[R] monte carlo simulations in permanova in vegan package

[Sean Porter]

Thank you Jari,

It seems now that my question is morphing more into a statistical one, and
perhaps not appropriate for R-help list, so apologies. Yes we are talking
about the latest versions of the vegan and permute packages. 

When there are an insufficient number of permutations available due to low
sample sizes apparently an alternative is to use the result given in
Anderson & Robinson (2003) regarding the asymptotic permutation of the
numerator (or denominator) of the test statistic under permutation. And I
quote from Anderson et al. 2008 "It is demonstrated that each of the sums of
squares has, under permutation, an asymptotic distribution that is a linear
form in chi-square variables, where the coefficients are actually the
eigenvalues from a PCO of the resemblance matrix. Thus, chi-square variables
can be drawn randomly and independently, using Monte Carlo sampling, and
these can be combined with the eigenvalues to construct the asymptotic
permutation distribution for each of the numerator and denominator and,
thus,  for the entire pseudo-F statistic, in the event that too few actual
unique permutations exist."

Anderson, Gorley & Clarke. 2008. PERMANOVA+ for PRIMER: Guide to software
and statistical models.
Anderson & Robinson 2003. Generalised discriminant analysis based on
distances. Australian and New Zealand Journal of Statistics. 45: 301-318

I am sure you already know this! The above is what I am trying to do in the
vegan package though.. 

Apologies if I am missing something and if what you have said still applies
(that is not appropriate to exceed the possible number of permutations), I
am not a statistician..so any help/clarity would be welcome.. 


Regards, sean

         


-----Original Message-----
From: R-help [mailto:r-help-bounces at r-project.org] On Behalf Of Jari Oksanen
Sent: 29 October 2015 03:23 PM
To: r-help at stat.math.ethz.ch
Subject: Re: [R] monte carlo simulations in permanova in vegan package

Sean Porter <sporter <at> ori.org.za> writes:

> I am trying to run a PERMANOVA in the vegan package with an 
> appropriate number of permutations (see example below), ideally 9999.
> Obviously that number of permutations does not exists so I would like 
> to use Monte Carlo permutation tests to derive the probability value, 
> as is done in the commercial package PERMANOVA+ for PRIMER. How can I 
> adapt my code so that adonis will do so ? Many thanks, Sean
[...clip...]
> 
> > permanova <- adonis(species ~ time, data = time, permutations=999,
> method="bray")
> 
> 'nperm' > set of all permutations; Resetting 'nperm'.
> 
I assume we are talking about the latest version of vegan and permute
packages. In that case you really should switch to complete enumeration if
you request exceeds the number of distinct permutations. As people have told
you, you should be satisfied with that because there are no more distinct
permutations. Alternatively, you need more data.

If you mean by Monte Carlo that the same that you have a sampling with
return instead of permutation, or that the same observation can appear
several times and therefore some other unit is missing, then there are two
pieces of advice:

1. You should not do so.
2. If you want to do so, you can generate your resampling matrices by hand
and use that matrix as the argument of permutations=. See the documentations
(?adonis) which tells how to do so.

Cheers, Jari Oksanen

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