verbyla.lupin {agridat} | R Documentation

## Multi-environment trial of lupin, multiple varieties and densities

### Description

Yield of 9 varieties of lupin at different planting densities across 2 years and multiple locations.

### Format

`gen`

  genotype, 9 varieties

`site`

  site, 11 levels

`rep`

  rep, 2-3 levels

`rate`

  seeding rate in plants/m^2

`row`

  row

`col`

  column

`serp`

  factor of 4 levels for serpentine seeding effect

`linrow`

  centered row position as a numeric variate (row-8.5)/10

`lincol`

  centered column position as a numeric variate (col-3.5)

`linrate`

  linear effect of seedrate, scaled (seedrate-41.92958)/10

`yield`

  yield in tons/hectare

`year`

  year, 1991-1992

`loc`

  location

### Details

Nine varieties of lupin were tested for yield response to plant density at 11 sites. The target density in 1991 was 10, 20, ..., 60 plants per m^2, and in 1992 was 20, 30, ..., 70 plants per m^2.

Plot dimensions are not given.

The variety Myallie was grown only in 1992.

Each site had 2 reps in 1991 and 3 reps in 1992. Each rep was laid out as a factorial RCB design; one randomization was used for all sites in 1991 and one (different) randomization was used for all sites in 1992. (This was confirmed with the principal investigator.)

In 1991 at the Mt. Barker location, the data for columns 5 and 6 was discarded due to problems with weeds.

Variety 'Myallie' was called '84L:439' in Verbyla 1997.

The year of release for the varieties is

Unicrop | 1973
Illyarrie | 1979
Yandee | 1980
Danja | 1986
Gungurru | 1988
Yorrel | 1989
Warrah | 1989
Merrit | 1991
Myallie | 1995

### Source

Arunas P. Verbyla and Brian R. Cullis and Michael G. Kenward and Sue J. Welham, (1999). The analysis of designed experiments and longitudinal data by using smoothing splines. Appl. Statist., 48, 269–311. http://doi.org/10.1111/1467-9876.00154

Arunas P. Verbyla and Brian R. Cullis and Michael G. Kenward and Sue J. Welham, (1997). The analysis of designed experiments and longitudinal data by using smoothing splines. University of Adelaide, Department of Statistics, Research Report 97/4. http://http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.56.808

Data retrieved Oct 2010 from http://www.blackwellpublishers.co.uk/rss. (No longer available).

Used with permission of Blackwell Publishing.

### Examples

    data(verbyla.lupin)
    dat <- verbyla.lupin

    # The same RCB randomization was used at all sites in each year
    if(require(desplot)){
      desplot(gen~col+row|site, data=dat,
              out1=rep, num=rate,
              # aspect unknown
              main="verbyla.lupin - experiment design")
    }

    # Figure 3 of Verbyla
    require(lattice)
    foo <- xyplot(yield ~ rate|loc*gen, data=dat, subset=year==92,
                  type=c('p','smooth'), cex=.5,
                  main="verbyla.lupin: 1992 yield response curves",
                  xlab="Seed rate (plants/m^2)",
                  ylab="Yield (tons/ha)",
                  strip=strip.custom(par.strip.text=list(cex=.7)))

    if (require(latticeExtra)) { # for useOuterStrips
      useOuterStrips(foo,
                     strip=strip.custom(par.strip.text=list(cex=.7)),
                     strip.left=strip.custom(par.strip.text=list(cex=.7)))
    }

    # ----------------------------------------------------------------------------

    ## Not run:

      # We try to reproduce the analysis of Verbyla 1999.
      # May not be exactly the same, but is pretty close.

      # Check nlevels for size of random-coefficient structures
      length(with(dat, table(gen)))      # 9 varieties for RC1
      length(with(dat, table(gen,site))) # 99 site:gen combinations for RC2

      # Make row and col into factors
      dat <- transform(dat, colf=factor(col), rowf=factor(row))
      # sort for asreml
      dat <- dat[order(dat$site, dat$rowf, dat$colf),]

      # Make site names more useful for plots
      dat <- transform(dat, site=factor(paste0(year,".",substring(loc,1,4))))

      # Initial model from top of Verbyla table 9.
    #  require(asreml4)
      # FIXME asreml4 This is not working in asreml4

    ##   m0 <- asreml(yield ~ 1
    ##                + site
    ##                + linrate
    ##                + site:linrate,
    ##                data = dat,
    ##                random = ~ spl(rate)
    ##                + dev(rate)
    ##                + site:spl(rate)
    ##                + site:dev(rate)
    ##                + str(~gen+gen:linrate, ~us(2):id(9)) # RC1
    ##                + gen:spl(rate)
    ##                + gen:dev(rate)
    ##                + str(~site:gen+site:gen:linrate, ~us(2):id(99)) # RC2
    ##                + site:gen:spl(rate)
    ##                + site:gen:dev(rate),
    ##                residual = ~ dsum( ~ ar1(rowf):ar1(colf)|site) # Spatial AR1 x AR1
    ##              )
    ## m0 <- update(m0)
    ## m0 <- update(m0) # to get convergence

    ## # Variograms match Verbyla 1999 figure 7 (scale slightly different)
    ## plot(varioGram(m0), xlim=c(1:19), zlim=c(0,2),
    ##      main="verbyla.lupin - variogram by site")

    ##   # Sequence of models in Verbyla 1999 table 10
    ## m1 <- update(m0, fixed= ~ .
    ##              + at(site, c(2,5,6,8,9,10)):lincol
    ##              + at(site, c(3,5,7,8)):linrow
    ##              + at(site, c(2,3,5,7,8,9,11)):serp
    ##              , random = ~ .
    ##              + at(site, c(3,6,7,9)):rowf
    ##              + at(site, c(1,2,3,9,10)):colf
    ##              + at(site, c(5,7,8,10)):units)
    ## m1 <- update(m1)

    ## m2 <- update(m1,
    ##              random = ~ .
    ##              - site:gen:spl(rate) - site:gen:dev(rate))

    ## m3 <- update(m2,
    ##              random = ~ .
    ##              - site:dev(rate) - gen:dev(rate))

    ## m4 <- update(m3,
    ##              random = ~ .
    ##              - dev(rate))

    ## m5 <- update(m4,
    ##              random = ~ .
    ##              - at(site, c(5,7,8,10)):units + at(site, c(5,7,8)):units)

    ## # Variance components are a pretty good match to Verbyla 1997, table 15
    ## require(lucid)
    ## vc(m5)
    ## .001004/sqrt(.005446*.0003662) # .711 correlation for RC1
    ## .00175/sqrt(.01881*.000167) # .987 correlation for RC2

    ## # Matches Verbyla 1999 figure 5
    ## plot(varioGram(m5),
    ##      main="verbyla.lupin - final model variograms",
    ##      xlim=c(1:19), zlim=c(0,1.5))

    ## End(Not run)

[Package agridat version 1.16 Index]