如何用固定的嵌套因子解释permanova adonis的输出？

Question

I am not quite sure how to interpret ":" in adonis2 output (vegan package) when using both nested factors and interactions.

For exemple, without nested factors :

        adonis_data <- adonis2(Y ~ 
                       A*B*C , data=factors, 
                       permutations = 9999, method = "euclidean")

        adonis_data

Interactions between factors are represented with ":" in the result output such as:

   Terms added sequentially (first to last)
        A       ***
        B       ***
        C       ***
        A:C     ***
        B:C     ***

However, when integrating a nested effect (either with ":" or "/") :

        adonis_data <- adonis2(Y ~ 
                       A:B*C , data=factors, 
                       permutations = 9999, method = "euclidean")

        adonis_data

I have difficulty to interpret this output as I don't know how nested factors are showed here (with or without ":")

   Terms added sequentially (first to last)
        A      ***
        C      ***
        A:B    ***
        A:C    ***
        A:C:B  ***

So here, I'm not quite sure if A:B is showing an effect of my nested factor rather than an interaction...

My last thought on the matter was that if nested factors are written as interactions in the output (eg A:B), we could differentiated both by the order of results considering that the terms are added sequentially.

So, if this is correct, that would mean that nested B should be between A and C and that A:B here is rather an interaction ?

Is it correct to conclude here that the B effect within A on Y is different according to A value ?

Does anyone can enlighten me ? Many thanks, Laura

Answer 1

This is a general issue with R formula and in no way special to adonis or vegan . Anyway, in default adonis2 (which currently is just adonis ), the tests are sequential, and this really means that previous terms will influence the results, but later (subsequent) terms have no effect. What the terms are, depends on the way you define your model, like you demonstrated in you question.