[R-sig-ME] Interpreting posterior mean and effective sample size

[Iker Vaquero Alba]

   Hello everyone,
   I would just like to ask some questions about the interpretation of the results of an MCMCglmm model. There is not so much information about that specific topic out there, after all!
   This is my model:
   extphenmodel5t<-MCMCglmm(cbind(appcareshort,appcarelong)~trait-1+trait:gender+trait:age+trait:religion+trait:sexor+trait:selfattr+trait:partnerattr+trait:gender:age+trait:gender:religion+trait:gender:sexor+trait:gender:selfattr+trait:gender:partnerattr+trait:age:religion+trait:age:sexor+trait:age:selfattr+trait:age:partnerattr+trait:religion:sexor+trait:religion:selfattr+trait:religion:partnerattr+trait:sexor:selfattr+trait:sexor:partnerattr+trait:selfattr:partnerattr,random=NULL,rcov=~corg(trait):units,family=c("threshold","threshold"),data=extphen,nitt=100000,singular.ok=TRUE)
   And my results (a small part of them, the significant p was just made up for the sake of the question):
   > summary(extphenmodel5t)  Iterations = 3001:99991 Thinning interval  = 10 Sample size  = 9700   DIC:   R-structure:  ~corg(trait):units                                           post.mean l-95% CI u-95% CI eff.samptraitappcareshort:traitappcareshort.units    1.0000   1.0000   1.0000        0traitappcarelong:traitappcareshort.units     0.7409   0.6613   0.8096     7274traitappcareshort:traitappcarelong.units     0.7409   0.6613   0.8096     7274traitappcarelong:traitappcarelong.units      1.0000   1.0000   1.0000        0  Location effects: cbind(appcareshort, appcarelong) ~ trait - 1 + trait:gender + trait:age + trait:religion + trait:sexor + trait:selfattr + trait:partnerattr + trait:gender:age + trait:gender:religion + trait:gender:sexor + trait:gender:selfattr + trait:gender:partnerattr + trait:age:religion + trait:age:sexor + trait:age:selfattr + trait:age:partnerattr + trait:religion:sexor + trait:religion:selfattr + trait:religion:partnerattr + trait:sexor:selfattr + trait:sexor:partnerattr + trait:selfattr:partnerattr                                           post.mean   l-95% CI   u-95% CI  eff.samp  pMCMC    traitappcareshort                        3.242e+00 -3.209e+00  9.638e+00  9201.037 0.3247    traitappcarelong                         3.700e+00 -2.789e+00  1.034e+01  8610.520 0.2625    traitappcareshort:genderM               -1.128e-01 -2.526e+00  2.356e+00  9113.094 0.009**    traitappcarelong:genderM                 1.273e-01 -2.270e+00  2.663e+00  8641.121 0.9243    traitappcareshort:genderO                1.005e+03 -1.787e+05  1.873e+05  9700.000 0.9872    traitappcarelong:genderO                -2.177e+03 -1.895e+05  1.855e+05 10368.220 0.9839    traitappcareshort:age                   -7.331e-01 -3.681e+00  2.267e+00 10202.025 0.6200    traitappcarelong:age                    -1.433e+00 -4.507e+00  1.571e+00  8834.924 0.3546    traitappcareshort:religionY             -2.229e+00 -5.144e+00  6.142e-01  9157.812 0.1214    traitappcarelong:religionY:sexorOT       1.087e+02  5.110e+00  1.925e+02     1.404 <1e-04 ***    



   My first question is about the posterior mean. Could we somehow interpret it (with all the possible cautions and if you allow me) as kind of an effect size of each predictor? I mean, for example, the intercept for "appcareshort" (score from 1 to 5 given by participants in a survey to the attractiveness in a potential partner of appearance care for a short, casual relationship) is 3.242. So, is, for example, the effect of gender M on "appcareshort" more negative than the intercept? Or in other words, do male participants in the survey value care of appearance in potential partners significantly less than people of other gender?

   And my second question: as far as I can understand, the effective sample size is the number of iterations that MCMCglmm actually stores, and from which it "constructs" the posterior distribution. In this case, the total number of iterations was 100,000 and effective sample was always around 10,000 (which makes sense given that thin=10). My doubt is in that predictor with an effective sample size of 1.404. My experience tells me that when I plot the model for diagnostic purposes, that very predictor is going to show a clear lack of convergence. I would just like to ask whether I am right in what effective sample size means, what is the difference between the sample size (9700) and the effective sample size of the predictors, and how it's possible an effective sample size of 10,202 with 100,000 iterations and thin=10.

   Thank you very much in advance to everyone.

   Kind regards,
   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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