2-way adonis (PERMANOVA) incl interaction - how to test for main effects?

adonis(t(otu_fungi_out) ~ Stage + Growhouse + Stage : Growhouse,

adonis(t(otu_fungi_out) ~ Growhouse + Stage + Stage : Growhouse,

Gian,

I am bit confused by what your concern is. First, if the imbalance is not
that severe, the approach you take to analyzing a two-way permanova (type
I, type II, type III ss) is not going to matter that much. Indeed, if the
design were balanced, they would give you identical results. Second,
regardless of the lack of balance, for the models y ~ A + B + A:B  and y ~
B + A + A:B, the test for the interaction will be the same. So, I don?t
understand why you would want to drop the main effects from the model,
effectively combining them with interaction. That doesn?t make any sense to
me. The problem is with the tests of the main effects.

My advice is to run both models (i.e., A first, then B first) using type I
ss. As mentioned, both models will give you the same interaction result. If
the interaction is all that you?re interested in, problem solved. Interpret
only the interaction and and ignore the main effects. If the interaction is
not significant and low, then interpret only the main effects, focusing
only on the second main effect in each of the differently-ordered models
(which are equivalent to Type II ss tests). And these results will tell you
pretty the same thing as type III tests if there is little or no
interaction. I would not worry about trying to estimate the main effects
while controlling for the interaction (Ellen?s question), which cannot be
done using type I or type II SS in 2-way permanova using adonis. But why
would you want to? The lack of a balanced design results in the main
effects and the interaction not being independent of one another.  Forcing
that independence by using type III ss can only work by essentially
"throwing away" some of the information associated with the main effects,
possibly resulting in an overly conservative test. The lower the
interaction, however, the less is thrown away and the less it matters.


Steve




Stephen Brewer
jbrewer at olemiss.edu
Professor
Department of Biology
PO Box 1848
 University of Mississippi
University, Mississippi 38677-1848
 Brewer web page - https://jstephenbrewer.wordpress.com
FAX - 662-915-5144 Phone - 662-202-5877





On Oct 31, 2018, at 5:45 PM, Gian Maria Niccol? Benucci <
gian.benucci at gmail.com> wrote:

Thank you Jari,

So to test if there are significant interaction I should use
Stage:Growhouse
i.e. A:B. This will test the interaction and main effects that are marginal
and so removed. How matters then if I include by="margin" or not? The R2
are the same (please see below) but the p-value changes. I assume the
second way is most correct, is it?

*> adonis2(t(otu_fungi_out) ~ Stage : Growhouse, data=metadata_fungi_out,
permutations=9999)*
Permutation test for adonis under reduced model
Terms added sequentially (first to last)
Permutation: free
Number of permutations: 9999

adonis2(formula = t(otu_fungi_out) ~ Stage:Growhouse, data =
metadata_fungi_out, permutations = 9999)
               Df SumOfSqs      R2      F Pr(>F)
Stage:Growhouse  3   1.0812 0.23075 1.9998 0.0211 *
Residual        20   3.6045 0.76925
Total           23   4.6857 1.00000
---
Signif. codes:  0 ?***? 0.001 ?**? 0.01 ?*? 0.05 ?.? 0.1 ? ? 1


*> adonis2(t(otu_fungi_out) ~ Stage : Growhouse, data=metadata_fungi_out,
by = "margin", permutations=9999)*
Permutation test for adonis under reduced model
Marginal effects of terms
Permutation: free
Number of permutations: 9999

adonis2(formula = t(otu_fungi_out) ~ Stage:Growhouse, data =
metadata_fungi_out, permutations = 9999, by = "margin")
               Df SumOfSqs      R2      F Pr(>F)
Stage:Growhouse  3   1.0812 0.23075 1.9998  0.006 **
Residual        20   3.6045 0.76925
Total           23   4.6857 1.00000
---
Signif. codes:  0 ?***? 0.001 ?**? 0.01 ?*? 0.05 ?.? 0.1 ? ? 1


Cheers,

Gian

On Tue, 30 Oct 2018 at 05:47, Jari Oksanen <jari.oksanen at oulu.fi> wrote:

Hello Gian,

These formulae expand into different models. Compare

model.matrix(~ Stage:Growhouse, data=metadata_fungi_out)
model.matrix(~ Stage*Growhouse, data=metadata_fungi_out)

The first model (Stage:Growhouse) will also contain (implicitly) main
effects and all these terms are marginal and can be removed, whereas the
latter Stage*Growhouse expands to explicit main effects and interaction
effects, and only the interaction effects are marginal and can be removed.
This is also reflected in the degrees of freedom in your anova table: In
the first case Stage:Growhouse has 3 df, and in the latter only 1 df (and
the main effects ignored had 2 df).

Ciao, Giari

On 29 Oct 2018, at 19:11, Gian Maria Niccol? Benucci <

gian.benucci at gmail.com> wrote:


Hello Jari,

It is a little bit confusing. If A*B unfolds in A+B+A:B then A:B is the
real interaction component.
So, which if the code below will test the variance for the interaction
alone?

adonis2(t(otu_fungi_out) ~ *Stage : Growhouse*, data=metadata_fungi_out,

by = "margin", permutations=9999)
Permutation test for adonis under reduced model
Marginal effects of terms
Permutation: free
Number of permutations: 9999

adonis2(formula = t(otu_fungi_out) ~ Stage:Growhouse, data =
metadata_fungi_out, permutations = 9999, by = "margin")
              Df SumOfSqs      R2      F Pr(>F)
Stage:Growhouse  3   1.0812 0.23075 1.9998  1e-04 ***
Residual        20   3.6045 0.76925
Total           23   4.6857 1.00000
---
Signif. codes:  0 ?***? 0.001 ?**? 0.01 ?*? 0.05 ?.? 0.1 ? ? 1


adonis2(t(otu_fungi_out) ~ *Stage * Growhouse*, data=metadata_fungi_out,

by = "margin", permutations=9999)
Permutation test for adonis under reduced model
Marginal effects of terms
Permutation: free
Number of permutations: 9999

adonis2(formula = t(otu_fungi_out) ~ Stage * Growhouse, data =
metadata_fungi_out, permutations = 9999, by = "margin")
              Df SumOfSqs      R2      F Pr(>F)
Stage:Growhouse  1   0.2171 0.04633 1.2045 0.2443
Residual        20   3.6045 0.76925
Total           23   4.6857 1.00000



The results is clearly very different. Also, in a normal adonis call I
didn't have any significance for the interaction that I have instead if I
use A:B. So ~ A*B will not test for interactions at all?

*adonis*(t(otu_fungi_out) ~ Stage * Growhouse, data=metadata_fungi_out,

permutations=9999)
Call:
adonis(formula = t(otu_fungi_out) ~ Stage * Growhouse, data =
metadata_fungi_out,      permutations = 9999)

Permutation: free
Number of permutations: 9999

Terms added sequentially (first to last)

              Df SumsOfSqs MeanSqs F.Model      R2 Pr(>F)
Stage            1    0.4877 0.48769  2.7060 0.10408 0.0247 *
Growhouse        1    0.3765 0.37647  2.0889 0.08034 0.0542 .
Stage:Growhouse  1    0.2171 0.21708  1.2045 0.04633 0.2507
Residuals       20    3.6045 0.18023         0.76925
Total           23    4.6857                 1.00000
---
Signif. codes:  0 ?***? 0.001 ?**? 0.01 ?*? 0.05 ?.? 0.1 ? ? 1



Thank you!

Gian





On Tue, 16 Oct 2018 at 08:54, Jari Oksanen <jari.oksanen at oulu.fi> wrote:



On 16/10/18 11:23, Torsten Hauffe wrote:

"adonis2(speciesdataset~A*B, by="margin") but then only the effect of

the

interaction is tested."

This is not entirely correct.
adonis2(speciesdataset~A:B, by="margin") would test the interaction

alone.

~A*B unfolds to ~A+B+A:B


Well, it was correct: the only **marginal** effect in ~A+B+A:B is A:B (A
and B are not marginal), and by = "margin" will only analyse marginal
effects.

Cheers, Jari Oksanen


On Tue, 16 Oct 2018 at 11:51, Ellen Pape <ellen.pape at gmail.com> wrote:

Hi all,

I don't know whether this is the correct mailing group to address this
question:

I would like to perform a 2-way permanova analysis in R (using adonis

in

vegan). By default you are performing sequential tests (by="terms"),

so

when you have 2 or more factors, the order of these factors matter.
However, since I wanted to circumvent this, I chose for the option
by="margin" (adonis2(speciesdataset~A*B, by="margin")) but then only

the

effect of the interaction is tested. On the "help page" of anova. cca

it

says: "if you select by="margin" -> the current function only

evaluates

marginal terms. It will, for instance, ignore main effects that are
included in interaction terms."


My question now is: can I somehow get the main effects tested anyhow,

when

the interaction term is not significant?

Thanks,
Ellen

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