Redundancy analysis
rda performs redundancy analysis and stores extensive output
in a list object.
rda(X, Y, scaling = 1)
X |
a matrix of x variables |
Y |
a matrix of y variables |
scaling |
scaling used for x and y variables. 0: x and y only centered. 1: x and y standardized |
Results are computed by doing a principal component analyis of the fitted values of the regression of y on x.
Plotting the first two columns of Gxs and Gyp, or of Gxp and Gys provides a biplots of the matrix of regression coefficients.
Plotting the first two columns of Fs and Gp or of Fp and Gs provides a biplot of the matrix of fitted values.
Returns a list with the following results
Yh |
fitted values of the regression of y on x |
B |
regression coefficients of the regresson of y on x |
decom |
variance decomposition/goodness of fit of the fitted values AND of the regression coefficients |
Fs |
biplot markers of the rows of Yh (standard coordinates) |
Fp |
biplot markers of the rows of Yh (principal coordinates) |
Gys |
biplot markers for the y variables (standard coordinates) |
Gyp |
biplot markers for the y variables (principal coordinates) |
Gxs |
biplot markers for the x variables (standard coordinates) |
Gxp |
biplot markers for the x variables (principal coordinates) |
Jan Graffelman (jan.graffelman@upc.edu)
Van den Wollenberg, A.L. (1977) Redundancy Analysis, an alternative for canonical correlation analysis. Psychometrika 42(2): pp. 207-219.
Ter Braak, C. J. F. and Looman, C. W. N. (1994) Biplots in Reduced-Rank Regression. Biometrical Journal 36(8): pp. 983-1003.
X <- matrix(rnorm(75),ncol=3) Y <- matrix(rnorm(75),ncol=3) rda.results <- rda(X,Y)
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