[R] monte carlo simulations in permanova in vegan package

[Sean Porter]

Dear colleagues,



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



> permanova <- adonis(species ~ time, data = time, permutations=99,
method="bray")

> permanova



Call:

adonis(formula = species ~ time, data = time, permutations = 99, method
= "bray")



Permutation: free

Number of permutations: 99



Terms added sequentially (first to last)



Df SumsOfSqs MeanSqs F.Model R2 Pr(>F)

time 1 0.070504 0.070504 123.65 0.96866 0.01 **

Residuals 4 0.002281 0.000570 0.03134

Total 5 0.072785 1.00000

---

Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1





> permanova <- adonis(species ~ time, data = time, permutations=999,
method="bray")

'nperm' > set of all permutations; Resetting 'nperm'.










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[stephen sefick]

The example code works, and reports 9999 permutations. Can you provide more
information?

data(dune)
data(dune.env)
adonis(dune ~ Management*A1, data=dune.env, permutations=9999)

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[Sean Porter]

Hi Stephen and others,

I am trying to run a one-way permanova where I have only 2 levels in the factor “time”, and each level contains only 3 replicates. So because I have such few observations (6 in total) and levels (2) there are not enough possible permutations to get a reasonable test (i.e. (2*3)!/ [2!(3!)^2]. That is why for example if I run the analysis with only 99 permutations it completes the task. However, if I set the number of permutations to anything larger it returns the message “'nperm' > set of all permutations; Resetting 'nperm'.” as the number of possible permutations exceeds the number set by the argument “permutations=”. In PERMANOVA + for PRIMER there is a way of dealing with this issue – by using Monte Carlo simulations to generate the p value with a reasonable number of permutations. Hopefully this clarifies my situation and aim?

I was therefore hoping there was a way of coding for the Monte-Carlo permutation procedure into adonis?

Thanks for your help!

[Cade, Brian]

Sean: There are only 20 possible combinations, 6!/(3! x 3!), so you just
need to enumerate them completely (no Monte Carlo approximation required).
I don't know if permanova() can do this but you can do it with the mrpp()
functions and argument (,exact=TRUE) in Blossom package for R.

Brian

Brian S. Cade, PhD

U. S. Geological Survey
Fort Collins Science Center
2150 Centre Ave., Bldg. C
Fort Collins, CO 80526-8818

email: ca...@usgs.gov <brian...@usgs.gov>
tel: 970 226-9326

[stephen sefick]

Look at the permute package. I believe this functionality is there.

Please excuse my brevity; this message was sent from my telephone.

[Jari Oksanen]

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

[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-...@r-project.org] On Behalf Of Jari Oksanen
Sent: 29 October 2015 03:23 PM
To: r-h...@stat.math.ethz.ch
Subject: Re: [R] monte carlo simulations in permanova in vegan package

[Sean Porter]