precision {genridge} | R Documentation |
Measures of Precision and Shrinkage for Ridge Regression
Description
Calculates measures of precision based on the size of the estimated covariance matrices of the parameters and shrinkage of the parameters in a ridge regression model. function does. ~~
Three measures of (inverse) precision based on the “size” of the
covariance matrix of the parameters are calculated. Let be the
covariance matrix for a given ridge constant, and let
be its eigenvalues
-
or
measures the linearized volume of the covariance ellipsoid and corresponds conceptually to Wilks' Lambda criterion
-
corresponds conceptually to Pillai's trace criterion
-
corresponds to Roy's largest root criterion.
Usage
precision(object, det.fun, normalize, ...)
Arguments
object |
An object of class |
det.fun |
Function to be applied to the determinants of the covariance
matrices, one of |
normalize |
If |
... |
Other arguments (currently unused) |
Value
A data.frame with the following columns
lambda |
The ridge constant |
df |
The equivalent effective degrees of freedom |
det |
The |
trace |
The trace of the covariance matrix |
max.eig |
Maximum eigen value of the covariance matrix |
norm.beta |
The root mean square of the estimated coefficients, possibly normalized |
Note
Models fit by lm
and ridge
use a different scaling for
the predictors, so the results of precision
for an lm
model
will not correspond to those for ridge
with ridge constant = 0.
Author(s)
Michael Friendly
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)
clr <- c("black", rainbow(length(lambda)-1, start=.6, end=.1))
coef(lridge)
(pdat <- precision(lridge))
# plot log |Var(b)| vs. length(beta)
with(pdat, {
plot(norm.beta, det, type="b",
cex.lab=1.25, pch=16, cex=1.5, col=clr, lwd=2,
xlab='shrinkage: ||b|| / max(||b||)',
ylab='variance: log |Var(b)|')
text(norm.beta, det, lambda, cex=1.25, pos=c(rep(2,length(lambda)-1),4))
text(min(norm.beta), max(det), "Variance vs. Shrinkage", cex=1.5, pos=4)
})
# plot trace[Var(b)] vs. length(beta)
with(pdat, {
plot(norm.beta, trace, type="b",
cex.lab=1.25, pch=16, cex=1.5, col=clr, lwd=2,
xlab='shrinkage: ||b|| / max(||b||)',
ylab='variance: trace [Var(b)]')
text(norm.beta, trace, lambda, cex=1.25, pos=c(2, rep(4,length(lambda)-1)))
# text(min(norm.beta), max(det), "Variance vs. Shrinkage", cex=1.5, pos=4)
})