How do I create a random contingency table in R?

I would like to create random two-way contingency tables, given fixed row and column marginals. Supposing I have a table like this:

      A   C   G   T
  A  79   6  13  53
  C  16   7   6  17
  G   9   3   1   6
  T  58  28  18 114

with given row marginals:

  A   C   G   T 
151  46  19 218 

and column marginals:

  A   C   G   T 
162  44  38 190 

I'd like to create a random contingency table, for example:

   A  C  G  T
A 49 16 10 76
C 23  2  6 15
G 11  0  1  7
T 79 26 21 92

which preserves those marginals.

Since n is not too large in this case, I tried to approach this by "untabling" the marginal vectors, i.e. by converti开发者_如何学JAVAng the marginals into vectors of the form

A A A ...C C C ... G G G ... T T T 

and then permuting and tabling them.

My current method for "untabling" the marginals is highly unnatural and inefficient, and I was curious to know if there's a better way. Certain built-in functions must create random contingency tables, for instance chisq.test when simulate.p.value=TRUE. Is random contingency table construction also built in?

Thanks in advance for any suggestions.

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I'm not entirely sure what you mean by 'untabling', and since you didn't actually specify the method you're currently using, I can't be sure that this isn't what you're currently doing.

But given marginals of (162, 44, 38, 190) you can 'recreate' the vector just by doing this:

rep(c('A','C','G','T'),times = c(162, 44, 38, 190))

which you can then permute as needed.

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I'm sorry, but @joran's answer is not correct. His formula correctly simulates tables with the correct column totals, but the OP requested a simulation that respects both row and column totals. The solution to this was given in 1981 by W.M. Patefield. Algorithm AS159. An efficient method of generation r x c tables given row and column totals. Applied Statistics, 30. 91-97.

Patefield's algorithm is implemented in Base R function r2dtable().