varmx {fda}

Rotate a Matrix of Component Loadings using the VARIMAX Criterion

Description

The matrix being rotated contains the values of the component functional data objects computed in either a principal components analysis or a canonical correlation analysis. The values are computed over a fine mesh of argument values.

Usage

varmx(amat, normalize=FALSE)

Arguments

amat

the matrix to be rotated. The number of rows is equal to the number of argument values nx used in a fine mesh. The number of columns is the number of components to be rotated.

normalize

either TRUE or FALSE. If TRUE, the columns of amat are normalized prior to computing the rotation matrix. However, this is seldom needed for functional data.

Details

The VARIMAX criterion is the variance of the squared component values. As this criterion is maximized with respect to a rotation of the space spanned by the columns of the matrix, the squared loadings tend more and more to be either near 0 or near 1, and this tends to help with the process of labelling or interpreting the rotated matrix.

Value

a square rotation matrix of order equal to the number of components that are rotated. A rotation matrix $T$ has that property that $T'T = TT' = I$.

References

Ramsay, James O., Hooker, Giles, and Graves, Spencer (2009), Functional data analysis with R and Matlab, Springer, New York.

Ramsay, James O., and Silverman, Bernard W. (2005), Functional Data Analysis, 2nd ed., Springer, New York.

Ramsay, James O., and Silverman, Bernard W. (2002), Applied Functional Data Analysis, Springer, New York.

See Also

varmx.pca.fd, varmx.cca.fd