R: Making sense of the output of a MCMCglmm

Question

I performed a MCMCglmm (MCMCglmm package). Here is the summary of this model

 Iterations = 3001:12991
 Thinning interval  = 10
 Sample size  = 1000 

 DIC: 211.0108 

 G-structure:  ~Region

       post.mean  l-95% CI u-95% CI eff.samp
Region    0.2164 5.163e-17    0.358     1000

 R-structure:  ~units

      post.mean l-95% CI u-95% CI eff.samp
units    0.5529   0.1808    1.045    449.3

 Location effects: Abondance ~ Human_impact/Fish.sp 

                                   post.mean  l-95% CI  u-95% CI eff.samp  pMCMC    
(Intercept)                         1.335628  0.780363  1.907249    642.4  0.004 ** 
Human_impact                        0.005781 -0.294084  0.347743    876.6  0.914    
Human_impact:Fish.spA. perideraion -0.782846 -1.158798 -0.399131    649.9 <0.001 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

1. Where are the coefficients?
2. post.mean is the mean of the posterior distribution?
3. Can post.mean be somehow considered as the equivalent of the estimates of a standard lm
4. What does eff.samp mean?
5. How can I find the degrees of freedom?
6. This model is based on bayesian statistics. Is it correct?

Answer 1

You can use summary.MCMCglmm from MCMCglmm package

summary method for class "MCMCglmm". The returned object is suitable for printing with the print.summary.MCMCglmm method.

DIC Deviance Information Criterion

fixed.formula model formula for the fixed terms

random.formula model formula for the random terms

residual.formula model formula for the residual terms

solutions posterior mean, 95% HPD interval, MCMC p-values and effective sample size of fixed (and random) effects

Gcovariances posterior mean, 95% HPD interval and effective sample size of random effect (co)variance components

Rcovariances posterior mean, 95% HPD interval and effective sample size of residual (co)variance components

cutpoints posterior mean, 95% HPD interval and effective sample size of cut-points from an ordinal model

csats chain length, burn-in and thinning interval

Gterms indexes random effect (co)variances by the component terms defined in the random formula

I am under the impression that MCMCglmm does not implement a "true" Bayesian glmmm. Similarly to the frequentist model, one has g(E(y∣u))=Xβ+Zu and there is a prior required on the dispersion parameter ϕ1 in addition to the fixed parameters β and the "G" variance of the random effect u.

But according to this MCMCglmm vignette, the model implemented in MCMCglmm is given by g(E(y∣u,e))=Xβ+Zu+e , and it does not involve the dispersion parameter ϕ1. It is not similar to the classical frequentist model.

Degree of Freedom
mcmcglmm is a wrapper for the MCMCglmm() function. The wrapper function allows for two variants of two defualt priors on the covariance matrices. The two defaults are InvW for an inverse- Wishart prior, which sets the degrees of freedom parameter equal to the dimension of each covariance matrix, and InvG for an inverse-Gamma prior, which sets the degrees of freedom parameter to 0.002 more than one less than the dimensions of the covariance matrix.