Four-way factorial agronomic experiment in triticale

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

# \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)
#> Analysis of Variance Table
#> 
#> Response: yield
#>           Df Sum Sq Mean Sq F value  Pr(>F)  
#> gen        2  68245   34123  3.4115 0.04174 *
#> rate       1  31344   31344  3.1338 0.08346 .
#> nitro      1   5547    5547  0.5546 0.46032  
#> regulator  2  36612   18306  1.8302 0.17212  
#> yf         2  34756   17378  1.7374 0.18757  
#> Residuals 45 450098   10002                  
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

  # 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")
  
  libs(asreml) # asreml4

  # 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))
#> Model fitted using the gamma parameterization.
#> ASReml 4.1.0 Mon Jan 11 17:07:52 2021
#>           LogLik        Sigma2     DF     wall    cpu
#>  1      -177.197      8485.373     32 17:07:52    0.0 (1 restrained)
#>  2      -170.008      6592.311     32 17:07:52    0.0 (1 restrained)
#>  3      -165.648      8290.072     32 17:07:52    0.0
#>  4      -165.203     13100.375     32 17:07:52    0.0
#>  5      -165.198     12237.087     32 17:07:52    0.0
#>  6      -165.198     12425.594     32 17:07:52    0.0
  wald(m3) # Strongly significant gen, rate, regulator
#> Wald tests for fixed effects.
#> Response: yield
#> Terms added sequentially; adjusted for those above.
#> 
#>                 Df Sum of Sq Wald statistic Pr(Chisq)    
#> (Intercept)      1   1283427        103.289 < 2.2e-16 ***
#> gen              2    908222         36.546 1.159e-08 ***
#> rate             1    105412          8.483  0.003584 ** 
#> nitro            1       275          0.022  0.881825    
#> regulator        2    232696          9.364  0.009262 ** 
#> yf               2      3787          0.152  0.926634    
#> gen:rate         2      1383          0.056  0.972564    
#> gen:nitro        2     30994          1.247  0.536019    
#> gen:regulator    4     37599          0.756  0.944186    
#> rate:nitro       1      1484          0.119  0.729610    
#> rate:regulator   2     49772          2.003  0.367366    
#> nitro:regulator  2     41220          1.659  0.436342    
#> residual (MS)          12426                             
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
  ##                 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                             
  
# }