[R-sig-ME] Interpreting a MCMCglmm model with a bivariate response variable

[Iker Vaquero Alba]

   Hello all,
   I am implementing a model with a multiple (bivariate) response variable using MCMCglmm. Both response variables and all the explanatory variables are categorical variables, with between 2 and 6 levels. The model is as follows:
   
testmodel1<-MCMCglmm(cbind(natapshort,nataplong)~gender+age+religion+sexor+selfattr+partnerattr+gender:age+gender:religion+gender:sexor+gender:selfattr+gender:partnerattr+age:religion+age:sexor+age:selfattr+age:partnerattr+religion:sexor+religion:selfattr+religion:partnerattr+sexor:selfattr+sexor:partnerattr+selfattr:partnerattr,random=NULL,rcov=~us(trait):units,family=c("threshold","threshold"),data=extphen,nitt=100000,singular.ok=TRUE)
   And this is the summary of the model after all the iterations:
   
summary(testmodel1)  Iterations =3001:99991 Thinninginterval  = 10 Sample size  = 9700   DIC:   R-structure:  ~us(trait):units                            post.mean l-95% CI u-95% CI eff.sampnatapshort:natapshort.units    114108   992.1   213000    7.105nataplong:natapshort.units      33245   310.8    66300    4.656natapshort:nataplong.units      33245   310.8    66300    4.656nataplong:nataplong.units       82964   671.5   155869    2.218  Location effects:cbind(natapshort, nataplong) ~ gender + age + religion + sexor + selfattr +partnerattr + gender:age + gender:religion + gender:sexor + gender:selfattr +gender:partnerattr + age:religion + age:sexor + age:selfattr + age:partnerattr+ religion:sexor + religion:selfattr + religion:partnerattr + sexor:selfattr +sexor:partnerattr + selfattr:partnerattr                        post.mean   l-95% CI  u-95% CI eff.samp   pMCMC   (Intercept)           8.934e+02 -6.995e+02 2.596e+03   275.73 0.22660   genderM              -8.936e+01 -7.437e+02 5.066e+02  4236.67 0.75794   genderO              -1.292e+03 -1.934e+05 1.765e+05  9700.00 0.99052   age                  -3.493e+02 -1.170e+03 3.615e+02   505.92 0.31918   religionY            -7.361e+02 -1.598e+03 1.481e+01    33.71 0.03402 * sexorHOM             -1.235e+03 -1.808e+05 1.679e+05  9700.00 0.99814   sexorOT                2.193e+03 -1.589e+05  1.687e+05 10583.09 0.97814   selfattr             -2.367e+02 -7.424e+02 1.706e+02   314.82 0.24948   partnerattr           1.391e+02 -2.667e+02 6.147e+02   966.40 0.49546   genderM:age           2.696e+01 -1.313e+02  1.748e+02  3786.10 0.69670   genderO:age          -1.055e+04 -8.325e+04 7.163e+04  1722.63 0.78474   genderM:religionY    -1.295e+02 -3.725e+02 8.194e+01   200.08 0.20495   genderO:religionY    -1.016e+04 -1.589e+05 1.505e+05  8731.86 0.89052   genderM:sexorHOM     -2.245e+02 -5.713e+02 4.443e+01   105.67 0.10495   genderO:sexorHOM     -8.104e+03 -1.620e+05 1.385e+05  5318.22 0.90474   genderM:sexorOT      -1.520e+02 -5.124e+02 1.856e+02   423.76 0.33402   genderO:sexorOT       2.628e+03 -1.654e+05 1.658e+05  9700.00 0.97670   genderM:selfattr      9.029e+01 -3.152e+01 2.334e+02   119.78 0.12907   genderO:selfattr      6.281e+03 -6.511e+04 8.524e+04  3504.67 0.88412   genderM:partnerattr  -7.284e+01 -2.160e+02 6.729e+01   263.29 0.25052   genderO:partnerattr   2.536e+02 -5.113e+02 1.121e+03  1291.76 0.49113   age:religionY         8.732e+01 -1.283e+02 3.457e+02   727.46 0.42289   age:sexorHOM          2.809e+02 -8.592e+04 8.847e+04  9700.00 0.99711   age:sexorOT          -1.246e+03 -8.447e+04 7.941e+04  9370.57 0.97526   age:selfattr          1.195e+02 -6.636e+01 3.452e+02   212.35 0.19567   age:partnerattr      -8.598e+00 -1.963e+02 1.714e+02  9700.00 0.92227   religionY:sexorHOM    8.506e+01 -2.392e+02 4.612e+02  2059.92 0.59959   religionY:sexorOT     1.420e+01 -5.170e+02 5.464e+02  9700.00 0.96268   religionY:selfattr    2.782e+01 -1.198e+02 1.833e+02  3520.80 0.68701   religionY:partnerattr 1.407e+02  1.423e+01  2.886e+02   22.99 0.00928 **sexorHOM:selfattr     1.160e+02 -1.141e+02 3.707e+02   394.74 0.28495   sexorOT:selfattr      1.006e+02 -8.528e+01 3.050e+02   305.50 0.24577   sexorHOM:partnerattr  1.231e+02 -1.246e+02 3.990e+02   415.43 0.31072   sexorOT:partnerattr  -1.401e+00 -2.007e+02  1.956e+02 9700.00 0.99237   selfattr:partnerattr  5.483e+00 -6.017e+01 7.207e+01  3007.45 0.85464   ---Signif. codes:  0‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1  Cutpoints:                           post.mean l-95% CI u-95% CI eff.sampcutpoint.traitnatapshort.1     235.2   62.34    376.2    8.822cutpoint.traitnatapshort.2     633.4  202.16    944.0    3.578cutpoint.traitnatapshort.3   1139.5   364.35   1683.7   5.832cutpoint.traitnataplong.1      293.4   54.85    433.7    5.203cutpoint.traitnataplong.2      651.8  223.70    961.6    2.604cutpoint.traitnataplong.3    1023.1   344.82   1483.0   2.353
   
So, my question is: in that summary, where are the effect sizes, are they the "post. mean" column? And have they been transformed in some way? Because obviously, for response variables that can only take values 1,2,3,4 or 5, I would expect to see those as the effect size. 
Also, is there any way of knowing to what extent are those results due to each specific response variable, and the degree of covariance between both? Is it possible to get all that information from that summary output I have copied above?
   Thank you very much.   Iker

__________________________________________________________________

   Iker Vaquero-Alba
   Visiting Postdoctoral Research Associate
   Laboratory of Evolutionary Ecology of Adaptations 
   Joseph Banks Laboratories
   School of Life Sciences
   University of Lincoln   Brayford Campus, Lincoln
   LN6 7DL
   United Kingdom

   https://eric.exeter.ac.uk/repository/handle/10036/3381


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