Weight of cork samples on four sides of trees

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

Format

Data frame with 28 observations on the following 5 variables.

tree

tree number

dir

direction N,E,S,W

y

weight of cork deposit (centigrams), north direction

Source

C.R. Rao (1948). Tests of significance in multivariate analysis. Biometrika, 35, 58-79. https://doi.org/10.2307/2332629

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

# \dontrun{

  library(agridat)
  data(box.cork)
  dat <- box.cork

  libs(reshape2, lattice)
  dat2 <- acast(dat, tree ~ dir, value.var='y')
  splom(dat2, pscales=3,
        prepanel.limits = function(x) c(25,100),
        main="box.cork", xlab="Cork yield on side of tree",
        panel=function(x,y,...){
          panel.splom(x,y,...)
          panel.abline(0,1,col="gray80")
        })


  ## Radial star plot, each tree is one line
  libs(plotrix)
  libs(reshape2)
  dat2 <- acast(dat, tree ~ dir, value.var='y')
  radial.plot(dat2, start=pi/2, rp.type='p', clockwise=TRUE,
              radial.lim=c(0,100), main="box.cork",
              lwd=2, labels=c('North','East','South','West'),
              line.col=rep(c("royalblue","red","#009900","dark orange",
                             "#999999","#a6761d","deep pink"),
                           length=nrow(dat2)))
  
  # asreml 4
  libs(asreml)

  # Unstructured covariance
  dat$dir <- factor(dat$dir)
  dat$tree <- factor(dat$tree)  
  dat <- dat[order(dat$tree, dat$dir), ]
  
  # Unstructured covariance matrix
  m1 <- asreml(y~dir, data=dat, residual = ~ tree:us(dir))
#> Model fitted using the sigma parameterization.
#> ASReml 4.1.0 Fri Dec 11 17:31:56 2020
#>           LogLik        Sigma2     DF     wall    cpu
#>  1      -307.529           1.0    108 17:31:56    0.0
#>  2      -300.714           1.0    108 17:31:56    0.0
#>  3      -294.337           1.0    108 17:31:56    0.0
#>  4      -291.522           1.0    108 17:31:56    0.0
#>  5      -290.967           1.0    108 17:31:56    0.0
#>  6      -290.959           1.0    108 17:31:56    0.0
    
  libs(lucid)
  vc(m1)
#>            effect component std.error z.ratio bound %ch
#>        tree:dir!R       1          NA      NA     F   0
#>  tree:dir!dir_E:E     219.9     59.83     3.7     P   0
#>  tree:dir!dir_N:E     223.8     64.93     3.4     P   0
#>  tree:dir!dir_N:N     290.4     79        3.7     P   0
#>  tree:dir!dir_S:E     229.1     69.21     3.3     P   0
#>  tree:dir!dir_S:N     288.4     82.7      3.5     P   0
#>  tree:dir!dir_S:S     350       95.22     3.7     P   0
#>  tree:dir!dir_W:E     171.4     54.09     3.2     P   0
#>  tree:dir!dir_W:N     226.3     65.75     3.4     P   0
#>  tree:dir!dir_W:S     259.5     73.62     3.5     P   0
#>  tree:dir!dir_W:W     226       61.48     3.7     P   0
    
  # Note: 'rcor' is a personal function to extract the correlations
  # into a matrix format
  # round(kw::rcor(m1)$dir, 2)
  #        E      N      S      W
  # E 219.93 223.75 229.06 171.37
  # N 223.75 290.41 288.44 226.27
  # S 229.06 288.44 350.00 259.54
  # W 171.37 226.27 259.54 226.00
    
  # Note: Wolfinger used a common diagonal variance
  
  # Factor Analytic with different specific variances
  # fixme: does not work with asreml4
  # m2 <- update(m1, residual = ~tree:facv(dir,1))
  # round(kw::rcor(m2)$dir, 2)
  #       E       N      S      W
  # E 219.94 209.46 232.85 182.27
  # N 209.46 290.41 291.82 228.43
  # S 232.85 291.82 349.99 253.94
  # W 182.27 228.43 253.94 225.99
    
# }