Here a new attempt in trying to improve the visual of my request:
I'm running a bayesian regression using the package MCMCglmm (Hadfield 2010)
and to reach a normal posterior distribution of estimates, I increased the
number of iteration as well as the burnin threshold. However, it had unexpected
outcomes. Although it improved posterior distribution, it also increased
dramatically the value of estimates and decrease DIC.
Here an example:
>head(spring)
pres large_road small_road cab
0 2011 32 78
1 102 179 204
0 1256 654 984
1 187 986 756
0 21 438 57
1 13 5 439
>#pres is presence/absence data and other variable are distance to these
>features
>## with 200,000 iteration and 30,000 burnin
>prior <- list(R = list(V = 1, nu=0.002))
>sp.simple <- MCMCglmm(pres ~ large_road + cab + small_road, family =
>"categorical", nitt = 200000, thin = 200, burnin = 30000,
data = spring, prior = prior, verbose = FALSE, pr = TRUE)
>summary(sp.simple)
Iterations = 30001:199801
Thinning interval = 200
Sample size = 850
DIC: 14045.31
R-structure: ~units
post.mean l-95% CI u-95% CI eff.samp
units 294.7 1.621 621.9 1.982
Location effects: pres ~ large_road + cab + small_road
post.mean l-95% CI u-95% CI eff.samp pMCMC
(Intercept) 5.76781 0.77622 9.24375 1.829 <0.001 **
large_road 0.37487 0.02692 0.75282 3.310 <0.001 **
cab 0.94639 0.09906 1.57939 2.096 <0.001 **
small_raod -1.62192 -2.60873 -0.20191 2.002 <0.001 **
>## with 1,000,000 iteration and 500,000 burnin
>prior <- list(R = list(V = 1, nu=0.002))
>sp.simple <- MCMCglmm(pres ~ large_road + cab + small_road, family =
>"categorical", nitt = 1000000, thin = 200, burnin = 500000,
data = spring, prior = prior, verbose = FALSE, pr = TRUE)
>summary(sp.simple)
Iterations = 500001:999801
Thinning interval = 200
Sample size = 2500
DIC: 858.6316
R-structure: ~units
post.mean l-95% CI u-95% CI eff.samp
units 26764 17548 34226 124.5
Location effects: pres ~ large_road + cab + small_road
post.mean l-95% CI u-95% CI eff.samp pMCMC
(Intercept) 60.033 47.360 70.042 137.9 <4e-04 ***
large_road 3.977 1.279 6.616 1484.6 0.0080 **
cab 9.913 6.761 13.020 333.7 <4e-04 ***
small_raod -16.945 -20.694 -13.492 194.9 <4e-04 ***
I'm then wandering if it is because more iteration produce better estimates and
then a model that had a better fit with the data.
Anyone can help me?
Rémi Lesmerises
Université du Québec à Rimouski
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