[R-sig-eco] Mantel test with skew-symmetric matrices?

[Jari Oksanen]

On 1/10/09 20:36 PM, "Sarah Goslee" <sarah.goslee at gmail.com> wrote:

> I can only speak for the mantel() within ecodist, but I can tell you that it
> will not take full matrices - the upper triangle will be dropped. You could
> roll your own very easily, but it would be exceedingly slow, eg:
> 
> mat1 <- # some square skew-symmetric matrix
> mat2 <- # some other square skew-symmetric matrix
> 
> mantelr <- cor(as.vector(mat1), as.vector(mat2))
> nperm <- 100 # bigger for real problem, of course
> permresults <- numeric(nperm)
> permresults[1] <- mantelr
> 
> for(thisperm in 2:nperm) {
>    randsample <- sample(1:nrow(mat1))
>    permresults[thisperm] <- cor(as.vector(mat1[randsample,
> randsample]), as.vector(mat2))
> }
> and then use permresults to estimate your test statistic of interest.
> 
Sarah & Steve,

This was the design I had on my mind. However, I was not sure how
skew-symmetry actually was defined, and therefore I didn't know if free
permutation of rows and columns (even when done correctly like above) will
retain the skew-symmetry. The free permutation would be OK for non-symmetric
matrices, but what about skew-symmetric? (Little thinking and pen & paper
probably would give a quick answer, but I won't do that for a while).

Cheers, Jari

> I haven't thought at all about any statistical issues raised by use of full
> non-symmetric matrices - you're on your own there. It's certainly
> *possible*, and
> I don't see any immediate reason why it would be wrong, but haven't
> pondered the issue.
> 
> I see Jari replied as well while I was writing - as for vegan, the
> ecodist function would
> need to be heavily modified to do this. If I'm persuaded that there's
> enough interest,
> I could add it to the list.
> 
> Sarah
> 
> On Thu, Oct 1, 2009 at 1:20 PM, Steve Arnott <ArnottS at dnr.sc.gov> wrote:
>> Hello All,
> 
>> 1) Is it wrong to use skew-symmetric matrices - i.e. should I just forget
>> about the skew data and use absolute values to make all my matrices
>> symmetric? The original Mantel paper (1967, Cancer Research, 2: 209-220) does
>> talk about skew-symmetric matrices, but the published applications I've come
>> across only seem to use symmetric matrices.
>> 
>>  2) If it is ok to use skew-symmetric matrices, do the mantel() and
>> mantel.partial() functions in 'vegan' (or related functions in other
>> packages, such as 'ecodist') handle them correctly? I've found that it is
>> possible to process skew data and generate results using these functions, but
>> I'm uncertain from the documentation whether the results are meaningful (i.e.
>> is the coding designed to handle such cases appropriately?)