[R-sig-ME] Set and interpret interaction terms in MCMCglmm

[Patricia Soto]

Greetings Everyone,

I am using Bayesian statistics for the first time in my life and while I am
delighted with MCMCglmm, I do need extra input to move on to the next part
of my analysis. The basic question I have is how to set and interpret the
output of interaction terms.

First the description of my data:

Dependent variable D: 10 categories
Explanatory variable X1: 2 categories: 0, 1
Explanatory variable X2: 2 categories: 0, 1
Random effects: X3 and X4.

Second: The reason why I am testing interaction terms:

The reviewer of the paper (that I need to resubmit!) suggests we analyze
the effect of the interaction X1 * X2 on the dependent variable. After tons
of reading (this mailing lists, online examples, and so), I was able to
craft a prior and a model:

Third: my model (so far):

m<- MCMCglmm(D ~ trait - 1 + X1 + X1:trait * X2:trait, random = ~
us(trait):X3 + us(trait):X4, prior = prior3, rcov = ~us(trait):units, data
= our_data, family = "categorical", verbose = TRUE, nitt = 13000*1,
burnin=3000*1, thin = 10*1)

Fourth: The issue;

1. To account for whether the interaction between X1 and X2 has an effect
on the dependent variable, do I have to explicitly add the interaction term
X1 * X2, or D ~ trait - 1 + X1 + X2 would be enough?
2. How could I interpret the following outputs?:
             post.mean  l-95% CI  u-95% CI eff.samp  pMCMC
D.8:X1:X2            -1.98682       -3.40467     -0.79391
15.226       0.002 **
 Would it make sense to say: When X2 = 1 and X1 = 1, then the probability
of getting D.8 decreases? (motivation: when we started our study, our
expectation was exactly the opposite; therefore, I want to rule out any
misunderstanding in the statistical modeling).

Thanks!

Patricia

patricia.soto.b at gmail.com

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