# [R] lda, collinear variables and CV

Christian Hennig ucakche at ucl.ac.uk
Thu Jul 26 15:17:30 CEST 2012

```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

```