agridat (version 1.8.1)

box.cork: Weight of cork samples on four sides of trees

Description

The cork datagives the weights of cork borings of the trunk for 28 trees on the north (N), east (E), south (S) and west (W) directions.

source

C.R. Rao (1948) Tests of significance in multivariate analysis. Biometrika, 35, 58-79.

References

K.V. Mardia, J.T. Kent and J.M. Bibby (1979) Multivariate Analysis, Academic Press. Russell D Wolfinger, (1996). Heterogeneous Variance: Covariance Structures for Repeated Measures. Journal of Agricultural, Biological, and Environmental Statistics, 1, 205-230.

Examples

dat <- box.cork

pairs(dat[,2:5], xlim=c(25,100), ylim=c(25,100))

## Each tree is one line
require(plotrix)
radial.plot(dat[, 2:5], start=pi/2, rp.type='p', clockwise=TRUE,
            radial.lim=c(0,100),
            lwd=2, labels=c('North','East','South','West'),
            line.col=rep(c("royalblue","red","#009900","dark orange",
              "#999999","#a6761d","deep pink"), length=nrow(dat)))

require(reshape2)
dat$tree <- factor(dat$tree)
d2 <- melt(dat)
names(d2) <- c('tree','dir','y')

require(asreml)
d2 <- d2[order(d2$tree, d2$dir), ]

# Unstructured covariance matrix
m1 <- asreml(y~dir, data=d2, rcov=~tree:us(dir, init=rep(200,10)))
## Note: 'rcor' is a personal function to extract the correlation
## round(rcor(m1)$dir, 2)
##         N      E      S      W
##  N 290.41 223.75 288.44 226.27
##  E 223.75 219.93 229.06 171.37
##  S 288.44 229.06 350.00 259.54
##  W 226.27 171.37 259.54 226.00

# Factor Analytic with different specific variances
# Note: Wolfinger used a common diagonal variance
m2 <- update(m1, rcov=~tree:facv(dir,1))
## round(rcor(m2)$dir, 2)
##        N      E      S      W
## N 290.42 209.46 291.82 228.44
## E 209.46 219.95 232.85 182.28
## S 291.82 232.85 350.00 253.95
## W 228.44 182.28 253.95 225.99