[R-sig-eco] testing interactions in a permanova when you have non-independent data

[Henrik Eckermann]

Hi there,

I am a M.Sc. student without training in PERMANOVA with only some basic knowledge in multivariate analysis (much more in univariate analyses).  I am currently working on a project with 2 other people but nobody is really familiar with the PERMANOVA. If someone could help us with the following questions that would be nice. Please check out the question.html document where I simulate a dataframe similar to our original data.



Here a short description what we have and want to test:

We have the log abundances of 130 bacterial genus levels for 96 subjects determined from stool samples collected at 2 timepoints pre/post treatment.
Subjects come from two distinct environments (treatment_A) and also had different feeding types (treatment_B)
We hypothesized that there is no difference in overall community composition at timepoint 1 (pre) but that there is a difference at timepoint 2 (post) between the treatment_A groups. The difference between the treatment_A groups at timepoint 2 is only present for 2 of the 4 treatment_B groups. 


Thus, we want to test whether we can reject the following H0s:

H0 (1): There is a difference in community composition at timepoint 1 between treatment_A groups.
H0 (2): There is no difference at timepoint 2 (in overall community composition).
H0 (3): Whether there is an effect at timepoint 2 is independet treatment_B such that the effect occurs similarly in all treatment_B groups.


Specific questions: 

How do we make sure that we do not violate the assumptions of independent observations when we test the effect of treatment A in the PERMANOVA framework?
How to specify our model correctly to test all our effects?
How to proceed if the interaction time:treatment_A or time:treatment_A:treatment_B is significant? What are posthoc procedures that could be done?
Is it possible to include a continuous predictor as covariate. E.g. if you wanted to statistically "control" for the variation explained by this predictor?



Thank you for any help!

Henrik

P.S.:
Feel free to edit the .Rmd file if you prefer answering in this way!