[Rd] Are r2dtable and C_r2dtable behaving correctly?
Martin Maechler
maechler at stat.math.ethz.ch
Fri Aug 25 10:30:49 CEST 2017
>>>>> Gustavo Fernandez Bayon <gbayon at gmail.com>
>>>>> on Thu, 24 Aug 2017 16:42:36 +0200 writes:
> Hello,
> While doing some enrichment tests using chisq.test() with simulated
> p-values, I noticed some strange behaviour. The computed p-value was
> extremely small, so I decided to dig a little deeper and debug
> chisq.test(). I noticed then that the simulated statistics returned by the
> following call
> tmp <- .Call(C_chisq_sim, sr, sc, B, E)
> were all the same, very small numbers. This, at first, seemed strange to
> me. So I decided to do some simulations myself, and started playing around
> with the r2dtable() function. Problem is, using my row and column
> marginals, r2dtable() always returns the same matrix. Let's provide a
> minimal example:
> rr <- c(209410, 276167)
> cc <- c(25000, 460577)
> ms <- r2dtable(3, rr, cc)
> I have tested this code in two machines and it always returned the same
> list of length three containing the same matrix three times. The repeated
> matrix is the following:
> [[1]]
> [,1] [,2]
> [1,] 10782 198628
> [2,] 14218 261949
> [[2]]
> [,1] [,2]
> [1,] 10782 198628
> [2,] 14218 261949
> [[3]]
> [,1] [,2]
> [1,] 10782 198628
> [2,] 14218 261949
Yes. You can also do
unique(r2dtable(100, rr, cc))
and see that the result is constant.
I'm pretty sure this is still due to some integer overflow,
in spite of the fact that I had spent quite some time to fix
such problem in Dec 2003, see the 14 years old bug PR#5701
https://bugs.r-project.org/bugzilla/show_bug.cgi?id=5701#c2
It has to be said that this is based on an algorithm published
in 1981, specifically - from help(r2dtable) -
Patefield, W. M. (1981) Algorithm AS159. An efficient method of
generating r x c tables with given row and column totals.
_Applied Statistics_ *30*, 91-97.
For those with JSTOR access (typically via your University),
available at http://www.jstor.org/stable/2346669
When I start reading it, indeed the algorithm seems start from the
expected value of a cell entry and then "explore from there"...
and I do wonder if there is not a flaw somewhere in the
algorithm:
I've now found that a bit more than a year ago, 'paljenczy' found on SO
https://stackoverflow.com/questions/37309276/r-r2dtable-contingency-tables-are-too-concentrated
that indeed the generated tables seem to be too much around the mean.
Basically his example:
https://stackoverflow.com/questions/37309276/r-r2dtable-contingency-tables-are-too-concentrated
> set.seed(1); system.time(tabs <- r2dtable(1e6, c(100, 100), c(100, 100))); A11 <- vapply(tabs, function(x) x[1, 1], numeric(1))
user system elapsed
0.218 0.025 0.244
> table(A11)
34 35 36 37 38 39 40 41 42 43
2 17 40 129 334 883 2026 4522 8766 15786
44 45 46 47 48 49 50 51 52 53
26850 42142 59535 78851 96217 107686 112438 108237 95761 78737
54 55 56 57 58 59 60 61 62 63
59732 41474 26939 16006 8827 4633 2050 865 340 116
64 65 66 67
38 13 7 1
>
For a 2x2 table, there's really only one degree of freedom,
hence the above characterizes the full distribution for that
case.
I would have expected to see all possible values in 0:100
instead of such a "normal like" distribution with carrier only
in [34, 67].
There are newer publications and maybe algorithms.
So maybe the algorithm is "flawed by design" for really large
total number of observations, rather than wrong
Seems interesting ...
Martin Maechler
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