[R-sig-ME] multivariate mixed model for composition data : RRPP, mvabund as alternatives to permanova?

[Guillaume Adeux]

Hi everyone,

Does anybody have any experience with multivariate "mixed" models? And more
specifically with the RRPP package or other alternatives to vegan::adonis
for complex hierarchical designs?

I took knowledge of the RRPP package (associated publication:
https://besjournals.onlinelibrary.wiley.com/doi/10.1111/2041-210X.13029 )
but I am having a real hard time transcribing my design into actual code
and defining against what Mean Square the different effects (including
random) should be tested.

The design is the following (split split split plot, very similar to oats
dataset):
    - 4 blocks  -> "block"
    - each block is split into two tillage types (conventional vs.reduced)
-> "tillage"
    - each tillage type is split into 4 nitrogen levels   -> "N"
    - each nitrogen level is split into 4 cover crop types  -> "CC"

To complicate things further, 2 pseudo-replicates were carried out in the
plots at the lowest hierarchical level (cover crops). This results in 32
combinations of tillage, nitrogen and cover crops (128 plots total, x2 =
256 observations). My response is the cover per species of segetal plants.

My objective would be to test all simple effects, first order interactions
and the second order interaction in order to investigate things further.
I'm really looking for something similar to vegan::adonis that takes into
account more than one level of nesting (BiodiversityR::nested.permanova
also only takes into account one level of nesting and does not test the
interaction).

Moreover, reading the Supp. Mat. of the article cited above, it is written
that "mixed model ANOVA is possible via multimodel comparison" with
{mvabund}. Could anyone give me more insight?

Thank you once again for your very appreciated help,

Guillaume ADEUX

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