R help - Jul 2009 - MCMCpack: Selecting a better model using BayesFactor

Dear R users,
 
Thanks in advance.

I am Deb, Statistician at NSW Department of Commerce, Sydney.
 
I am using R 2.9.1 on Windows XP.
 
This has reference to the package “MCMCpack”.  My objective is to
select a better model using various alternatives. I have provided here
an example code from MCMCpack.pdf.
 
The matrix of Bayes Factors is:

            model1 model2 model3
model1    1.000   14.08    7.289
model2    0.071    1.00    0.518
model3    0.137    1.93    1.000
> PostProbMod(BF)
    model1     model2     model3 
0.82766865 0.05878317 0.11354819 
 
I need assistance to interpret the results. If I am wrong, please
correct me.
 
1. By looking at the matrix of Bayes Factors, Can I say that model1 is
better then the other models. Because Bayes Factor for Model1 relative
to Model2 is 14.08 > Bayes Factor for Model1 relative to Model3 is
7.289.
 
2. By looking at the values for PostProbMod(BF), Can I say that model1
is better then the other models because the posterior probability is
higher for model1 (0.83 approximately) than the other models.
 
3. Overall, by looking at the values for PostProbMod(BF), one can say
that higher posterior probability indicates the better model.
 
Once again, thank you very much for the time you have given.
 
I am looking forward for your reply.
 
Regards,
 
Deb

R Code:
 
library(MCMCpack)
data(birthwt)
model1 <- MCMCregress(bwt~age+lwt+as.factor(race) + smoke + ht,
data=birthwt,
b0=c(2700, 0, 0, -500, -500, -500, -500),
B0=c(1e-6, .01, .01, 1.6e-5, 1.6e-5, 1.6e-5,
1.6e-5), c0=10, d0=4500000,
marginal.likelihood="Chib95", mcmc=50000)
model2 <- MCMCregress(bwt~age+lwt+as.factor(race) + smoke,
data=birthwt,
b0=c(2700, 0, 0, -500, -500, -500),
B0=c(1e-6, .01, .01, 1.6e-5, 1.6e-5, 1.6e-5),
c0=10, d0=4500000,
marginal.likelihood="Chib95", mcmc=50000)
model3 <- MCMCregress(bwt~as.factor(race) + smoke + ht,
data=birthwt,
b0=c(2700, -500, -500, -500, -500),
B0=c(1e-6, 1.6e-5, 1.6e-5, 1.6e-5,
1.6e-5), c0=10, d0=4500000,
marginal.likelihood="Chib95", mcmc=50000)
BF <- BayesFactor(model1, model2, model3)
BF
PostProbMod(BF)
 


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