| pca {genridge} | R Documentation |
Transform Ridge Estimates to PCA Space
Description
The function pca.ridge transforms a ridge object from
parameter space, where the estimated coefficients are \beta_k with
covariance matrices \Sigma_k, to the principal component space defined
by the right singular vectors, V, of the singular value decomposition
of the scaled predictor matrix, X.
In this space, the transformed coefficients are V \beta_k, with
covariance matrices
V \Sigma_k V^T
.
This transformation provides alternative views of ridge estimates in low-rank approximations. In particular, it allows one to see where the effects of collinearity typically reside — in the smallest PCA dimensions.
Usage
pca(x, ...)
Arguments
x |
A |
... |
Other arguments passed down. Not presently used in this implementation. |
Value
An object of class c("ridge", "pcaridge"), with the same
components as the original ridge object.
Author(s)
Michael Friendly
References
Friendly, M. (2013). The Generalized Ridge Trace Plot: Visualizing Bias and Precision. Journal of Computational and Graphical Statistics, 22(1), 50-68, doi:10.1080/10618600.2012.681237, https://www.datavis.ca/papers/genridge-jcgs.pdf
See Also
Examples
longley.y <- longley[, "Employed"]
longley.X <- data.matrix(longley[, c(2:6,1)])
lambda <- c(0, 0.005, 0.01, 0.02, 0.04, 0.08)
lridge <- ridge(longley.y, longley.X, lambda=lambda)
plridge <- pca(lridge)
traceplot(plridge)
pairs(plridge)
# view in space of smallest singular values
plot(plridge, variables=5:6)