[R-sig-ME] MCMCglmm interaction and posterior mode

[Kamal Atmeh]

Dear all,

I have some questions, which may sound trivial, pertaining to 
interaction models with MCMCglmm.

I am running the following model with a gaussian distribution and a 
3-way interaction between two categorical two-level variables (tactic: 
F/H and period PB/B) and one continuous variable (env):

model <- MCMCglmm(lD ~ tactic*period*env
                                      , random = 
~sp_phylo+species2+phylo_pop+phylo_popY+phylo_pop_id
                                      , family = "gaussian"
                                      , ginverse = list(sp_phylo = 
inv.phylo$Ainv) # include a custom matrix for argument phylo
                                      , prior = prior1
                                      , data = Data
                                      , nitt = 22e+04
                                      , burnin = 20000
                                      , thin = 100
                                      , pr=TRUE)

After looking at the results, I found that the 2-way interaction 
tactic*env from the tactic*period*env interaction was not significant, 
however the 3-way interaction itself was, with the following output in 
the summary:

 >>>   tacticH:periodB:env      0.17831  0.05360 0.30512     5000  
0.0052 ** (the intercept represents tactic F and period PB)

I tried to run the model again in order to simplify it using ":" and 
therefore remove the non-significant 2-way interaction:

model2 <- MCMCglmm(lD ~ tactic*period + period*env + *tactic:period:env*
                                      , random = 
~sp_phylo+species2+phylo_pop+phylo_popY+phylo_pop_id
                                      , family = "gaussian"
                                      , ginverse = list(sp_phylo = 
inv.phylo$Ainv) # include a custom matrix for argument phylo
                                      , prior = prior1
                                      , data = Data
                                      , nitt = 22e+04
                                      , burnin = 20000
                                      , thin = 100
                                      , pr=TRUE)

When using ":", the output of my model returns the posterior mean for 
each level of the categorical variables instead of one level as before:

tacticF:periodPB:env -0.1668620 -0.3554264  0.0005143    195.0 0.0923 .
tacticF:periodB:env  -0.2018706 -0.3783204 -0.0174366    195.0 0.0410 *
tacticH:periodPB:env -0.1561097 -0.2066183 -0.1093840    118.2 <0.005 **

How should I define the interaction in the model in order to obtain an 
output similar to the one when the "*" interaction was used 
(tacticH:periodB:env) while simplifying and removing the non-significant 
interaction from the 3-way interaction?

Finally, is there a way to automatically compute the posterior mean of 
the continuous variable for each modality of the interaction?

Thank you and stay safe!

Kamal


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