# Problem 1
#
# assume the data is in a matrix named "fla"
#
# part (a)
model1 <- lm(fla$bush04 ~ fla$etouch)
summary(model1)
#
# part (b)
index <- c(1:67)
trt.ix <- index[fla$etouch == 1]
ctl.ix <- index[fla$etouch == 0]
ntrt <- length(trt.ix)
nctl <- length(ctl.ix)
covbal <- matrix(0, 13, 3)
for (k in (4:16)) {
   sp <- sqrt(((ntrt-1)*var(fla[trt.ix,k]) + (nctl-1)*var(fla[ctl.ix,k])) / (ntrt + nctl - 2))
   covbal[k-3,] <- c(mean(fla[trt.ix,k]), mean(fla[ctl.ix,k]), (mean(fla[trt.ix,k]) - mean(fla[ctl.ix,k])) / sp)
   }
covbal
#
# part (c)
model2 <- lm(fla$bush04 ~ fla$etouch + fla$votePer96.rep + fla$votePer00.rep + fla$regPer00.rep + fla$turnout00)
summary(model2)
#
# part (d)
model3 <- lm(fla$bush04 ~ fla$etouch + fla$votePer96.rep + fla$votePer00.rep + fla$hisp00 + fla$white00 + fla$black00)
summary(model3)
model4 <- lm(fla$bush04 ~ fla$etouch + fla$votePer96.rep + fla$votePer00.rep + fla$hisp00 + fla$black00 + fla$lowEduc00 + fla$foreignBorn00)
summary(model4)


# Problem 2
# 
# part (a)
index <- c(1:67)
trt.ix <- index[fla$etouch == 1]
ctl.ix <- index[fla$etouch == 0]
ntrt <- length(trt.ix)
nctl <- length(ctl.ix)
#
# write distance function - here computes absolute diff between
# percent registered republican in the two cases
distance <- function(x,y) {abs(x[,10]-y[,10])}
#
# compute distance matrix between each treatment unit and all controls
dis <- matrix(0, ntrt, nctl)
for (i in (1:ntrt)) {
   for (j in (1:nctl)) { 
      dis[i,j]  <- distance(fla[trt.ix[i],],fla[ctl.ix[j],])
      }}
#
# find matches (note: to get matching without replacement I have
# set distances to a very large number after using a control)
matches <- matrix(0,length(trt),3)
for (i in (1:length(trt))) {
   dist <- dis[i,]
   match.ix <- which(dist == min(dist))
   matches[i,] <- c(trt.ix[i], ctl.ix[match.ix], min(dist)) 
   dis[,match.ix] <- 999999
   }
matches
#
# part (b)
covbal <- matrix(0, 13, 3)
for (k in (4:16)) {
   sp <- sqrt(((ntrt-1)*var(fla[matches[,1],k]) + (ntrt-1)*var(fla[matches[,2],k])) / (ntrt + ntrt - 2))
   covbal[k-3,] <- c(mean(fla[matches[,1],k]), mean(fla[matches[,2],k]), (mean(fla[matches[,1],k]) - mean(fla[matches[,2],k])) / sp)
   }
covbal
#
# part (c)
diffs1 <- fla$bush04[matches[,1]] - fla$bush04[matches[,2]]
treat1 <- mean(diffs1)
stderr1 <- sqrt(var(diffs1)/ntrt)
c(treat1,stderr1)
#
# part (d)
z <- matches[,3] < .01
diffs2 <- fla$bush04[matches[z,1]] - fla$bush04[matches[z,2]]
treat2 <- mean(diffs2)
stderr2 <- sqrt(var(diffs2)/sum(z))
c(treat2,stderr2, sum(z))
z <- matches[,3] < .005
diffs3 <- fla$bush04[matches[z,1]] - fla$bush04[matches[z,2]]
treat3 <- mean(diffs3)
stderr3 <- sqrt(var(diffs3)/sum(z))
c(treat3,stderr3, sum(z))
#
# part (e)  (define new distance function and then repeat above steps; only 
#         modification required is to part (d) where I used 25 and 12 as cuts)
vtrt <- var(fla[trt.ix,4:16])
vctl <- var(fla[ctl.ix,4:16])
v <- (ntrt*vtrt + nctl*vctl) / (ntrt + nctl)
distance <- function(x,y) {
    zz <- x[,4:16]-y[,4:16]
    dim(zz) <- c(13,1)
    zz <- t(zz)
    t(zz)%*%solve(v)%*%zz
    }