adonis

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Alan,

A few comments on your procedure. You have two non-standard things in your message: you try to do something that looks like post hoc tests, and you use non-standard contrasts. There is nothing post hoc in your post hoc tests. What you do is that you break your factor variable into separate contrasts. If do so, you should carefully read the adonis output which says

"Terms added sequentially (first to last)"

If your contrasts are correlated, like they are in the example you gave, the results for individual terms will depend on the order of terms. Usually people associate post hoc tests with multiple testing problem, but there is nothing about that in the example you gave. It is just simple testing of individual contrasts.

Second point is that you used non-standard contrasts. The species coefficients will depend on contrasts and therefore they change. There are easier way of doing the same. For instance, you seem to want to have sum contrasts, but with different baseline level. Check functions like model.matrix, contrasts, relevel, and as.data.frame. However, the magnitude of coefficient also depends on specific contrasts that you use.

Cheers, Jari Oksanen

Hi all,

Im using adonis for some plant community analysis and have been following
theBioBucket example of how to posthoc tests (
http://thebiobucket.blogspot.ch/2011/08/two-way-permanova-adonis-with-custom.html
)

data(dune)
data(dune.env)
ad1 <- adonis(dune ~ Management, data=dune.env, permutations=99)
# Call:
# adonis(formula = dune ~ Management, data = dune.env, permutations = 99)
#
# Terms added sequentially (first to last)
#
# Df SumsOfSqs MeanSqs F.Model      R2 Pr(>F)
# Management  3    1.4686 0.48953  2.7672 0.34161   0.01 **
# Residuals  16    2.8304 0.17690         0.65839
# Total      19    4.2990                 1.00000
# ---
#      Signif. codes:  0 ?***? 0.001 ?**? 0.01 ?*? 0.05 ?.? 0.1 ? ? 1

man <- dune.env$Management
contmat <- cbind(c(1,-1,0,0), c(1,0,-1,0), # construct a new contrast matrix
                c(1,0,0,-1), c(0,1,-1,0),
                c(0,1,0,-1), c(0,0,1,-1))
contrasts(man) <- contmat[,1:4]
trt1.2 <- model.matrix(~ man)[,2]
trt1.3 <- model.matrix(~ man)[,3]
trt1.4 <- model.matrix(~ man)[,4]

ad2 <- adonis(dune ~ trt1.2 + trt1.3 + trt1.4 )
# Call:
#      adonis(formula = dune ~ trt1.2 + trt1.3 + trt1.4)
#
# Terms added sequentially (first to last)
#
# Df SumsOfSqs MeanSqs F.Model      R2 Pr(>F)
# trt1.2     1    0.1483 0.14827  0.8381 0.03449  0.545
# trt1.3     1    0.8371 0.83712  4.7321 0.19472  0.001 ***
# trt1.4     1    0.4832 0.48321  2.7315 0.11240  0.032 *
# Residuals 16    2.8304 0.17690         0.65839
# Total     19    4.2990                 1.00000
# ---
# Signif. codes:  0 ?***? 0.001 ?**? 0.01 ?*? 0.05 ?.? 0.1 ? ? 1

I was just wondering whether it was fair to say that the species with high
coefficients (adonis(...)$coefficients) were the ones causing that
difference?

ad2$coefficients[3,abs(ad$coefficients[3,])>1]
# Elepal    Poapra    Salrep    Poatri    Elyrep    Lolper    Alogen
# -1.091667  1.975000 -1.375000  3.283333  1.333333  3.000000  1.650000

If so, would it be better to take the coefficients from the original model
or the model used for the contrast, as these yield different results:

ad1$coefficients[3,abs(ad1$coefficients[3,])>1]
# Rumace   Tripra   Poatri   Plalan
# 2.316667 1.350000 1.516667 1.541667

Cheers,

Alan

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Email: aghaynes at gmail.com
Mobile: +41763389128
Skype: aghaynes

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Jari Oksanen, Dept Biology, Univ Oulu, 90014 Finland
jari.oksanen at oulu.fi, Ph. +358 400 408593, http://cc.oulu.fi/~jarioksa
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Alan,

You should remember that adonis() models are sequential and the order of terms matters. Moreover, redundant terms will be ignored. This also applies to terms which are made of single contrasts. In balanced design with non-redundant contrasts you can easily get the results (statistics, significances) for single terms, but your description sounds like this is not the case.

cheers, Jari Oksanen

Thanks Jari. 

Perhaps I can pose my question slightly differently. In the example I gave using the dune data, there is an effect of management. How would you go about finding where the differences among levels are? In this example its perhaps easy...plot it. But for examples where sites differ substantially so that treatments within sites are still closer to a site centroid than a treatment centroid but consistently shifts in one direction in ordination space? 
In that sense, using the custom contrasts is a posthoc procedure, because having found a significant effect, I tried to find where that difference originated. I am aware that I only included the first three contrasts, but I thought that would be enough to give the idea of what I was doing. Having done all pairwise contrasts I would correct for the multiple comparisons with Bonferroni or such.

Once you know where the differences are, how would you then go about finding out what is causing the difference? (This is why I was asking about the coefficients)

Thanks again,

Alan

--------------------------------------------------
Email: aghaynes at gmail.com
Mobile: +41763389128
Skype: aghaynes

On 27 May 2013 07:27, Jari Oksanen <jari.oksanen at oulu.fi> wrote:
Alan,