Distance-based linear models, such as those implemented by the
adonis package in R, allow us to fit one or more predictors to a multivariate response represented by a distance table. These allow us to test whether any of the predictor variables have a "location" effect on the set of response variables.
Is there any method currently available that would allow the inclusion of a random effect in such a model? (Bonus points if the method is implemented by an existing R package...)
For example, we have some data on the microbiota (gut bacteria) of a group of humans, with repeated measures from each individual. Each data point consists of a set of abundances for a large number (hundreds) of bacterial species, making up the response data, as well as some predictors such as individual ID and recent diet.
The model I would like to fit is essentially
microbiota ~ diet + (1|individual).
This is no problem if
microbiota is boiled down to a single variable, such as a single bacterial family/species or even a Principal Coordinate Axis produced from the distance table (which is the kind of approach that I usually see in the literature). But ideally I would like to use the full distance table as the response variable. Is there a method that makes it possible?
adonis can cope with a model such as
microbiota ~ diet + individual, but there "individual" is treated as a fixed effect which is infeasible if the number of individuals is too large.