Testing assumptions for running adonis2 over continuous data

[NThie]

Hi,
As I understand from the documentation, adonis2 function can be used to test community differences between groups as well as over continuous data. When testing between groups, there is the assumption that the variance / dispersal needs to be equal between the two groups to properly use adonis2 - which can be checked with the betadisper function. However, betadisper does not work with continuous data - so how do I check the assumptions for using adonis2 with continuous data?

Thanks for your help!

[gavinsimpson]

The idea behind betadisper() is as a multivariate analogue for univariate tests of homogeneity of group variance such as Bartlet's or Levene's tests. I suppose this is because the model adonis2() fits was originally described as a multivariate analogue of ANOVA, and ANOVA is for categorical covariates.

Homogeneity of variances is harder to check within a linear model framework; one often resorts to graphical techniques like scatter plots of residuals or QQ plots.

I suppose you could artificially create groups by cutting the continuous covariate in k group using cut() and that way check if each bin had roughly the same variance by passing the created factor to betadisper().

[jarioksa]

There is no direct way of finding that information directly from adonis2. However, you can build a corresponging dbrda model and use tools to analyse its residuals:

library(vegan)
data(mite, mite.env)
mad2 <- adonis2(dist(decostand(mite, "hell")) ~ SubsDens + WatrCont, mite.env)
mdb <- dbrda(dist(decostand(mite, "hell")) ~ SubsDens + WatrCont, mite.env)
ordiresids(mdb, residuals="working")
ordiresids(mdb, "scale", residuals="working")
ordiresids(mdb, "qq", residuals="working")

The internal mathematical models are identical in dbrda and adonis2 justifying this approach. However, the residuals concern internal ("working") form of dissimilarities (Gower double-centred dissimilarities), and for N observations there are N(N–1)/2 distinct points in the plot. The plots are similar as the diagnostic plots for linear model (lm).

[jarioksa]

Here a simple test to see how adequate the ordiresids approach may be. Let's see if residuals of dbrda are similar to betadisper distances to group centroids.

library(vegan)
data(mite, mite.env)
mbb <- betadisper(vegdist(sqrt(mite)), mite.env$Shrub, type="centroid") # default type = "median" is worse
mdb <- dbrda(vegdist(sqrt(mite)) ~ Shrub, mite.env)
dbb <- mbb$distances # distances to betadisper centroids
dw <- residuals(mdb, type="working")
dr <- as.matrix(residuals(mdb, type="response")) # needs as.matrix
plot(dbb, sqrt(rowSums(dw^2)))  # not quite similar
plot(dbb, sqrt(rowSums(dr^2))) # not quite linear, but exact mapping

So this would indicate that response residuals are more or less similar to betadisper distances whereas the internal forms are not. However, my gut feeling is that working residuals (on which the methods actually work!) are the ones that should be OK (and this conjecture rather has consequences to betadisper). You can also specify type = "response" in ordiresids, but for dbrda object you get a harmless warning as the response residuals are not returned as a symmetric square matrix, but as distances.