# [R] Retraction WAS: Re: Randomising matrices

Charles C. Berry cberry at tajo.ucsd.edu
Sat Apr 28 23:45:25 CEST 2007

```Sorry folks,

With some further checking, it turns out that this sampling
scheme does not conform to the relevant null.

:-(

Chuck

On Sat, 28 Apr 2007, Charles C. Berry wrote:

> Nick Cutler <s0455078 <at> sms.ed.ac.uk> writes:
>
>>
>> I would like to be able to randomise presence-absence (i.e. binary)
>> matrices whilst keeping both the row and column totals constant. Is
>> there a function in R that would allow me to do this?
>>
>> I'm working with vegetation presence-absence matrices based on field
>> observations. The matrices are formatted to have sites as rows and
>> species as columns. The presence of a species on a site is indicated
>> with a 1 (absence is obviously indicated with a 0).
>>
>> I would like to randomise the matrices many times in order to construct
>> null models. However, I cannot identify a function in R to do this, and
>> the programming looks tricky for someone of my limited skills.
>>
>> Can anybody help me out?
>
> Nick,
>
> For a 1001 x 1001 matrix, this method takes less than 2 seconds on my 2 year old
> Windows PC.
>
> ronetab( marg1, marg2 ) returns a table of 0's and 1's according to the marginal
> contraints.
>
> ck.ronetab( marg1, marg2 ) checks that all the constraints were honored.
>
>
> msample <- function(x,marg)
> {
>  ## Purpose: sample at most one each from each cell of a margin
>  ## ----------------------------------------------------------------------
>  ## Arguments: x - number to sample, marg - a vector of integers
>  ## ----------------------------------------------------------------------
>  ## Author: Charles C. Berry, Date: 28 Apr 2007, 08:17
>  ## GPL 2.0 or better
>
>  if (!(x<=sum(marg) && all(marg>=0))) browser()
>  wm <- which(marg!=0)
>  if (length(wm)==1) {
>    wm
>  } else {
>    sample( seq(along=marg), x, prob=marg )
>  }
> }
>
> ronetab <- function(m1,m2,debug=F)
> {
>  ## Purpose: sample from a table with fixed margins and {0,1} cell values
>  ## ----------------------------------------------------------------------
>  ## Arguments: m1, m2 - two margins
>  ## ----------------------------------------------------------------------
>  ## Author: Charles C. Berry, Date: 28 Apr 2007, 08:21
>  ## GPL 2.0 or better
>
>  stopifnot( sum(m1)==sum(m2)|| max(m1)>length(m2) || max(m2)>length(m1) )
>
>  i.list <- j.list <- list()
>  k <- 0
>  while( sum(m1)>0 ){
>    k <- k+1
>    if ( sum(m1!=0) > sum(m2!=0) ){
>      i <- which.max( m1)
>      j <- msample( m1[i], m2 )
>      i.list[[ k ]] <- rep( i, m1[i] )
>      j.list[[ k ]] <- j
>      m1[i] <- 0
>      m2[ j ] <- m2[ j ] - 1
>    } else {
>      j <- which.max( m2 )
>      i <- msample( m2[j], m1 )
>      i.list[[ k ]] <- i
>      j.list[[ k ]] <- rep( j, m2[j] )
>      m2[j] <- 0
>      m1[ i ] <- m1[ i ] - 1
>    }
>  }
>  res <- array(0, c(length(m1), length(m2) ) )
>  res[ cbind( unlist(i.list), unlist(j.list) ) ] <- 1
>  res
> }
>
> ck.ronetab <- function(m1,m2){
>  tab <- ronetab(m1,m2)
>  m1.ck <- all(m1==rowSums(tab))
>  m2.ck <- all(m2==colSums(tab))
>  cell.ck <- all( tab %in% 0:1 )
>  res <- m1.ck & m2.ck & cell.ck
>  if (!res) attr(res,"tab") <- tab
>  res
> }
>
> I'll warn you that I have not worked through what looks to be a tedious proof
> that this randomly samples matrices under the constraints. The heuristics seem
> right, and a few simulation spot checks look reasonable. If you do not want to
> trust it, you can still use it to generate a starting value for an MCMC run.
>
> HTH,
>
> Chuck
>
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