### Week 7: Binary Dependent Variables
### Code from class


## MLE example
y <- c(0,1,1,0,1,1,0,1,1,1)
coin.mle <- function(y, pi) {
  lik <- pi^y * (1-pi)^(1-y)
  loglik <- log(lik)
  cat("prod L = ", prod(lik), ",  sum ln(L) = ", sum(loglik), "\n")
  (mle <- list(L=prod(lik), lnL=sum(loglik)))
}
ll <- numeric(9)
pi <- seq(.1,.9,.1)
for (i in 1:9) (ll[i] <- coin.mle(y, pi[i])$lnL)
par(mar=c(4,4,1,1))
plot(pi, ll, type="b", ylab="log-likelihood")

## show the functional forms
par(mar=c(3,4,2,1))
x <- seq(-6,6,.1)
plot(x,pnorm(x), type="l", col="red", ylab="Probability")
lines(x,(1/(1+exp(-x))), col="blue")
text(c(-2,-.25), c(.2,.2), c("Logit","Probit"), col=c("blue","red"))

## estimate logit and probit models in R
dail <- read.dta("dailcorrected.dta")
won.logit <- glm(wonseat ~ incumb*spend_total + electorate,
                 family=binomial(link="logit"), data=dail)
summary(won.logit)
won.probit <- glm(wonseat ~ incumb*spend_total + electorate,
                 family=binomial(link="probit"), data=dail)
summary(won.logit)$coeff
summary(won.probit)$coeff

## interpretation 1: fitted values
x <- seq(0,40000,5000)
bhat <- won.logit$coefficients
xfitted <- cbind(rep(1,length(x)), rep(0,length(x)), x, mean(dail$electorate),
                 rep(0,length(x)))
xbfitted <- xfitted %*% matrix(bhat,nrow=length(bhat))
pfitted <- 1/(1+exp(-xbfitted))
data.frame(Spend_Total=x,PrWin=pfitted)
              
## interpretation 2: graphical methods
x <- seq(0,40000,100)
bhat <- won.logit$coefficients
xfitted <- cbind(rep(1,length(x)), rep(0,length(x)), x, mean(dail$electorate),
                 rep(0,length(x)))
xbfitted <- xfitted %*% matrix(bhat,nrow=length(bhat))
pfitted <- 1/(1+exp(-xbfitted))
plot(x, pfitted, type="l",
     xlab="Total Spending", ylab="Probability of Winning a Seat")
abline(h=.5, col="red")

## interpretation 3: first differences
# students can do this for homework??