I'm trying to write a formula method for canonical correlation analysis,
that could be called similarly to lm() for
a multivariate response:
cancor(cbind(y1,y2,y3) ~ x1+x2+x3+x4, data=, ...)
or perhaps more naturally,
cancor(cbind(y1,y2,y3) ~ cbind(x1,x2,x3,x4), data=, ...)
I've adapted the code from lm() to my case, but in this situation, it
doesn't make sense to
include an intercept, since X & Y are mean centered by default in the
computation.
In the code below, I can't see where the intercept gets included in the
model matrix and therefore
how to suppress it. There is a test case at the end, showing that the
method fails when called
normally, but works if I explicitly use -1 in the formula. I could hack
the result of model.matrix(),
but maybe there's an easier way?
cancor <- function(x, ...) {
UseMethod("cancor", x)
}
cancor.default <- candisc:::cancor
# TODO: make cancisc::cancor() use x, y, not X, Y
cancor.formula <- function(formula, data, subset, weights,
na.action,
method = "qr",
model = TRUE,
x = FALSE, y = FALSE, qr = TRUE,
contrasts = NULL, ...) {
cl <- match.call()
mf <- match.call(expand.dots = FALSE)
m <- match(c("formula", "data", "subset", "weights", "na.action"),
names(mf), 0L)
mf <- mf[c(1L, m)]
mf[[1L]] <- as.name("model.frame")
mf <- eval(mf, parent.frame())
mt <- attr(mf, "terms")
y <- model.response(mf, "numeric")
w <- as.vector(model.weights(mf))
if (!is.null(w) && !is.numeric(w))
stop("'weights' must be a numeric vector")
x <- model.matrix(mt, mf, contrasts)
# fixup to remove intercept???
z <- if (is.null(w))
cancor.default(x, y, ...)
else stop("weights are not yet implemented") # lm.wfit(x, y, w, ...)
z$call <- cl
z$terms <- mt
z
}
TESTME <- FALSE
if (TESTME) {
# need to get latest version, 0.6-1 from R-Forge
install.packages("candisc", repo="http://R-Forge.R-project.org";)
library(candisc)
data(Rohwer)
# this bombs: needs intercept removed
cc <- cancor.formula(cbind(SAT, PPVT, Raven) ~ n + s + ns + na + ss,
data=Rohwer)
## Error in chol.default(Rxx) :
## the leading minor of order 1 is not positive definite
#this works as is
cc <- cancor.formula(cbind(SAT, PPVT, Raven) ~ -1 + n + s + ns + na +
ss, data=Rohwer)
cc
## Canonical correlation analysis of:
## 5 X variables: n, s, ns, na, ss
## with 3 Y variables: SAT, PPVT, Raven
##
## CanR CanRSQ Eigen percent cum
## 1 0.6703 0.44934 0.81599 77.30 77.30
## 2 0.3837 0.14719 0.17260 16.35 93.65
## 3 0.2506 0.06282 0.06704 6.35 100.00
##
## Test of H0: The canonical correlations in the
## current row and all that follow are zero
##
...
}
--
Michael Friendly Email: friendly AT yorku DOT ca
Professor, Psychology Dept. & Chair, Quantitative Methods
York University Voice: 416 736-2100 x66249 Fax: 416 736-5814
4700 Keele Street Web: http://www.datavis.ca
Toronto, ONT M3J 1P3 CANADA
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