some aspects of multivariate analysis, 1957, New York: John Wiley.Google Scholar
Stewart, D. K. and Love, W. A. A general canonical correlation index. Psychological Bulletin, 1968, 70, 160–163.CrossRefGoogle ScholarPubMed
Timm, N. H. Multivariate analysis with applications in education and psychology, 1975, Belmont: Brooks/Cole.Google Scholar
Williams, E. J. The analysis of association among many variables. Journal of the Royal Statistical Society, Series B, 1967, 29, 199–242.CrossRefGoogle Scholar
Yule, G. U. On the theory of correlation. Journal of the Royal Statistical Society, 1897, 60, 812–854.CrossRefGoogle Scholar
Yule, G. U. On the theory of correlation for any number of variables, treated by a new system of notation. Proceedings of the Royal Society of London, Series A, 1907, 79, 182–193.Google Scholar
Anderson, T. W. An introduction to multivariate statistical analysis, 1958, New York: John Wiley.Google Scholar
Bartlett, M. S. Further aspects of the theory of multiple regression. Proceedings of the Cambridge Philosophical Society, 1938, 34, 33–40.CrossRefGoogle Scholar
Bartlett, M. S. The goodness of fit of a single hypothetical discriminant function in the case of several groups. Annals of Eugenics, 1951, 16, 199–214.CrossRefGoogle ScholarPubMed
Ezekiel, M. Methods of correlation analysis, 2nd Ed., New York: John Wiley, 1941.Google Scholar
Fisher, R. A. The frequency distribution of the values of the correlation coefficient in samples from an indefinitely large population. Biometrika, 1915, 10, 507–521.Google Scholar
Fisher, R. A. The distribution of the partial correlation coefficient. Metron, 1924, 3, 329–332.Google Scholar
Galton, F. Natural inheritance. London-Macmillan, 1889.Google Scholar
Heck, D. L. Charts of some upper percentage points of the distribution of the largest characteristic root. Annals of Mathematical Statistics, 1960, 31, 625–642.CrossRefGoogle Scholar
Hotelling, H. The most predictable criterion. Journal of Educational Psychology, 1935, 26, 139–142.CrossRefGoogle Scholar
Hotelling, H. Relations between two sets of variates. Biometrika, 1936, 28, 321–377.CrossRefGoogle Scholar
McNemar, Q. Psychological statistics, 4th Ed., New York: John Wiley, 1969.Google Scholar
Miller, J. K. In defense of the general canonical correlation index: Reply to Nicewander and Wood. Psychological Bulletin, 1975, 82, 207–209.CrossRefGoogle Scholar
Morrison, D. F. Multivariate statistical methods, 1967, New York: McGraw Hill.Google Scholar
Olson, C. L. Comparative robustness of six tests in multivariate analysis of variance. Journal of the American Statistical Association, 1974, 69, 894–908.CrossRefGoogle Scholar
Pearson, K. Mathematical contributions to the theory of evolution III. Regression, heredity and panmixia. Philosophical Transactions of the Royal Society of London, Series A, 1886, 187, 253–318.Google Scholar
Pearson, K. Mathematical contributions to the theory of evolution V. On the reconstruction of the stature of prehistoric races. Philosophical Transactions of the Royal Society of London, Series A, 1898, 192, 169–244.Google Scholar
Rao, B. R. Partial canonical correlations. Trabajos de Estadistica y de Investigacion operativa, 1969, 20, 211–219.CrossRefGoogle Scholar
Rao, C. R. Advanced statistical methods in biometric research, 1952, New York: John Wiley.Google Scholar
Rao, C. R. Linear statistical inference and its applications, 2nd Ed., New York: John Wiley, 1973.CrossRefGoogle Scholar
Roy, S. N. On a heuristic method of test construction and its use in multivariate analysis. Annals of Mathematical Statistics, 1953, 24, 220–238.CrossRefGoogle Scholar
Roy, S. N. Some aspects of multivariate analysis, 1957, New York: John Wiley.Google Scholar
Stewart, D. K. and Love, W. A. A general canonical correlation index. Psychological Bulletin, 1968, 70, 160–163.CrossRefGoogle ScholarPubMed
Timm, N. H. Multivariate analysis with applications in education and psychology, 1975, Belmont: Brooks/Cole.Google Scholar
Williams, E. J. The analysis of association among many variables. Journal of the Royal Statistical Society, Series B, 1967, 29, 199–242.CrossRefGoogle Scholar
Yule, G. U. On the theory of correlation. Journal of the Royal Statistical Society, 1897, 60, 812–854.CrossRefGoogle Scholar
Yule, G. U. On the theory of correlation for any number of variables, treated by a new system of notation. Proceedings of the Royal Society of London, Series A, 1907, 79, 182–193.Google Scholar