candisc {candisc}  R Documentation 
Canonical discriminant analysis
Description
candisc
performs a generalized canonical discriminant analysis for
one term in a multivariate linear model (i.e., an mlm
object),
computing canonical scores and vectors. It represents a transformation of
the original variables into a canonical space of maximal differences for the
term, controlling for other model terms.
Usage
candisc(mod, ...)
## S3 method for class 'mlm'
candisc(mod, term, type = "2", manova, ndim = rank, ...)
## S3 method for class 'candisc'
print(x, digits = max(getOption("digits")  2, 3), LRtests = TRUE, ...)
## S3 method for class 'candisc'
summary(
object,
means = TRUE,
scores = FALSE,
coef = c("std"),
ndim,
digits = max(getOption("digits")  2, 4),
...
)
## S3 method for class 'candisc'
coef(object, type = c("std", "raw", "structure"), ...)
## S3 method for class 'candisc'
plot(
x,
which = 1:2,
conf = 0.95,
col,
pch,
scale,
asp = 1,
var.col = "blue",
var.lwd = par("lwd"),
var.labels,
var.cex = 1,
var.pos,
rev.axes = c(FALSE, FALSE),
ellipse = FALSE,
ellipse.prob = 0.68,
fill.alpha = 0.1,
prefix = "Can",
suffix = TRUE,
titles.1d = c("Canonical scores", "Structure"),
points.1d = FALSE,
...
)
Arguments
mod 
An mlm object, such as computed by 
... 
arguments to be passed down. In particular, 
term 
the name of one term from 
type 
type of test for the model 
manova 
the 
ndim 
Number of dimensions to store in (or retrieve from, for the

digits 
significant digits to print. 
LRtests 
logical; should likelihood ratio tests for the canonical dimensions be printed? 
object , x 
A candisc object 
means 
Logical value used to determine if canonical means are printed 
scores 
Logical value used to determine if canonical scores are printed 
coef 
Type of coefficients printed by the summary method. Any one or
more of 
which 
A vector of one or two integers, selecting the canonical
dimension(s) to plot. If the canonical structure for a 
conf 
Confidence coefficient for the confidence circles around
canonical means plotted in the 
col 
A vector of the unique colors to be used for the levels of the
term in the 
pch 
A vector of the unique point symbols to be used for the levels of
the term in the 
scale 
Scale factor for the variable vectors in canonical space. If not specified, a scale factor is calculated to make the variable vectors approximately fill the plot space. 
asp 
Aspect ratio for the 
var.col 
Color used to plot variable vectors 
var.lwd 
Line width used to plot variable vectors 
var.labels 
Optional vector of variable labels to replace variable names in the plots 
var.cex 
Character expansion size for variable labels in the plots 
var.pos 
Position(s) of variable vector labels wrt. the end point. If not specified, the labels are outjustified left and right with respect to the end points. 
rev.axes 
Logical, a vector of 
ellipse 
Draw data ellipses for canonical scores? 
ellipse.prob 
Coverage probability for the data ellipses 
fill.alpha 
Transparency value for the color used to fill the
ellipses. Use 
prefix 
Prefix used to label the canonical dimensions plotted 
suffix 
Suffix for labels of canonical dimensions. If

titles.1d 
A character vector of length 2, containing titles for the panels used to plot the canonical scores and structure vectors, for the case in which there is only one canonical dimension. 
points.1d 
Logical value for 
Details
In typical usage, the term
should be a factor or interaction
corresponding to a multivariate test with 2 or more degrees of freedom for
the null hypothesis.
Canonical discriminant analysis is typically carried out in conjunction with
a oneway MANOVA design. It represents a linear transformation of the
response variables into a canonical space in which (a) each successive
canonical variate produces maximal separation among the groups (e.g.,
maximum univariate F statistics), and (b) all canonical variates are
mutually uncorrelated. For a oneway MANOVA with g groups and p responses,
there are dfh
= min( g1, p) such canonical dimensions, and tests,
initially stated by Bartlett (1938) allow one to determine the number of
significant canonical dimensions.
Computational details for the oneway case are described in Cooley & Lohnes (1971), and in the SAS/STAT User's Guide, "The CANDISC procedure: Computational Details," http://support.sas.com/documentation/cdl/en/statug/63962/HTML/default/viewer.htm#statug_candisc_sect012.htm.
A generalized canonical discriminant analysis extends this idea to a general
multivariate linear model. Analysis of each term in the mlm
produces
a rank df_h
H matrix sum of squares and crossproducts matrix that
is tested against the rank df_e
E matrix by the standard
multivariate tests (Wilks' Lambda, HotellingLawley trace, Pillai trace,
Roy's maximum root test). For any given term in the mlm
, the
generalized canonical discriminant analysis amounts to a standard
discriminant analysis based on the H matrix for that term in relation to the
fullmodel E matrix.
The plot method for candisc objects is typically a 2D plot, similar to a
biplot. It shows the canonical scores for the groups defined by the
term
as points and the canonical structure coefficients as vectors
from the origin.
If the canonical structure for a term
has ndim==1
, or
length(which)==1
, the 1D representation consists of a boxplot of
canonical scores and a vector diagram showing the magnitudes of the
structure coefficients.
Value
An object of class candisc
with the following components:
dfh 
hypothesis degrees of freedom for 
dfe 
error degrees of freedom for the 
rank 
number of nonzero eigenvalues of 
eigenvalues 
eigenvalues of 
canrsq 
squared canonical correlations 
pct 
A vector containing the percentages of the 
ndim 
Number of canonical dimensions stored in the 
means 
A data.frame containing the class means for the levels of the factor(s) in the term 
factors 
A data frame containing the levels of the factor(s) in the 
term 
name of the 
terms 
A character vector containing the names of the terms in the

coeffs.raw 
A matrix containing the raw canonical coefficients 
coeffs.std 
A matrix containing the standardized canonical coefficients 
structure 
A matrix containing the canonical structure
coefficients on 
scores 
A data frame containing the
predictors in the 
Methods (by class)

candisc(mlm)
:"mlm"
method.
Methods (by generic)

print(candisc)
:print()
method for"candisc"
objects. 
summary(candisc)
:summary()
method for"candisc"
objects. 
coef(candisc)
:coef()
method for"candisc"
objects. 
plot(candisc)
:"plot"
method.
Author(s)
Michael Friendly and John Fox
References
Bartlett, M. S. (1938). Further aspects of the theory of multiple regression. Proc. Cambridge Philosophical Society 34, 3334.
Cooley, W.W. & Lohnes, P.R. (1971). Multivariate Data Analysis, New York: Wiley.
Gittins, R. (1985). Canonical Analysis: A Review with Applications in Ecology, Berlin: Springer.
See Also
Examples
grass.mod < lm(cbind(N1,N9,N27,N81,N243) ~ Block + Species, data=Grass)
car::Anova(grass.mod, test="Wilks")
grass.can1 <candisc(grass.mod, term="Species")
plot(grass.can1)
# library(heplots)
heplot(grass.can1, scale=6, fill=TRUE)
# iris data
iris.mod < lm(cbind(Petal.Length, Sepal.Length, Petal.Width, Sepal.Width) ~ Species, data=iris)
iris.can < candisc(iris.mod, data=iris)
# assign colors and symbols corresponding to species
col < c("red", "brown", "green3")
pch < 1:3
plot(iris.can, col=col, pch=pch)
heplot(iris.can)
# 1dim plot
iris.can1 < candisc(iris.mod, data=iris, ndim=1)
plot(iris.can1)