Plot Shrinkage vs. Variance for Ridge Precision

This function uses the results of precision to plot a measure of shrinkage of the coefficients in ridge regression against a selected measure of their estimated sampling variance, so as to provide a direct visualization of the tradeoff between bias and precision.

Usage

# S3 method for class 'precision'
plot(
  x,
  xvar = "norm.beta",
  yvar = c("det", "trace", "max.eig"),
  labels = c("lambda", "df"),
  label.cex = 1.25,
  label.prefix,
  criteria = NULL,
  pch = 16,
  cex = 1.5,
  col,
  main = NULL,
  xlab,
  ylab,
  ...
)

Arguments

x: A data frame of class "precision" resulting from precision called on a "ridge" object. Named x only to conform with the plot generic.
xvar: The character name of the column to be used for the horizontal axis. Typically, this is the normalized sum of squares of the coefficients ("norm.beta") used as a measure of shrinkage / bias.
yvar: The character name of the column to be used for the vertical axis. One of c("det", "trace", "max.eig"). See precision for definitions of these measures.
labels: The character name of the column to be used for point labels. One of c("lambda", "df").
label.cex: Character size for point labels.
label.prefix: Character or expression prefix for the point labels.
criteria: The vector of optimal shrinkage criteria from the ridge call to be added as points in the plot.
pch: Plotting character for points
cex: Character size for points
col: Point colors
main: Plot title
xlab: Label for horizontal axis
ylab: Label for vertical axis
...: Other arguments passed to plot.

Value

Returns nothing. Used for the side effect of plotting.

Author

Michael Friendly

Examples

lambda <- c(0, 0.001, 0.005, 0.01, 0.02, 0.04, 0.08)
lridge <- ridge(Employed ~ GNP + Unemployed + Armed.Forces + 
                  Population + Year + GNP.deflator, 
                data=longley, lambda=lambda)

criteria <- lridge$criteria |> print()
#>        kHKB         kLW        kGCV 
#> 0.004275357 0.032295308 0.005000000 

pridge <- precision(lridge) |> print()
#>       lambda       df       det      trace    max.eig norm.beta norm.diff
#> 0.000  0.000 6.000000 -12.92710 18.1189511 15.4191000 1.0000000 0.0000000
#> 0.001  0.001 5.829251 -13.29160 13.9320912 11.3430089 0.9178082 0.3960023
#> 0.005  0.005 5.415118 -14.41144  6.8209398  4.6064698 0.7406376 1.2760891
#> 0.010  0.010 5.135429 -15.41069  4.0422816  2.1806533 0.6365441 1.7831543
#> 0.020  0.020 4.818103 -16.82581  2.2180382  1.0254551 0.5282452 2.2620055
#> 0.040  0.040 4.477853 -18.69819  1.1647170  0.5807883 0.4232699 2.6793608
#> 0.080  0.080 4.127782 -21.05065  0.5873002  0.2599108 0.3372722 3.0266564

plot(pridge)
# also show optimal criteria
plot(pridge, criteria = criteria)


# use degrees of freedom as point labels 
plot(pridge, labels = "df")

plot(pridge, labels = "df", label.prefix="df:")

# show the trace measure
plot(pridge, yvar="trace")