# [R] random sampling with some limitive conditions?

Daniel Nordlund res90sx5 at verizon.net
Sat Jul 7 23:08:06 CEST 2007

```> -----Original Message-----
> From: r-help-bounces at stat.math.ethz.ch [mailto:r-help-bounces at stat.math.ethz.ch]
> On Behalf Of Zhang Jian
> Sent: Saturday, July 07, 2007 12:31 PM
> To: r-help
> Subject: [R] random sampling with some limitive conditions?
>
> I want to gain thousands of random sampling data by randomizing the
> presence-absence data. Meantime, one important limition is that the row and
> column sums must be fixed. For example, the data "tst" is following:
>    site1 site2 site3 site4 site5 site6 site7 site8 1 0 0 0 1 1 0 0 0 1 1 1 0
> 1 0 1 1 0 0 0 1 0 1 0 0 0 0 1 0 1 0 1 1 0 1 0 0 0 0 0 0 1 0 1 1 1 1 1 1 0 0
> 0 0 0 0 0 0 0 0 1 0 1 0 1
>
> sum(tst[1,]) = 3, sum(tst[,1])=4, and so on. When I randomize the data, the
> first row sums must equal to 3, and the first column sums must equal to 4.
> The rules need to be applied to each row and column.
> How to get the new random sampling data? I have no idea.
> Thanks.
>

You could reorder your table by stepping through your table a column at a time, and for each column randomly deciding to swap the current column with a column that has the same column total.  Repeat this process for each row, i.e. for each row, randomly choose a row with the same row total to swap with.

Here is some example code which is neither efficient nor general, but does demonstrate the basic idea.  You will need to decide if this approach meets you needs.

# I created a data file with your table (8x8) and read from it
sites
# get row and column totals
colsums <- apply(sites,2,sum)
rowsums <- apply(sites,1,sum)
# randomly swap columns
for(i in 1:8) {
if (runif(1) > .5) {
swapcol<-sample(which(colsums==colsums[i]),1)
temp<-sites[,swapcol]
sites[,swapcol]<-sites[,i]
sites[,i]<-temp
}
}
# randomly swap rows
for(i in 1:8) {
if (runif(1) > .5) {
swaprow<-sample(which(rowsums==rowsums[i]),1)
temp<-sites[swaprow,]
sites[swaprow,]<-sites[i,]
sites[i,]<-temp
}
}
sites