## Not run: 
  
  library(agridat)
  data(vsn.lupin3)
  dat <- vsn.lupin3
  
  # Split gen into check/test, make factors
  dat <- within(dat, {
    check <- ifelse(gen>336, 0, gen)
    check <- ifelse(check<7, check, 7)
    check <- factor(check)
    test <- factor(ifelse(gen>6 & gen<337, gen, 0))
    gen=factor(gen)
  })

  libs(desplot)
  desplot(dat, yield~ col*row|site,
          # midpoint="midrange",
          # aspect unknown
          main="vsn.lupin3 - yield")
  # Site 1 & 2 used same randomization
  desplot(dat, check~ col*row|site,
          main="vsn.lupin3: check plot placement") 

  # asreml 4
  libs(asreml,lucid)
     
  # Single-site analyses suggested random row term for site 3,
  # random column terms for all sites,
  # AR1 was unnecessary for the col dimension of site 3
  dat <- transform(dat, colf=factor(col), rowf=factor(row))
  dat <- dat[order(dat$site, dat$colf, dat$rowf),] # Sort for asreml
  m1 <- asreml(yield ~ site + check:site, data=dat,
               random = ~ at(site):colf + at(site,3):rowf + test,
               residual = ~ dsum( ~ ar1(colf):ar1(rowf) +
                                    id(colf):ar1(rowf) | site,
                                 levels=list(1:2, 3)
                                 ) )
  m1$loglik
  ## [1] -314.2616
  
  vc(m1)
  ##                      effect component std.error z.ratio constr
  ##  at(site, S1):colf!colf.var   0.6228   0.4284       1.5    pos
  ##  at(site, S2):colf!colf.var   0.159    0.1139       1.4    pos
  ##  at(site, S3):colf!colf.var   0.04832  0.02618      1.8    pos
  ##  at(site, S3):rowf!rowf.var   0.0235   0.008483     2.8    pos
  ##               test!test.var   0.1031   0.01468      7      pos
  ##            site_S1!variance   2.771    0.314        8.8    pos
  ##            site_S1!colf.cor   0.1959   0.05375      3.6  uncon
  ##            site_S1!rowf.cor   0.6503   0.03873     17    uncon
  ##            site_S2!variance   0.9926   0.1079       9.2    pos
  ##            site_S2!colf.cor   0.2868   0.05246      5.5  uncon
  ##            site_S2!rowf.cor   0.5744   0.0421      14    uncon
  ##            site_S3!variance   0.1205   0.01875      6.4    pos
  ##            site_S3!rowf.cor   0.6394   0.06323     10    uncon
  
  # Add site:test
  m2 <- update(m1, random=~. + site:test)
  m2$loglik
  ## [1] -310.8794
  
  # CORUH structure on the site component of site:test
  m3 <- asreml(yield ~ site + check:site, data=dat,
               random = ~ at(site):colf + at(site,3):rowf + corh(site):test,
               residual = ~ dsum( ~ ar1(colf):ar1(rowf) +
                                    id(colf):ar1(rowf) | site,
                                 levels=list(1:2, 3)  ))
  m3$loglik
  ## [1] -288.4837
  
  # Unstructured genetic variance matrix
  m4 <- asreml(yield ~ site + check:site, data=dat,
               random = ~ at(site):colf + at(site,3):rowf + us(site):test,
               residual = ~ dsum( ~ ar1(colf):ar1(rowf) +
                                    id(colf):ar1(rowf) | site,
                                 levels=list(1:2, 3)  ))
  m4$loglik
  ## [1] -286.8239
  
  # Note that a 3x3 unstructured matrix can be written LL'+Psi with 1 factor L
  # Explicitly fit the factor analytic model
  m5 <- asreml(yield ~ site + check:site, data=dat,
               random = ~ at(site):colf + at(site,3):rowf
               + fa(site,1, init=c(.7,.1,.1,.5,.3,.2)):test,
               residual = ~ dsum( ~ ar1(colf):ar1(rowf) +
                                    id(colf):ar1(rowf) | site,
                                 levels=list(1:2, 3)  ))
  m5$loglik # Same as m4
  ## [1] -286.8484
  
  # Model 4, Unstructured (symmetric) genetic variance matrix
  un <- diag(3)
  un[upper.tri(un,TRUE)] <- m4$vparameters[5:10]
  round(un+t(un)-diag(diag(un)),3)
  ##       [,1]  [,2]  [,3]
  ## [1,] 0.992 0.158 0.132
  ## [2,] 0.158 0.073 0.078
  ## [3,] 0.132 0.078 0.122
  
  # Model 5, FA matrix = LL'+Psi.  Not quite the same as unstructured,
  # since the FA model fixes site 2 variance at 0.
  psi <- diag(m5$vparameters[5:7])
  lam <- matrix(m5$vparameters[8:10], ncol=1)
  round(tcrossprod(lam,lam)+psi,3)
  ##       [,1]  [,2]  [,3]
  ## [1,] 0.991 0.156 0.133
  ## [2,] 0.156 0.092 0.078
  ## [3,] 0.133 0.078 0.122

  

## End(Not run)