R: Redundancy analysis

rda {calibrate} | R Documentation

## Redundancy analysis

### Description

`rda` performs redundancy analysis and stores extensive output in a list object.

### Usage

    rda(X, Y, scaling = 1)

### Arguments

`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

### Details

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.

### Value

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)

### Author(s)

Jan Graffelman (jan.graffelman@upc.edu)

### References

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.

### See Also

`princomp`,`canocor`,`biplot`

### Examples

    X <- matrix(rnorm(75),ncol=3)
    Y <- matrix(rnorm(75),ncol=3)
    rda.results <- rda(X,Y)

[Package calibrate version 1.7.2 Index]