Model Selection with Bayesian Methods and Information Criteria
# Install mombf from CRAN
install.packages("mombf")
# from GitHub:
# install.packages("devtools")
devtools::install_github("davidrusi/mombf")The main Bayesian model selection (BMS) function is modelSelection. For information criteria
consider bestBIC, bestEBIC, bestAIC, bestIC.
Bayesian model averaging (BMA) is also available for some models,
mainly linear and generalized linear models.
Local variable selection is implemented in localnulltest and localnulltest_fda.
Details are in mombf's vignette,
here we illustrate quickly how to get posterior model probabilities,
marginal posterior inclusion probabilities, BMA point estimates and posterior
intervals for the regression coefficients and predicted outcomes.
library(mombf)
set.seed(1234)
x <- matrix(rnorm(100*3),nrow=100,ncol=3)
theta <- matrix(c(1,1,0),ncol=1)
y <- x %*% theta + rnorm(100)
priorCoef <- momprior(tau=0.348) # Default MOM prior on parameters
priorModel <- modelbbprior(1,1) # Beta-Binomial prior for model space
fit1 <- modelSelection(y ~ x[,1]+x[,2]+x[,3], priorCoef=priorCoef, priorModel=priorModel)
# Output
# Enumerating models...
# Computing posterior probabilities................ Done.from here, we can also get the posterior model probabilities:
postProb(fit1)
# Output
# modelid family pp
# 7 2,3 normal 9.854873e-01
# 8 2,3,4 normal 7.597369e-03
# 15 1,2,3 normal 6.771575e-03
# 16 1,2,3,4 normal 1.437990e-04
# 3 3 normal 3.240602e-17
# 5 2 normal 7.292230e-18
# 4 3,4 normal 2.150174e-19
# 11 1,3 normal 9.892869e-20
# 6 2,4 normal 5.615517e-20
# 13 1,2 normal 2.226164e-20
# 12 1,3,4 normal 1.477780e-21
# 14 1,2,4 normal 3.859388e-22
# 1 normal 2.409908e-25
# 2 4 normal 1.300748e-27
# 9 1 normal 2.757778e-28
# 10 1,4 normal 3.971521e-30also the BMA estimates, 95% intervals, marginal posterior probability
coef(fit1)
# Output
# estimate 2.5% 97.5% margpp
# (Intercept) 0.007230966 -0.02624289 0.04085951 0.006915374
# x[, 1] 1.134700387 0.93487948 1.33599873 1.000000000
# x[, 2] 1.135810652 0.94075622 1.33621298 1.000000000
# x[, 3] 0.000263446 0.00000000 0.00000000 0.007741168
# phi 1.100749637 0.83969879 1.44198567 1.000000000and BMA predictions for y, 95% intervals
ypred <- predict(fit1)
head(ypred)
# Output
# mean 2.5% 97.5%
# 1 -0.8936883 -1.1165154 -0.67003262
# 2 -0.2162846 -0.3509188 -0.08331286
# 3 1.3152329 1.0673711 1.56348261
# 4 -3.2299241 -3.6826696 -2.77728625
# 5 -0.4431820 -0.6501280 -0.23919345
# 6 0.7727824 0.6348189 0.90977798
cor(y, ypred[,1])
# Output
# [,1]
# [1,] 0.8468436Please submit bug reports to the issue tracker.