I am trying to use permanova to test for treatment effects and interaction in a study design where blocking needs to be considered as a random effect, and one treatment is paired within the other.
There are plots with high or low density, and in each plot are subplots with treatment A in one subplot, treatment B in the other. The design is a latin square, with only one replicate of each treatment combination in each block effect (vertical blocking and horizontal blocking) so that blocking needs to be treated as a random effect.
The response variable is percent cover of plant species in the community.
The data is set up thus:
Treatment hblock vblock Inoc sp1 sp2 …
1 1 1 1 0.2 0.25
2 2 1 2 0.3 0.9
1 3 1 2 0.2 0.2
2 4 1 1 0.01 0.001
Where "Treatment" is the high and low density treatment, and "Inoc" is the treatment "A or B" in the subplots.
My question is, since I can't use random effects in permanova, so far as I can tell from reading about it, can I account for the blocking effects by nesting the interaction within the blocks - like this:
adonis(formula = temp[, -c(1:4)] ~ temp$Inoc * temp$Treatment , method = "bray", strata = temp$Vblock * temp$Hblock, permuatations = 1000)
Or is this approach invalid?