# Exercise 4.11 in Davis, 2002
# Continuation of Exercises 2.3 and 3.11

week <- c(0,2,4,6,8,10,12,14,16,18,19)
m <- matrix(scan("c:\\data.ext\\davis\\kenward.dat"),ncol=13,byrow=T)
group <- m[,1]
calf <- m[,2]
y <- m[,3:13]

# (a) test for linearity using divided differences
c <- matrix(0,nrow=9,ncol=11)
d <- c()
for (i in 1:10) d=c(d,1/(week[i+1]-week[i]))
for (i in 1:9) {
  c[i,i] <- -d[i]
  c[i,i+1] <- d[i]+d[i+1]
  c[i,i+2] <- -d[i+1]
  }
nlinddiff <- y %*% t(c)
summary(manova(nlinddiff~as.factor(group)-1),test="Wilk")
group1 <- 2-group
group2 <- group-1
summary(manova(nlinddiff~group1+group2-1),test="Wilk")

# (b) growth curve analysis, orthogonal (orthonormal) T
orth <- poly(week,10)
t <- matrix(c(rep(sqrt(1/11),11),orth),nrow=11,ncol=11,byrow=TRUE)
z <- y %*% t(t)
summary.aov(manova(z~as.factor(group)-1)) # combined groups
summary.aov(manova(z~group1+group2-1))    # separate groups
summary(manova(z[,10:11]~as.factor(group)-1),test="Wilk") # combined order 10-11
summary(manova(z[,9:11]~as.factor(group)-1),test="Wilk") # combined order 9-11
summary(manova(z[,8:11]~as.factor(group)-1),test="Wilk") # combined order 8-11
summary(manova(z[,7:11]~as.factor(group)-1),test="Wilk") # combined order 7-11
summary(manova(z[,6:11]~as.factor(group)-1),test="Wilk") # combined order 6-11

# (c)
# The growth curve approach is not useful for these data, due to the high order
# significant effects.