Row-column experiment of wheat — kempton.rowcol • agridat

Row-column experiment of wheat, 35 genotypes, 2 reps.

Format

A data frame with 68 observations on the following 5 variables.

rep: replicate factor, 2 levels
row: row
col: column
gen: genotype factor, 35 levels
yield: yield

Details

Included to illustrate REML analysis of a row-column design.

Source

R A Kempton and P N Fox, Statistical Methods for Plant Variety Evaluation, Chapman and Hall, 1997.

Examples

# \dontrun{

library(agridat)
data(kempton.rowcol)
dat <- kempton.rowcol
dat <- transform(dat, rowf=factor(row), colf=factor(col))

libs(desplot)
desplot(dat, yield~col*row|rep,
        num=gen, out1=rep, # unknown aspect
        main="kempton.rowcol")


# Model with rep, row, col as random.  Kempton, page 62.
# Use "-1" so that the vcov matrix doesn't include intercept
libs(lme4)
m1 <- lmer(yield ~ -1 + gen + rep + (1|rep:rowf) + (1|rep:colf), data=dat)

# Variance components match Kempton.
print(m1, corr=FALSE)
#> Linear mixed model fit by REML ['lmerMod']
#> Formula: yield ~ -1 + gen + rep + (1 | rep:rowf) + (1 | rep:colf)
#>    Data: dat
#> REML criterion at convergence: 70.0235
#> Random effects:
#>  Groups   Name        Std.Dev.
#>  rep:colf (Intercept) 0.4387  
#>  rep:rowf (Intercept) 0.2531  
#>  Residual             0.3002  
#> Number of obs: 68, groups:  rep:colf, 14; rep:rowf, 10
#> Fixed Effects:
#> genG01  genG02  genG03  genG04  genG05  genG06  genG07  genG08  genG09  genG10  
#>  4.203   3.304   4.487   2.910   3.785   4.799   4.474   3.991   3.739   3.717  
#> genG11  genG12  genG13  genG14  genG15  genG16  genG17  genG18  genG19  genG20  
#>  4.320   4.335   4.071   4.154   2.605   3.344   3.542   3.953   5.059   3.708  
#> genG21  genG22  genG23  genG24  genG25  genG26  genG27  genG28  genG29  genG30  
#>  3.982   3.401   2.813   3.277   4.029   3.148   4.089   3.682   3.183   3.342  
#> genG31  genG32  genG33  genG34  genG35   repR2  
#>  3.248   3.652   4.303   3.687   2.991   1.222  

# Standard error of difference for genotypes.  Kempton page 62, bottom.
covs <- as.matrix(vcov(m1)[1:35, 1:35])
vars <- diag(covs)
vdiff <- outer(vars, vars, "+") - 2 * covs
sed <- sqrt(vdiff[upper.tri(vdiff)])
min(sed) # Minimum SED
#> [1] 0.35107
mean(sed) # Average SED
#> [1] 0.3853689
max(sed) # Maximum SED
#> [1] 0.5357671

# }