Early generation lupin trial with 3 sites

Description

Early generation lupin trial with 3 sites, 330 test lines, 6 check lines.

Format

A data frame with 1236 observations on the following 5 variables.

site

a factor with levels S1 S2 S3

col

a numeric vector

row

a numeric vector

gen

a numeric vector

yield

a numeric vector

Details

An early-stage multi-environment trial, with 6 check lines and 300 test lines. The 6 check lines were replicated in each environment.

Source

Multi-Environment Trials - Lupins. http://www.vsni.co.uk/software/asreml/htmlhelp/asreml/xlupin.htm

Used with permission of Arthur Gilmour, Brian Cullis, Robin Thompson.

Examples

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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)
})

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

## Not run: 
require(asreml)

# 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$rowf),] # Sort for asreml
m1 <- asreml(yield ~ site + check:site, data=dat,
             random = ~ at(site):colf + at(site,3):rowf + test,
             rcov = ~ at(site,c(1,2)):ar1(colf):ar1(rowf)
             + at(site,3):id(colf):ar1(rowf))
m1$loglik
## [1] -314.2616

require(lucid)
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,
             rcov = ~ at(site,c(1,2)):ar1(colf):ar1(rowf)
             + at(site,3):id(colf):ar1(rowf))
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,
             rcov = ~ at(site,c(1,2)):ar1(colf):ar1(rowf)
             + at(site,3):id(colf):ar1(rowf))
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,
             rcov = ~ at(site,c(1,2)):ar1(colf):ar1(rowf)
             + at(site,3):id(colf):ar1(rowf))
m5$loglik # Same as m4
## [1] -286.8484

# Model 4, Unstructured (symmetric) genetic variance matrix
un <- diag(3)
un[upper.tri(un,TRUE)] <- m4$gammas[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$gammas[5:7])
lam <- matrix(m5$gammas[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)

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