some R code for conference #5

### conf #5

library("arm")

###########
### 5.5 ###
###########

### a

# plot of invlogit
curve(invlogit(x), from=-10, to=10)

# plot of invlogit(-24 +.4*x) with different ranges of x
curve(invlogit(-24 +.4*x), from=0, to=100)
curve(invlogit(-24 +.4*x), from=45, to=75)
curve(invlogit(-24 +.4*x), from=30, to=90)

midterm <- rnorm(50, mean=60, sd=15)
midterm <- ifelse(midterm<0, 0, ifelse(midterm>100, 100, midterm))

jitter.binary <- function(a, jitt=.05){
ifelse(a==0, runif(length(a), 0, jitt), runif(length(a), 1-jitt, 1))
}

# generate consistent final results using the model and midterm results
# do not just use the predicted value...
final.bad <- ifelse(invlogit(-24 + .4*midterm)>.5, 1, 0)
final.good <- rbinom(length(midterm), 1, invlogit(-24 + .4*midterm))

# little test to check the syntax above
# test <- c(rep(.1,100),rep(.9,100))
# rbinom(length(test), 1, test)

plot(midterm,jitter.binary(final.good), cex=.25)
curve(invlogit(-24 + .4*x), add=T)
abline(v=60)

plot(midterm,jitter.binary(final.bad), cex=.25)
curve(invlogit(-24 + .4*x), add=T)
abline(v=60)

### b








# test the transformation
logit1 <- glm(final.good ~ midterm, family=binomial(link="logit"))
display(logit1)

midterm.cs <- (midterm-mean(midterm))/sd(midterm)
logit2 <- glm(final.good ~ midterm.cs, family=binomial(link="logit"))
display(logit2)

### c
newpred <- rnorm(length(midterm), 0, 1)
logit3 <- glm(final.good ~ midterm + newpred, family=binomial(link="logit"))
display(logit3)

###########
### 5.6 ###
###########

curve(dlogis(x), from=-6, to=6)

curve(dlogis(x, location=4.5), from=-2, to=11)
abline(h=0)
#abline(v=0)
polygon(c(0,seq(0,12, length=100),12), c(0,dlogis(seq(0,12, length=100), location=4.5),0), col="grey")
polygon(c(0,seq(0,12, length=10),12), c(0,dlogis(seq(0,12, length=10), location=4.5),0), col="grey")