3D Ridge Trace Plots

The 3D ridge trace plot displays 3D projections of the covariance ellipsoids for a set of ridge regression estimates indexed by a ridge tuning constant.

The centers of these ellipses show the bias induced for each parameter, and also how the change in the ridge estimate for one parameter is related to changes for other parameters.

The size and shapes of the covariance ellipsoids show directly the effect on precision of the estimates as a function of the ridge tuning constant.

plot3d.ridge and plot3d.pcaridge differ only in the defaults for the variables plotted.

Usage

plot3d(x, ...)

# S3 method for class 'pcaridge'
plot3d(x, variables = (p - 2):p, ...)

# S3 method for class 'ridge'
plot3d(
  x,
  variables = 1:3,
  radius = 1,
  which.lambda = 1:length(x$lambda),
  lwd = 1,
  lty = 1,
  xlim,
  ylim,
  zlim,
  xlab,
  ylab,
  zlab,
  col = c("black", "red", "darkgreen", "blue", "darkcyan", "magenta", "brown",
    "darkgray"),
  labels = lambda,
  ref = TRUE,
  ref.col = gray(0.7),
  segments = 40,
  shade = TRUE,
  shade.alpha = 0.1,
  wire = FALSE,
  aspect = 1,
  add = FALSE,
  ...
)

Arguments

x: A ridge object, as fit by ridge or a pcaridge object as transformed by pca.ridge
...: Other arguments passed down
variables: Predictors in the model to be displayed in the plot: an integer or character vector of length 3, giving the indices or names of the variables. Defaults to the first three predictors for ridge objects or the last three dimensions for pcaridge objects.
radius: Radius of the ellipse-generating circle for the covariance ellipsoids. The default, radius=1 gives a standard “unit” ellipsoid. Typically, radius<1 gives less cluttered displays.
which.lambda: A vector of indices used to select the values of lambda for which ellipsoids are plotted. The default is to plot ellipsoids for all values of lambda in the ridge object.
lwd, lty: Line width and line type for the covariance ellipsoids. Recycled as necessary.
xlim, ylim, zlim: X, Y, Z limits for the plot, each a vector of length 2. If missing, the range of the covariance ellipsoids is used.
xlab, ylab, zlab: Labels for the X, Y, Z variables in the plot. If missing, the names of the predictors given in variables is used.
col: A numeric or character vector giving the colors used to plot the covariance ellipsoids. Recycled as necessary.
labels: A numeric or character vector giving the labels to be drawn at the centers of the covariance ellipsoids.
ref: Logical: whether to draw horizontal and vertical reference lines at 0. This is not yet implemented.
ref.col: Color of reference lines.
segments: Number of line segments used in drawing each dimension of a covariance ellipsoid.
shade: a logical scalar or vector, indicating whether the ellipsoids should be rendered with shade3d. Recycled as necessary.
shade.alpha: a numeric value in the range [0,1], or a vector of such values, giving the alpha transparency for ellipsoids rendered with shade=TRUE.
wire: a logical scalar or vector, indicating whether the ellipsoids should be rendered with wire3d. Recycled as necessary.
aspect: a scalar or vector of length 3, or the character string "iso", indicating the ratios of the x, y, and z axes of the bounding box. The default, aspect=1 makes the bounding box display as a cube approximately filling the display. See aspect3d for details.
add: if TRUE, add to the current rgl plot; the default is FALSE.

Value

None. Used for its side-effect of plotting

Note

This is an initial implementation. The details and arguments are subject to change.

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

Author

Michael Friendly

Examples


lmod <- lm(Employed ~ GNP + Unemployed + Armed.Forces + Population + 
                      Year + GNP.deflator, data=longley)
longley.y <- longley[, "Employed"]
longley.X <- model.matrix(lmod)[,-1]

lambda <- c(0, 0.005, 0.01, 0.02, 0.04, 0.08)
lambdaf <- c("0", ".005", ".01", ".02", ".04", ".08")
lridge <- ridge(longley.y, longley.X, lambda=lambda)

# \donttest{
plot3d(lridge, var=c(1,4,5), radius=0.5)

# view in SVD/PCA space
plridge <- pca(lridge)
plot3d(plridge, radius=0.5)
# }