Incomplete block alpha design

Usage

data("burgueno.alpha")

Format

A data frame with 48 observations on the following 6 variables.

rep: rep, 3 levels
block: block, 12 levels
row: row
col: column
gen: genotype, 16 levels
yield: yield

Details

A field experiment with 3 reps, 4 blocks per rep, laid out as an alpha design.

The plot size is not given.

Electronic version of the data obtained from CropStat software.

Used with permission of Juan Burgueno.

Source

J Burgueno, A Cadena, J Crossa, M Banziger, A Gilmour, B Cullis. 2000. User's guide for spatial analysis of field variety trials using ASREML. CIMMYT. https://books.google.com/books?id=PR_tYCFyLCYC&pg=PA1

Examples

if (FALSE) { # \dontrun{

  library(agridat)
  data(burgueno.alpha)
  dat <- burgueno.alpha

  libs(desplot)
  desplot(dat, yield~col*row,
          out1=rep, out2=block, # aspect unknown
          text=gen, cex=1,shorten="none",
          main='burgueno.alpha')


  libs(lme4,lucid)
  # Inc block model
  m0 <- lmer(yield ~ gen + (1|rep/block), data=dat)
  vc(m0) # Matches Burgueno p. 26
  ##        grp        var1 var2   vcov sdcor
  ##  block:rep (Intercept) <NA>  86900 294.8
  ##        rep (Intercept) <NA> 200900 448.2
  ##   Residual        <NA> <NA> 133200 365  


  if(require("asreml", quietly=TRUE)) {
    libs(asreml)
    
    dat <- transform(dat, xf=factor(col), yf=factor(row))
    dat <- dat[order(dat$xf, dat$yf),]                 
    
    # Sequence of models on page 36 of Burgueno
    
    m1 <- asreml(yield ~  gen, data=dat)
    m1$loglik # -232.13
    
    m2 <- asreml(yield ~  gen, data=dat,
                 random = ~ rep)
    m2$loglik # -223.48
    
    # Inc Block model
    m3 <- asreml(yield ~  gen, data=dat,
                 random = ~ rep/block)
    m3$loglik # -221.42
    m3$coef$fixed # Matches solution on p. 27
    
    # AR1xAR1 model
    m4 <- asreml(yield ~ 1 + gen, data=dat,
                 resid = ~ar1(xf):ar1(yf))
    m4$loglik # -221.47
    plot(varioGram(m4), main="burgueno.alpha") # Figure 1
    
    m5 <- asreml(yield ~ 1 + gen, data=dat,
                 random= ~ yf, resid = ~ar1(xf):ar1(yf))
    m5$loglik # -220.07
    
    m6 <- asreml(yield ~ 1 + gen + pol(yf,-2), data=dat,
                 resid = ~ar1(xf):ar1(yf))
    m6$loglik # -204.64
    
    m7 <- asreml(yield ~ 1 + gen + lin(yf), data=dat,
                 random= ~ spl(yf), resid = ~ar1(xf):ar1(yf))
    m7$loglik # -212.51
    
    m8 <- asreml(yield ~ 1 + gen + lin(yf), data=dat,
                 random= ~ spl(yf))
    m8$loglik # -213.91
    
    # Polynomial model with predictions
    m9 <- asreml(yield ~ 1 + gen + pol(yf,-2) + pol(xf,-2), data=dat,
                 random= ~ spl(yf),
                 resid = ~ar1(xf):ar1(yf))
    m9 <- update(m9)
    m9$loglik # -191.44 vs -189.61
  
    m10 <- asreml(yield ~ 1 + gen + lin(yf)+lin(xf), data=dat,
                  resid = ~ar1(xf):ar1(yf))
    m10$loglik # -211.56
    
    m11 <- asreml(yield ~ 1 + gen + lin(yf)+lin(xf), data=dat,
                  random= ~ spl(yf),
                  resid = ~ar1(xf):ar1(yf))
    m11$loglik # -208.90
    
    m12 <- asreml(yield ~ 1 + gen + lin(yf)+lin(xf), data=dat,
                  random= ~ spl(yf)+spl(xf),
                  resid = ~ar1(xf):ar1(yf))
    m12$loglik # -206.82
    
    m13 <- asreml(yield ~ 1 + gen + lin(yf)+lin(xf), data=dat,
                  random= ~ spl(yf)+spl(xf))
    m13$loglik # -207.52
  }
  
} # }