# R script for part 4

# ladder of powers and roots

postscript("transformations-ladder.ps",horizontal=FALSE)

# create vector of x-coordinates
x <- seq(from=0,to=4,by=.01)

# Use the command 'plot' to plot the first line. 
#   type = what type of plot should be drawn ("l" stands for lines)
#   lty = line type, lwd = line width, ylim = range on y-axis
plot(x, (x^(-1)-1)/(-1), col=1, lty=1, lwd=2, type="l", ylim=c(-4,6), 
main="Family of powers and roots",xlab="x", ylab="x^{(p)}")

# Use the command 'lines' to add the other lines to the plot
lines(x, log(x), col=2, lty=2, lwd=2)
lines(x, (x-1)/1, col=3, lty=3, lwd=2)
lines(x, (x^2-1)/2, col=4, lty=4, lwd=2)
lines(x, (x^3-1)/3, col=5, lty=5, lwd=2)

# Add a legend:
legend(0,6,c("p=-1", "p=0 (log)", "p=1", "p=2", "p=3"), col=c(1,2,3,4,5), 
       lty=c(1,2,3,4,5), lwd=2)

dev.off()

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# negative values -> use positive start

postscript("transformations-NegativeValues.ps", horizontal=FALSE)

# subsequent figures will be drawn in a 2 x 1 array
par(mfrow=c(2,1))

x <- seq(from=-2, to=2, by=.01)
plot(x,x^2,type="l",lwd=2,
     main="Negative values give nonmonotone transformation")
plot(x,(x+3)^2,type="l",lwd=2,main="Solution: use a positive 'start'")
dev.off()

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# ratio of larges to smallest value close to 1 -> use negative start

postscript("transformations-RatioCloseTo1.ps", horizontal=FALSE)
par(mfrow=c(2,1))
x <- seq(from=1991,to=1995, by=.01)
plot(x,log(x),type="l", lwd=2, 
  main="If the ratio between the largest and smallest value is close to 1, 
  then the power tranformations are almost linear and hence ineffective")
plot(x,log(x-1990), type="l", lwd=2, main="Solution: use a negative 'start'")
dev.off()

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# transforming skewness

library(car)
library(Hmisc)  # needed to add tick marks to histograms
data(Angell)
attach(Angell)

hist(mobility,probability=TRUE)
scat1d(mobility,side=1)
lines(density(mobility))

hist(log(mobility),probability=TRUE)
scat1d(log(mobility),side=1)
lines(density(log(mobility)))

hist(sqrt(mobility),probability=TRUE)
scat1d(sqrt(mobility),side=1)
lines(density(sqrt(mobility)))

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# transforming nonlinearity

data(Leinhardt)
attach(Leinhardt)
?Leinhardt
summary(Leinhardt)

# remove observations with missing values
# '!' stand for not
# is.na(..) indicates which elements are missing
# we only take the rows for which infant mortality is not missing
cleaned <- Leinhardt[!is.na(infant),]
attach(cleaned)

plot(income, infant, xlab="Per-capita income in U.S. dollars", 
     ylab="Infant mortality rate per 1,000")
lines(loess.smooth(income, infant), col="red", lwd=2)

plot(log(income),log(infant),xlab="Log(per-capita income)", 
     ylab="Log(infant mortality)")
lines(loess.smooth(log(income),log(infant)), col="red", lwd=2)