## code to accompany the binomial GLM slides
## from lecture 16 of PSTAT 215A, Bayesian Inference, UCSB
##
## Robert B. Gramacy

## logit is in the boot library
library(boot)

## plot g(mu) for mu in [0,1]
mu <- seq(0,1,length=100)

## plot the canonical logit link
y.logit <- logit(mu)
plot(mu, y.logit, type="l", lwd=2,
     main="Binomal GLM Link Functions",
     ylab="t(x) %*% beta", xlab="theta_x", bty="n")

## plot the probit link
y.probit <- qnorm(mu)
lines(mu, y.probit, lwd=2, lty=2, col=2)

## plot the complimentary log=log link
y.cll <- log(-log(1-mu))
lines(mu, y.cll, lwd=2, lty=3, col=3)

## add a descriptive legend
legend("topleft", c("logit", "probit", "cloglog"),
       lwd=2, lty=1:3, col=1:3, bty="n")