[R] Randomization test for interaction effect

[Pedro de Barros]

Dear All,

I am trying to build a randomization test for interaction

The problem is as follows: I have a set of stations where the ocurrence and 
biomass of each species being investigated was recorded.

For each group of stations, the relative importance of a set of species was 
calculated, as the Index of Relative Importance (IRI), given as

IRI(i)=(FO(i)*RW(i))/sum(FO(j)*RW(j))

FO(i) is the relative frequency of ocurrence of species i and RW(i) is the 
relative Biomass of species i (Total biomass of this species/Total biomass 
of all species). Stations are grouped according to 3 different criteria, 
say A, B and C, with 3 levels of A, 5 of B, and 3 of C.

The null hypothesis of interest is that the distribution of the IRI among 
the species is independent of these classification levels. I suggest using 
the average difference in IRI(i) of each grouping to the overall IRI(i) as 
the test statistic.

I have no difficulty building the randomization test for the main effects: 
Simply randomize the corresponding group membership factor. However, I am 
having difficulty building the test for the interaction effect: As far as I 
understand, the test should randomize the levels of say B, within the 
levels of A, so that the main effects should not be affected (all 
observations classified as level A1 would still be A1, and all observations 
classified as level B1 should stay as B1). My difficulty is how to 
calculate the "overall" distribution of the IRI in this case. This should 
consider all main effects, but no interaction.

I would really appreciate any pointer to a solution of this problem. I 
believe it is not complicated (and probably quite obvious) but the solution 
keeps out of reach, even though I have been searching for over a week.

Thanks,
Pedro

Pedro de Barros
Faculdade de Ciências do Mar e do Ambiente
Universidade do Algarve ,Campus de Gambelas
8000-117 FARO, Portugal
Tel: + 351 289 800 034
Fax: +351 289 818 353
e-mail: pbarros at ualg.pt