Four-way factorial agronomic experiment in triticale

Usage

data("besag.triticale")

Format

A data frame with 54 observations on the following 7 variables.

yield: yield, g/m^2
row: row
col: column
gen: genotype / variety, 3 levels
rate: seeding rate, kg/ha
nitro: nitrogen rate, kw/ha
regulator: growth regulator, 3 levels

Details

Experiment conducted as a factorial on the yields of triticale. Fully randomized. Plots were 1.5m x 5.5m, but the orientation is not clear.

Besag and Kempton show how accounting for neighbors changes non-significant genotype differences into significant differences.

Source

Julian Besag and Rob Kempton (1986). Statistical Analysis of Field Experiments Using Neighbouring Plots. Biometrics, 42, 231-251. Table 2. https://doi.org/10.2307/2531047

References

None.

Examples

if (FALSE) { # \dontrun{

  library(agridat)
  data(besag.triticale)
  dat <- besag.triticale
  dat <- transform(dat, rate=factor(rate), nitro=factor(nitro))
  dat <- transform(dat, xf=factor(col), yf=factor(row))

  libs(desplot)
  desplot(dat, yield ~ col*row,
          # aspect unknown
          main="besag.triticale")

  # Besag & Kempton are not perfectly clear on the model, but
  # indicate that there was no evidence of any two-way interactions.
  # A reduced, main-effect model had genotype effects that were
  # "close to significant" at the five percent level.
  # The model below has p-value of gen at .04, so must be slightly
  # different than their model.
  m2 <- lm(yield ~ gen + rate + nitro + regulator + yf, data=dat)
  anova(m2)

  # Similar, but not exact, to Besag figure 5
  dat$res <- resid(m2)
  libs(lattice)
  xyplot(res ~ col|as.character(row), data=dat,
         as.table=TRUE, type="s", layout=c(1,3),
         main="besag.triticale")
  
  if(require("asreml", quietly=TRUE)) {
    libs(asreml)

    # Besag uses an adjustment based on neighboring plots.
    # This analysis fits the standard AR1xAR1 residual model
    
    dat <- dat[order(dat$xf, dat$yf), ]
    m3 <- asreml(yield ~ gen + rate + nitro + regulator +
                   gen:rate + gen:nitro + gen:regulator +
                   rate:nitro + rate:regulator +
                   nitro:regulator + yf, data=dat,
                 resid = ~ ar1(xf):ar1(yf))
    wald(m3) # Strongly significant gen, rate, regulator
    ##                 Df Sum of Sq Wald statistic Pr(Chisq)    
    ## (Intercept)      1   1288255        103.971 < 2.2e-16 ***
    ## gen              2    903262         72.899 < 2.2e-16 ***
    ## rate             1    104774          8.456  0.003638 ** 
    ## nitro            1       282          0.023  0.880139    
    ## regulator        2    231403         18.676 8.802e-05 ***
    ## yf               2      3788          0.306  0.858263    
    ## gen:rate         2      1364          0.110  0.946461    
    ## gen:nitro        2     30822          2.488  0.288289    
    ## gen:regulator    4     37269          3.008  0.556507    
    ## rate:nitro       1      1488          0.120  0.728954    
    ## rate:regulator   2     49296          3.979  0.136795    
    ## nitro:regulator  2     41019          3.311  0.191042    
    ## residual (MS)          12391                             
  }
  
} # }