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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. Not yet implemented.

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.

See also

ridge for details on ridge regression as implemented here. precision for definitions of the measures

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
#> 0.000  0.000 6.000000 -12.92710 18.1189511 15.4191000 1.0000000
#> 0.001  0.001 5.829251 -13.29160 13.9320912 11.3430089 0.9178082
#> 0.005  0.005 5.415118 -14.41144  6.8209398  4.6064698 0.7406376
#> 0.010  0.010 5.135429 -15.41069  4.0422816  2.1806533 0.6365441
#> 0.020  0.020 4.818103 -16.82581  2.2180382  1.0254551 0.5282452
#> 0.040  0.040 4.477853 -18.69819  1.1647170  0.5807883 0.4232699
#> 0.080  0.080 4.127782 -21.05065  0.5873002  0.2599108 0.3372722

plot(pridge)

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

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

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