# Exercise 5.2 in Pinheiro & Bates, 2000

library(nlme)
data(Oats)

# (a)
fm4Oats <- lme(yield~nitro, data=Oats, random=~1|Block/Variety)
fm4Oats.cor1 <- update(fm4Oats, random=~1|Block, corr=corSymm(form=~1|Block/Variety))
summary(fm4Oats.cor1)

# (b)
intervals(fm4Oats.cor1)
fm4Oats.cor2 <- update(fm4Oats.cor1, correlation=corCompSymm(form=~1|Block/Variety))
anova(fm4Oats.cor1,fm4Oats.cor2)
summary(fm1BW.lme.het)

# (c)
summary(fm4Oats)
summary(fm4Oats.cor2)
sqrt(11.00500^2+12.8669^2) # within-block variance
11.00500^2/(11.00500^2+12.8669^2) # within-wholeplot variance

# (d)
fm4Oats.cor3 <- gls(yield~nitro, data=Oats, corr=corCompSymm(form=~1|Block/Variety))
summary(fm4Oats.cor3)
anova(fm4Oats.cor2,fm4Oats.cor3)