#Bayesian Analysis Module II examples:

library("BayesFactor")

#t-test
  #Data formatting
data(sleep)
diffScores <- sleep$extra[1:10] - sleep$extra[11:20]
  
  #Standard
t.test(diffScores)

  #Bayes
bf_t <- ttestBF(x = diffScores)
bf_t #alternative model
1/bf_t #null model

  #Chains
chains <-posterior(bf_t, iterations=1000)
summary(chains)
chains2 <- recompute(chains, iterations = 10000)
plot(chains2[,1:2])

  #Multiple
bfInterval <- ttestBF(x = diffScores, nullInterval=c(-Inf,0))
allbf <- c(bf_t, bfInterval)
allbf
plot(allbf)
#------------------------------------------------------------------------------;

#ANOVA
  #Data formatting
plot(chickwts$weight~chickwts$feed)

  #Standard
summary(aov(weight~feed, data=chickwts))
  
  #Bayes
bf_a <-anovaBF(weight~feed, data=chickwts)
bf_a

  #Chains
chains<-posterior(bf_a, iterations=1000)
summary(chains)
plot(chains[,2:7])
#------------------------------------------------------------------------------;

#Simple Linear Regression
  #Data formatting
data(attitude)
par(mfrow=c(1,1))
plot(x=attitude$complaints, y=attitude$rating)

  #Standard
lm1 = lm(rating ~ complaints, data = attitude)
summary(lm1)

  #Bayes
bf_r <-regressionBF(rating ~ complaints, data=attitude)
bf_r

  #Chains
chains<-posterior(bf_r, iterations=1000)
summary(chains)
#------------------------------------------------------------------------------;

#Multiple Linear Regression
  #Data formatting
data(attitude)

  #Standard
lm2 = lm(rating ~ ., data = attitude)
summary(lm2)

  #Bayes
bf_r2 <-regressionBF(rating ~ ., data=attitude)
length(bf_r2)
head(bf_r2, n=6)

  #Compare 5 models to best
bf_r2.2 <- head(bf_r2) / max(bf_r2)
bf_r2.2
plot(bf_r2.2)