Canonical Discriminant HE plots

These functions plot ellipses (or ellipsoids in 3D) in canonical discriminant space representing the hypothesis and error sums-of-squares-and-products matrices for terms in a multivariate linear model. They provide a low-rank 2D (or 3D) view of the effects for that term in the space of maximum discrimination.

Usage

# S3 method for candisc
heplot(
  mod,
  which = 1:2,
  scale,
  asp = 1,
  var.col = "blue",
  var.lwd = par("lwd"),
  var.cex = par("cex"),
  var.pos,
  rev.axes = c(FALSE, FALSE),
  prefix = "Can",
  suffix = TRUE,
  terms = mod$term,
  ...
)

Arguments

mod: A candisc object for one term in a mlm
which: A numeric vector containing the indices of the canonical dimensions to plot.
scale: Scale factor for the variable vectors in canonical space. If not specified, the function calculates one to make the variable vectors approximately fill the plot window.
asp: Aspect ratio for the horizontal and vertical dimensions. The defaults, asp=1 for heplot.candisc and asp="iso" for heplot3d.candisc ensure equal units on all axes, so that angles and lengths of variable vectors are interpretable. As well, the standardized canonical scores are uncorrelated, so the Error ellipse (ellipsoid) should plot as a circle (sphere) in canonical space. For heplot3d.candisc, use asp=NULL to suppress this transformation to iso-scaled axes.
var.col: Color for variable vectors and labels
var.lwd: Line width for variable vectors
var.cex: Text size for variable vector labels
var.pos: Position(s) of variable vector labels wrt. the end point. If not specified, the labels are out-justified left and right with respect to the end points.
rev.axes: Logical, a vector of length(which). TRUE causes the orientation of the canonical scores and structure coefficients to be reversed along a given axis.
prefix: Prefix for labels of canonical dimensions.
suffix: Suffix for labels of canonical dimensions. If suffix=TRUE the percent of hypothesis (H) variance accounted for by each canonical dimension is added to the axis label.
terms: Terms from the original mlm whose H ellipses are to be plotted in canonical space. The default is the one term for which the canonical scores were computed. If terms=TRUE, all terms are plotted.
...: Arguments to be passed down to heplot or heplot3d

Value

heplot.candisc returns invisibly an object of class "heplot", with coordinates for the various hypothesis ellipses and the error ellipse, and the limits of the horizontal and vertical axes.

Similarly, heploted.candisc returns an object of class "heplot3d".

Details

The generalized canonical discriminant analysis for one term in a mlm is based on the eigenvalues, \(\lambda_i\), and eigenvectors, V, of the H and E matrices for that term. This produces uncorrelated canonical scores which give the maximum univariate F statistics. The canonical HE plot is then just the HE plot of the canonical scores for the given term.

For heplot3d.candisc, the default asp="iso" now gives a geometrically correct plot, but the third dimension, CAN3, is often small. Passing an expanded range in zlim to heplot3d usually helps.

References

Friendly, M. (2006). Data Ellipses, HE Plots and Reduced-Rank Displays for Multivariate Linear Models: SAS Software and Examples Journal of Statistical Software, 17(6), 1-42. https://www.jstatsoft.org/v17/i06/ doi:10.18637/jss.v017.i06

Friendly, M. (2007). HE plots for Multivariate General Linear Models. Journal of Computational and Graphical Statistics, 16(2) 421--444. http://datavis.ca/papers/jcgs-heplots.pdf, doi:10.1198/106186007X208407 .

Author

Michael Friendly and John Fox

Examples


## Pottery data, from car package
data(Pottery, package = "carData")
pottery.mod <- lm(cbind(Al, Fe, Mg, Ca, Na) ~ Site, data=Pottery)
pottery.can <-candisc(pottery.mod)

heplot(pottery.can, var.lwd=3)

#> Vector scale factor set to  14.83312 
if(requireNamespace("rgl")){
heplot3d(pottery.can, var.lwd=3, scale=10, zlim=c(-3,3), wire=FALSE)
}


# reduce example for CRAN checks time
# \donttest{
grass.mod <- lm(cbind(N1,N9,N27,N81,N243) ~ Block + Species, data=Grass)

grass.can1 <-candisc(grass.mod,term="Species")
grass.canL <-candiscList(grass.mod)

heplot(grass.can1, scale=6)

heplot(grass.can1, scale=6, terms=TRUE)

heplot(grass.canL, terms=TRUE, ask=FALSE)

#> Vector scale factor set to  4.772952 

#> Vector scale factor set to  7.150784 

heplot3d(grass.can1, wire=FALSE)
#> Vector scale factor set to  5 
# compare with non-iso scaling
rgl::aspect3d(x=1,y=1,z=1)
# or,
# heplot3d(grass.can1, asp=NULL)
# }

## Can't run this in example
# rgl::play3d(rgl::spin3d(axis = c(1, 0, 0), rpm = 5), duration=12)

# reduce example for CRAN checks time
# \donttest{
## FootHead data, from heplots package
library(heplots)
data(FootHead)

# use Helmert contrasts for group
contrasts(FootHead$group) <- contr.helmert

foot.mod <- lm(cbind(width, circum,front.back,eye.top,ear.top,jaw)~group, data=FootHead)
foot.can <- candisc(foot.mod)
heplot(foot.can, main="Candisc HE plot", 
 hypotheses=list("group.1"="group1","group.2"="group2"),
 col=c("red", "blue", "green3", "green3" ), var.col="red")

#> Vector scale factor set to  8.776984 
# }