OpenBUGS-txt-study-guide-4a-Fa16.txt

# #SDS 384.7    Study Guide # 4a     Fall 2016 
# Building a Bayesian Model in OpenBUGS
# Bayesian Inferences after Fitting a Normal Linear 
# Regression, with INTERACTION TERMS.
# Data Source: Forced Expiratory Volume (FEV) Data, 
# as introduced on page 162 of CJBH Text 

model{
for(i in 1:n){
	FEV[i] ~ dnorm(mu[i],tau)
	mu[i] <- beta[1] + beta[2]*Age[i] + beta[3]*Smoke[i]  + beta[4]*Age[i]*Smoke[i]}

 # Diffuse prior
beta[1] ~ dnorm(0,0.001) 
beta[2] ~ dnorm(0,0.001)
beta[3] ~ dnorm(0,0.001)
beta[4] ~ dnorm(0,0.001)
tau ~ dgamma(0.01,0.001)

## Estimate mean FEV for smokers and nonsmokers who are 10, ..., 19 years old
for(i in 1:10){
meanFEVs[i] <-  beta[1] + beta[3] + (i+9)*(beta[2]+beta[4])
meanFEVns[i] <-  beta[1] + (i+9)*beta[2]}

## Estimate certain mean differences 
MD11 <-  meanFEVs[2]-meanFEVns[2] ## MD comparing 11 year old smoker to 11 year old nonsmoker
MD17 <-  meanFEVs[8]-meanFEVns[8] ## MD comparing 17 year old smoker to 17 year old nonsmoker

## Predict the FEV for a 20 year old smoker and nonsmoker
FEV20s ~ dnorm(mu20s,tau)
FEV20ns ~ dnorm(mu20ns,tau)
mu20s <-  beta[1] +  beta[3] + 20*(beta[2]+beta[4]) 
mu20ns <-  beta[1] + 20*beta[2] 

## Test H0: beta4 < 0
post.prob1 <- step(-beta[4])

## Test H0: beta2 + beta4 > 0
post.prob2 <- step(beta[2]+beta[4])

# Monitor DIC separately from Inference > DIC menu
}