heplot.cancor {candisc}  R Documentation 
Canonical Correlation HE plots
Description
Hypothesis  Error (HE) plots for canonical correlation analysis provide a new graphical method
for understanding the relations between two sets of variables, \mathbf{X}
and \mathbf{Y}
.
They are similar to HE plots for multivariate multiple regression (MMRA) problems,
except that ...
These functions plot ellipses (or ellipsoids in 3D) in canonical space representing the hypothesis and error sumsofsquaresandproducts matrices for terms in a multivariate linear model representing the result of a canonical correlation analysis. They provide a lowrank 2D (or 3D) view of the effects in the space of maximum canonical correlations, together with variable vectors representing the correlations of Y variables with the canonical dimensions.
For consistency with heplot.candisc
, the plots show effects in
the space of the canonical Y variables selected by which
.
The interpretation of variable vectors in these plots is different from that
of the terms
plotted as H "ellipses," which appear as degenerate
lines in the plot (because they correspond to 1 df tests of rank(H)=1).
In canonical space, the interpretation of the H ellipses for the
terms
is the same as in ordinary HE plots: a term is significant
iff its H ellipse projects outside the (orthogonalized) E ellipsoid
somewhere in the space of the Y canonical dimensions. The orientation of
each H ellipse with respect to the Y canonical dimensions indicates which
dimensions that X variate contributes to.
On the other hand, the variable vectors shown in these plots are intended
only to show the correlations of Y variables with the canonical dimensions.
Only their relative lengths and angles with respect to the Y canonical
dimensions have meaning. Relative lengths correspond to proportions of
variance accounted for in the Y canonical dimensions plotted; angles between
the variable vectors and the canonical axes correspond to the structure
correlations. The absolute lengths of these vectors are typically
manipulated by the scale
argument to provide better visual resolution
and labeling for the variables.
Setting the aspect ratio of these plots is important for the proper interpretation of angles between the variable vectors and the coordinate axes. However, this then makes it impossible to change the aspect ratio of the plot by resizing manually.
Usage
## S3 method for class 'cancor'
heplot(
mod,
which = 1:2,
scale,
asp = 1,
var.vectors = "Y",
var.col = c("blue", "darkgreen"),
var.lwd = par("lwd"),
var.cex = par("cex"),
var.xpd = TRUE,
prefix = "Ycan",
suffix = TRUE,
terms = TRUE,
...
)
Arguments
mod 
A 
which 
A numeric vector containing the indices of the Y 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 setting. Use 
var.vectors 
Which variable vectors to plot? A character vector
containing one or more of 
var.col 
Color(s) for variable vectors and labels, a vector of length 1 or 2. The first color is used for Y vectors and the second for X vectors, if these are plotted. 
var.lwd 
Line width for variable vectors 
var.cex 
Text size for variable vector labels 
var.xpd 
logical. Allow variable labels outside the plot box? Does not apply to 3D plots. 
prefix 
Prefix for labels of the Y canonical dimensions. 
suffix 
Suffix for labels of canonical dimensions. If

terms 
Terms for the X variables to be plotted in canonical space. The
default, 
... 
Other arguments passed to 
Value
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.
Author(s)
Michael Friendly
References
Gittins, R. (1985). Canonical Analysis: A Review with Applications in Ecology, Berlin: Springer.
Mardia, K. V., Kent, J. T. and Bibby, J. M. (1979). Multivariate Analysis. London: Academic Press.
See Also
cancor
for details on canonical correlation as
implemented here;
plot.cancor
for scatterplots of canonical
variable scores.
heplot.candisc
, heplot
,
linearHypothesis
Examples
data(Rohwer, package="heplots")
X < as.matrix(Rohwer[,6:10])
Y < as.matrix(Rohwer[,3:5])
cc < cancor(X, Y, set.names=c("PA", "Ability"))
# basic plot
heplot(cc)
# note relationship of joint hypothesis to individual ones
heplot(cc, scale=1.25, hypotheses=list("na+ns"=c("na", "ns")))
# more options
heplot(cc, hypotheses=list("All X"=colnames(X)),
fill=c(TRUE,FALSE), fill.alpha=0.2,
var.cex=1.5, var.col="red", var.lwd=3,
prefix="Y canonical dimension"
)
# 3D version
## Not run:
heplot3d(cc, var.lwd=3, var.col="red")
## End(Not run)