[R-sig-ME] interpretation of covariate effect on traits in multinomial mixed model (MCMCglmm)

[Dominique CARVAL]

Hi everybody,

I want to assess the possible effect of the density of 3 plants strata (herbaceous, ligneous, and banana plant; continuous variables) on the probability of 6 ant species to be the (numerically) dominant species.

The data come from samplings on 500 sites in plantain agrosystems in Cameroun, with 2 replicates per site.
The multinomial response variable is composed of the 6 following categories : DomSpecies1,DomSpecies2, DomSpecies3, DomSpecies4, DomSpecies5, DomSpecies6.

I used the DomSpecies5 as the baseline category.
I followed the instructions of J. Hadfield (MCMCglmm Course Notes)to specify covariance matrix and I specified the following random effect : siteid, which is the identification number of each of the 500 sampled sites. 

I suppose that each ant species may respond differently to the density of each stratum.
Therefore, I used the following model:

bayesId<-MCMCglmm(DomSpecies~trait + herbaceous:trait  + banana:trait + ligneous:trait - 1, rcov = ~idh(trait):units, random=~siteid, nitt=nbiterations, burnin=burning, prior=priors1, family="categorical", data=Dominance, pr = TRUE, pl = TRUE, saveX=TRUE, saveZ = TRUE,thin=10)

Here is the location effects part summary of the model: 

 Location effects: DomSpecies ~ trait + herbaceous:trait + banana:trait + ligneous:trait - 1 

                           post.mean l-95% CI u-95% CI eff.samp  pMCMC   
traitDomSpecies.1           -0.40504 -0.67616 -0.18239   32.804 <0.001 **
traitDomSpecies.2           -1.56674 -1.84566 -1.27239   18.023 <0.001 **
traitDomSpecies.3           -2.68457 -3.24824 -2.02872    4.320 <0.001 **
traitDomSpecies.4           -0.57887 -0.87424 -0.28980   21.054 <0.001 **
traitDomSpecies.6           -0.34739 -0.58999 -0.11550   28.079 <0.001 **
traitDomSpecies.1:herbaceous  -0.12314 -0.36278  0.08398   36.442 0.2300   
traitDomSpecies.2:herbaceous  -0.81781 -1.12423 -0.45659   13.293 <0.001 **
traitDomSpecies.3:herbaceous  -0.79766 -1.79822  0.20292    1.548 0.2225   
traitDomSpecies.4:herbaceous   0.06787 -0.17180  0.25493   18.361 0.5375   
traitDomSpecies.6:herbaceous  -0.38589 -0.67043 -0.10492   13.041 0.0050 **
traitDomSpecies.1:banana      -0.55612 -0.97868 -0.08495   20.617 0.0100 **
traitDomSpecies.2:banana      -0.35302 -0.74533  0.04908   19.673 0.0875 . 
traitDomSpecies.3:banana      -0.31290 -1.21542  0.57856    4.051 0.7075   
traitDomSpecies.4:banana       0.09981 -0.24120  0.47918   23.943 0.5850   
traitDomSpecies.6:banana      -0.36227 -0.76133 -0.02808   33.856 0.0350 * 
traitDomSpecies.1:ligneous    1.15269  0.79352  1.55125   32.402 <0.001 **
traitDomSpecies.2:ligneous    0.85504  0.26285  1.42060    9.794 0.0125 * 
traitDomSpecies.3:ligneous    1.30803  0.83209  1.92698   12.474 <0.001 **
traitDomSpecies.4:ligneous   -0.19435 -1.10642  0.42893    3.782 0.8575   
traitDomSpecies.6:ligneous    1.09109  0.68030  1.53037   20.792 <0.001 **

I understand that the probability of being in the categories 1,2,3,4 and 6 are significantly lower than the probability of being in the baseline category 5 (which is consistent with observed data).

I am more confused to interpret the effect of covariates. For instance, the 7th line of this summary dispalys:
                              post.mean l-95% CI u-95% CI eff.samp  pMCMC 
traitDomSpecies.2:herbaceous  -0.81781 -1.12423 -0.45659   13.293 <0.001 **

I understand that the hebaceous stratum affect negatively (and significantly) the probability of being in the trait category 2. 
If I look at the 6th line:
                              post.mean l-95% CI u-95% CI eff.samp  pMCMC 
traitDomSpecies.1:herbaceous  -0.12314 -0.36278  0.08398   36.442 0.2300  
 
I understand that the hebaceous stratum does not affect the probability of being in the trait category 1. 
My first question is then: Am I right?

My second question: where do I found the effect of covariates on the baseline category 5?

Third and fourth questions: Is it correct to select the best models using only difference in DIC (delta DIC)? How to decide if the delta DIC is sufficiently large to be considered?

Thanks for answering,

Cheers,

Dom

Dominique Carval (PhD) - Ecologue 
UR26 Système de Culture à base de Bananiers, Plantain et Ananas 
CIRAD 
Campus Agro-environnemental Caraïbes 
Quartier Petit Morne – BP214 
97285 Le Lamentin Cedex 2 

Tel : (+596) 0596 42 30 28 

Fax : (+596) 0596 42 30 01