[R-sig-eco] 2-way adonis (PERMANOVA) incl interaction - how to test for main effects?
Gian Maria Niccolò Benucci
gi@n@benucci @ending from gm@il@com
Wed Oct 31 23:45:46 CET 2018
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 using 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 Niccolò Benucci <
> gian.benucci using 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 using 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 using 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
> >>>>
> >>>> [[alternative HTML version deleted]]
> >>>>
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> >>>>
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--
Gian Maria Niccolò Benucci, Ph.D.
Postdoctoral research associate
Michigan State University
Department of Plant, Soil and Microbial Sciences
1066 Bogue Street
48825 East Lansing, MI
Lab: +1 (517) 844-6966
Email: gian.benucci using gmail.com
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