#  Here is an example of using the BMA model seleciton program

#  First, we will generate some data:

x<- rnorm(1000, mean=0, sd=4)
z<- rnorm(1000, mean=5, sd=20)
w<- rnorm(1000, mean=-3, sd=4)
y<- rnorm(1000, mean = 3*x + 2*z, sd=25)

#  Y will be our independent variable, and we will create a matrix for
#  the other variables as follows:

data.matrix <- matrix(c(x,w,z), byrow=F, nrow=1000)

#  Note that both x and z contribute to y, but not w.

#  Now run BMA program, which is downloadable from the R website in the
#  usual way (i.e., from R program, use the packages menu item, find
#  BMA, then download, and "load package")

#  There are many functions we can use, we will illustrate simple linear
#  regression model selection here using bicreg.

output<- bicreg(data.matrix, y)

output


# Call:
# bicreg(x = data.matrix, y = y)
#
#
# Posterior probabilities(%):
#   X1    X2    X3
# 100.0   6.8 100.0
#
# Coefficient posterior expected values:
# (Intercept)           X1           X2           X3
#    0.56763      3.19356     -0.01756      1.97760

#  We can also get some more info:

 output$postprob
[1] 0.93150804 0.06849196
output$namesx
[1] "X1" "X2" "X3"
output$label
[1] "X1X3"   "X1X2X3"
output$r2
 [1] 72.719 72.765
output$bic
 [1] -1285.164 -1279.944
output$size
 [1] 2 3
output$probne0
 [1] 100.0   6.8 100.0
output$postmean
 [1]  0.56762931  3.19355682 -0.01756048  1.97759807
output$postsd
 [1] 0.85994375 0.20177235 0.08305759 0.04085244
 output$ols
            Int       X1         X2       X3
[1,]  0.6194303 3.192800  0.0000000 1.977538
[2,] -0.1368776 3.203849 -0.2563875 1.978413
 output$se
          Int        X1        X2         X3
[1,] 0.824321 0.2017452 0.0000000 0.04085239
[2,] 1.011271 0.2018597 0.1987171 0.04084441