marketing action optimization with binomial test and frontier curve

input.csv

test.R

library(ggplot2)

input <- read.csv("input.csv",header=T)

ctr <- data.frame()
for (i in 1:nrow(input)) {
  r<-input[i,]
  bt1 <- binom.test(r$Clk,r$Imp,conf.level=0.80)
  bt2 <- binom.test(r$Clk,r$Imp,conf.level=0.95)
  p <- bt1$estimate
  conf1 <- bt1$conf.int
  conf2 <- bt2$conf.int
  p_var <- p*(1-p)/r$Imp
  tmp <- data.frame(CTR=p,CTRvar=p_var,
                    CTR11=conf1[1],CTR12=conf1[2],
                    CTR21=conf2[1],CTR22=conf2[2])
  ctr <- rbind(ctr,tmp)
}
input <- cbind(input,ctr)

g <- ggplot(
  input,
  aes (
    x = Ad,
    middle = CTR,
    ymin = CTR21,
    ymax = CTR22,
    lower = CTR11,
    upper = CTR12,
    color = Ad
  )
)

ymin <- min(input$CTR21)
ymax <- max(input$CTR22)

# relaxing ylim
margin <- (ymax-ymin)/5
ymin <- max(0,ymin-margin)
ymax <- min(1,ymax+margin)

g <- g+geom_boxplot(stat="identity")
g <- g+coord_cartesian(ylim=c(ymin,ymax))

png("bar.png")
plot(g)
dev.off()

V <- diag(input$CTRvar)
V1 <- V
V1 <- rbind(V1,0)
V1 <- rbind(V1,0)
V1 <- cbind(V1,0)
V1 <- cbind(V1,0)

N <- nrow(input)
V1[N+1,1:N] <- input$CTR
V1[N+2,1:N] <- 1
V1[1:N,N+1] <- -input$CTR
V1[1:N,N+2] <- -1

x <- c()
y <- c()
for (r in seq(ymin,ymax,length.out=100)) {
  bvec <- c(rep(0,N),r,1)
  wvec <- solve(V1,bvec)
  w <- wvec[1:N]
  if (all(w>=0)) {
    x1 <- sqrt(t(w) %*% V %*% w)
    x <- c(x,x1)
    y <- c(y,r)
    out <- c(r,x1,w*100)
    names(out) <- c('CTR','CTR_sd',paste(input$Ad,'_weight(%)',sep=''))
    print(out)
  }
} 

png("frontier.png")
plot(x,y,type="p",xlab="CTR_sd",ylab="CTR")
lines(x,y)
dev.off()