genridge (version 0.6-1)

pca.ridge: 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.

Usage

pca.ridge(x, ...)

Value

An object of class c("ridge", "pcaridge"), with the same components as the original ridge object.

References

Friendly, M. (2011). The Generalized Ridge Trace Plot: Visualizing Bias and Precision. In preparation.

See Also

ridge

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.ridge(lridge)
traceplot(plridge)
pairs(plridge)
# view in space of smallest singular values
plot(plridge, variables=5:6)