Dear R-help list,
apparently lda from the MASS package can be used in situations with
collinear variables. It only produces a warning then but at least it
defines a classification rule and produces results.
However, I can't find on the help page how exactly it does this. I have a
suspicion (it may look at the hyperplane containing the class means,
using some kind of default/trivial within-group covariance matrix) but I'd
like to know in detail if possible.
I find particularly puzzling that it produces different
results whether I choose CV=TRUE or I run a manual LOO cross-validation.
Constructing an example, I realised that I'm puzzled about
CV=TRUE not only in the collinear case. The example is below. Actually it
also produces different (though rather similar) results for p=10 (no
longer collinear).
See here:
library(MASS)
set.seed(12345)
n <- 50
p <- 200 # or p<- 10
testdata <- matrix(ncol=p,nrow=n)
for (i in 1:p)
testdata[,i] <- rnorm(n)
class <- as.factor(c(rep(1,25),rep(2,25)))
lda1 <- lda(x=testdata,grouping=class,CV=TRUE)
table1 <- table(lda1$class,class)
y.lda <- rep(NA, n)
for(i in 1:n){
testset <- testdata[i,,drop=FALSE]
trainset <- testdata[-i,]
model.lda <- lda(x=trainset,grouping=class[-i])
y.lda[i] <- predict(model.lda, testset)$class
}
table2 <-table(y.lda, class)
> table1
class
1 2
1 14 16
2 11 9
> table2
class
y.lda 1 2
1 15 10
2 10 15
With p=10:> table1
class
1 2
1 10 11
2 15 14> table2
class
y.lda 1 2
1 10 12
2 15 13
Any explanation?
Best regards,
Christian
*** --- ***
Christian Hennig
University College London, Department of Statistical Science
Gower St., London WC1E 6BT, phone +44 207 679 1698
chrish at stats.ucl.ac.uk, www.homepages.ucl.ac.uk/~ucakche
