Sample all possible contingency tables both margin fixed

Michael is correct. I answered too quickly. This will correct the original suggestion:

M <- c(15, 5, 15, 5) # New example where M[2] and M[4] are smaller
M[1]+M[2] == M[3]+M[4]

[1] TRUE

upper <- min(M[c(1,3)])
lower <- 0
if (min(M) < upper) lower <- upper - min(M)
all.2x2s <- t(sapply(lower:upper, function(i) c(a=i, b=M[1] - i, c=M[3] - i,

+ d=M[4] - M[1] + i)))

all.2x2s

a b c d
[1,] 10 5 5 0
[2,] 11 4 4 1
[3,] 12 3 3 2
[4,] 13 2 2 3
[5,] 14 1 1 4
[6,] 15 0 0 5

David C

From: Michael Peng [mailto:michael.gang.peng at gmail.com] 
Sent: Tuesday, June 24, 2014 1:32 PM
To: David L Carlson
Cc: Gabor Grothendieck; Tahira Jamil; r-help at r-project.org
Subject: Re: [R] Sample all possible contingency tables both margin fixed

David gave a great solution. I think it is better to start from 0 to min(M) instead of from min(M[c(1,3)]) to avoid negative values in the table. If the minimum is in M[1] or M[3], a = 1:min(M). Otherwise, d=1:min(M). 
Best,
Gang

2014-06-24 13:18 GMT-05:00 David L Carlson <dcarlson at tamu.edu>:
Since a 2x2 table with fixed row and column margins has only one degree of freedom, it is pretty easy to enumerate them:

? ?A ? ?B
A ?a ? ?c ? ?M[3]
B ?b ? ?d ? ?M[4]
? ?M[1] M[2] ? N

Create a vector of the margins:
M <- c(a+b, c+d, a+c, b+d)

The number of possible tables is min(M[c(1, 3)])+1 since a cannot be larger than the first column margin or the first row margin. The +1 recognizes that a can be 0.

Given any vector M of marginal values, the 2x2 tables are as follows:

M <- c(8, 9, 9, 8) # For example
M[1]+M[2]==M[3]+M[4] # Check to make sure these are valid margins
TRUE
all.2x2s <- t(sapply(0:min(M[c(1,3)]), function(i) c(a=i, b=M[1] - i,
? ? ? ? ? ? c=M[3] - i, d=M[4] - M[1] + i)))
all.2x2s
? ? ? a b c d
?[1,] 0 8 9 0
?[2,] 1 7 8 1
?[3,] 2 6 7 2
?[4,] 3 5 6 3
?[5,] 4 4 5 4
?[6,] 5 3 4 5
?[7,] 6 2 3 6
?[8,] 7 1 2 7
?[9,] 8 0 1 8

-------------------------------------
David L Carlson
Department of Anthropology
Texas A&M University
College Station, TX 77840-4352

----Original Message-----
From: r-help-bounces at r-project.org [mailto:r-help-bounces at r-project.org] On Behalf Of Gabor Grothendieck
Sent: Tuesday, June 24, 2014 12:07 PM
To: Tahira Jamil
Cc: r-help at r-project.org
Subject: Re: [R] Sample all possible contingency tables both margin fixed

Hi,

I am interested in generating all possible contingency table (2 by 2) with fixed row margins and column margins. Can anyone help me.

If the reason you want this is to sample them then r2dtable can do
that directly.

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______________________________________________
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PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.