Contingency table and confidence intervals - r

Question

Let me describe my problem by a simplified example
I have a contingency table
datatable<-array(c(1,2,3,4,5,6,dim=c(3,2))
datatable<-cbind(datatable,rowSums(datatable))
datatable<-rbind(datatable,colSums(datatable))
here, m=3,n=2 This is a (m+1)x(n+1)=4x3 table. Now, i want a new mxn array, where the ij'th entrance is a confidence interval (a list of size 2 if you will) for the estimate datatable[i,j]. Below is a function that computes an interval for the estimate datatable[i,j] from the arguments a<-datatable[i,j] and b<-datatable[i,n+1]
CIfunction<-function(a,b) c(-1,1)+a*b
I hope it is not too messy, i couldn't think of an easier example.
How do i create such a table in a elegant way? In the real example, this is a function that should take arbitrary contingency tables and return the corresponding CI table.
I already found a way, using double loop over i resp. j, but it really smells like something that could be done in an elegant way using mapply/outer or thelike.

Answer 1

The code below involves some trickery because it relies on how R recycles vectors (under what circumstances does R recycle?). array and matrix objects are just folded vectors (stored column-wise). It's not hard to come up with tricks like this once you understand the behavior
datatable <- array (1:6, dim=c(3,2))
datatable <-cbind(datatable,rowSums(datatable))
datatable <-rbind(datatable,colSums(datatable))
# last column recycled as necessary
lower <- -datatable[1:3, 1:2] * datatable[1:3, 3]
upper <- -lower
CIlist <- list(lower, upper)
I do suggest, however, that you store datatable without the row and column totals and compute them only on print.

Answer 2

Thank for your comments and answers. I had abit of trouble generalizing the (elegant) method provided by ilir to arbitrary CI functions. I ended up just doing the double loop mentioned above. My solution to the above problem would be something like
CItable<-function(datatable,CIfunction)
{
m<-dim(datatable)[1]-1
n<-dim(datatable)[2]-1
CItable<-array(NA,dim=c(m,2*n))
for(i in 1:m)
{
for(j in 1:n)
{
tempint<-CIfunction(datatable[i,j],datatable[i,n+1])
CItable[i,2*j]<-tempint[2]
CItable[i,2*j-1]<-tempint[1]
}
}
return(CItable)
}