[R] Randomization test for interaction effect
Pedro de Barros
pbarros at ualg.pt
Wed Jul 20 14:32:36 CEST 2005
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
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.
Pedro de Barros
Faculdade de Ciências 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
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