stroup.nin: RCB experiment of wheat at the Nebraska Intrastate Nursery

Description

The yield data from an advanced Nebraska Intrastate Nursery (NIN) breeding trial conducted at Alliance, Nebraska, in 1988/89.

Arguments

Format

gen: genotype, 56 levels
rep: replicate, 4 levels
yield: yield, bu/ac
col: column
row: row

Details

Four replicates of 19 released cultivars, 35 experimental wheat lines and 2 additional triticale lines were laid out in a 22 row by 11 column rectangular array of plots. The varieties were allocated to the plots using a randomised complete block (RCB) design. Each plot was sown in four rows 4.3 m long and 0.3 m apart. Plots were trimmed down to 2.4 m in length before harvest. The orientation of the plots is not clear from the paper, but the data in Littel et al are given in meters and make the orientation clear.

Field length: 11 plots * 4.3 m = 47.3 m

Field width: 22 plots * 1.2 m = 26.4 m

All plots with missing data are coded as being gen = "Lancer". (For ASREML, missing plots need to be included for spatial analysis and the level of 'gen' needs to be one that is already in the data.)

These data were first analyzed by Stroup et al (1994) and subsequently by Littell et al (1996, page 321), Pinheiro and Bates (2000, page 260), and Butler et al (2004).

This version of the data give the yield in bushels per acre. The yield values published in Stroup et al (1994) are expressed in kg/ha. For wheat, 1 bu/ac = 67.25 kg/ha.

Some of the gen names are different in Stroup et al (1994). (Sometimes an experimental genotype is given a new name when it is released for commercial use.) At a minimum, the following differences in gen names should be noted:

stroup.nin	Stroup et al
NE83498	Rawhide

Some published versions of the data use long/lat instead of col/row. To obtain the correct value of 'long', multiply 'col' by 1.2. To obtain the correct value of 'lat', multiply 'row' by 4.3.

Relatively low yields were clustered in the northwest corner, which is explained by a low rise in this part of the field, causing increased exposure to winter kill from wind damage and thus depressed yield. The genotype 'Buckskin' is a known superior variety, but was disadvantaged by assignment to unfavorable locations within the blocks.

Note that the figures in Stroup 2002 claim to be based on this data, but the number of rows and columns are both off by 1 and the positions of Buckskin as shown in Stroup 2002 do not appear to be quite right.

References

Littell, R.C. and Milliken, G.A. and Stroup, W.W. and Wolfinger, R.D. 1996. SAS system for mixed models, SAS Institute, Cary, NC.

Jose Pinheiro and Douglas Bates, 2000, Mixed Effects Models in S and S-Plus, Springer.

Butler, D., B R Cullis, A R Gilmour, B J Goegel. (2004) Spatial Analysis Mixed Models for S language environments

W. W. Stroup (2002). Power Analysis Based on Spatial Effects Mixed Models: A Tool for Comparing Design and Analysis Strategies in the Presence of Spatial Variability. Journal of Agricultural, Biological, and Environmental Statistics, 7(4), 491-511. http://doi.org/10.1198/108571102780

Examples

Run this code

# NOT RUN {
data(stroup.nin)
dat <- stroup.nin

# Experiment layout. All "Buckskin" plots are near left side
if(require(desplot)){
  desplot(yield~col*row, dat,
          aspect=47.3/26.4, out1="rep", num=gen, cex=0.6, # true aspect
          main="stroup.nin - yield heatmap (true shape)")
}

# ----- nlme -----

require(nlme)
# Random RCB model
lme1 <- lme(yield ~ 0 + gen, random=~1|rep, data=dat, na.action=na.omit)

# Linear (Manhattan distance) correlation model
lme2 <- gls(yield ~ 0 + gen, data=dat,
           correlation = corLin(form = ~ col + row, nugget=TRUE),
           na.action=na.omit)

# Random block and spatial correlation.
# Note: corExp and corSpher give nearly identical results
lme3 <- lme(yield ~ 0 + gen, data=dat,
            random = ~ 1 | rep,
            correlation = corExp(form = ~ col + row),
            na.action=na.omit)

AIC(lme1,lme2,lme3) # lme2 is lowest
##      df      AIC
## lme1 58 1333.702
## lme2 59 1189.135
## lme3 59 1216.704

# Compare the estimates from the two methods
eff = data.frame(ranblock=fixef(lme1), corLin = coef(lme2),
                 corExp = fixef(lme3))
rownames(eff) <- gsub("gen", "", rownames(eff))
plot(eff$ranblock, eff$corLin, xlim=c(13,37), ylim=c(13,37),
     main="stroup.nin - Gen estimates (intercepts differ)",
     xlab="RCB (random block)", ylab="corLin",type='n')
text(eff$ranblock, eff$corLin, rownames(eff), cex=0.5)
abline(0,1)

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

# Note, the 'sommer' package has dropped support for ar1

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

# }
# NOT RUN {
  if(require(SpATS)){
    
    dat <- transform(dat, yf = as.factor(row), xf = as.factor(col))
    
    sp1 <- SpATS(response = "yield",
                 spatial = ~ SAP(col, row, nseg = c(10,20), degree = 3, pord = 2),
                 genotype = "gen",
                 #fixed = ~ colcode + rowcode,
                 random = ~ yf + xf,
                 data = dat,
                 control = list(tolerance = 1e-03))
    plot(sp1)
    
    eff <- cbind(eff, spats=predict(sp1, which="gen")$predicted.values)
    plot(eff$ranblock, eff$spats, xlim=c(13,37), ylim=c(13,37),
         main="stroup.nin - Gen estimates",
         xlab="RCB (random block)", ylab="SpATS",type='n')
    text(eff$ranblock, eff$spats, rownames(eff), cex=0.5)
    abline(0,1)
  }
  
# }
# NOT RUN {
# ----------------------------------------------------------------------------

# }
# NOT RUN {
  # asreml3
  require(asreml)
 
  # RCB analysis
  dat.rcb <- asreml(yield ~ gen, random = ~ rep, data=dat,
                    na.method.X="omit")
  pred.rcb <- predict(dat.rcb, data=dat, classify="gen")$predictions

  # Two-dimensional AR1xAR1 spatial model
  dat <- transform(dat, xf=factor(col), yf=factor(row))
  dat <- dat[order(dat$xf, dat$yf),]
  dat.sp <- asreml(yield~gen, data=dat,
                   rcov=~ar1(xf):ar1(yf),
                   na.method.X='ignore')
  pred.sp <- predict(dat.sp, data=dat, classify="gen")$predictions

  require(lucid)
  vc(dat.sp)
  ##     effect component std.error z.ratio constr
  ## R!variance   48.7      7.155       6.8    pos
  ##   R!xf.cor    0.6555   0.05638    12      unc
  ##   R!yf.cor    0.4375   0.0806      5.4    unc

  # Compare the estimates from the two methods
  plot(pred.rcb$pvals[,2], pred.sp$pvals[,2], xlim=c(13,37), ylim=c(13,37),
       xlab="RCB",ylab="AR1xAR1",type='n')
  title("stroup.nin: Comparison of predicted values")
  text(pred.rcb$pvals[,2],pred.sp$pvals[,2],
       as.character(pred.rcb$pvals[,1]),cex=0.5)
  abline(0,1) 
# }
# NOT RUN {
# ----------------------------------------------------------------------------

# }
# NOT RUN {
  
  ## require(asreml4)
  ## data(stroup.nin)
  ## dat <- stroup.nin

  ## # Note, ASREML4 stand-alone might not need a completely-filled rectangle
  ## # of plots to perform AR1xAR1 analysis.  It might be able to fill in missing
  ## # combinations of rows/columns. The R version asreml4 still seems to require
  ## # rectangles.

  ## # RCB analysis
  ## dat.rcb <- asreml(yield ~ gen, random = ~ rep, data=dat,
  ##                   na.action=na.method(x="omit"))
  ## pred.rcb <- predict(dat.rcb, data=dat, classify="gen")

  ## # Two-dimensional AR1xAR1 spatial model
  ## dat <- transform(dat, xf=factor(col), yf=factor(row))
  ## #dat <- dat[order(dat$xf, dat$yf),]
  ## dat.sp <- asreml(yield~gen, data=dat,
  ##                  residual = ~ar1(xf):ar1(yf),
  ##                  na.action=na.method(x="omit"))
  ## pred.sp <- predict(dat.sp, data=dat, classify="gen")

  ## require(lucid)
  ## vc(dat.sp)
  ## ##     effect component std.error z.ratio constr
  ## ## R!variance   48.7      7.155       6.8    pos
  ## ##   R!xf.cor    0.6555   0.05638    12      unc
  ## ##   R!yf.cor    0.4375   0.0806      5.4    unc

  ## # Compare the estimates from the two methods
  ## plot(pred.rcb$pvals[,2], pred.sp$pvals[,2], xlim=c(13,37), ylim=c(13,37),
  ##      xlab="RCB", ylab="AR1xAR1", type='n')
  ## title("stroup.nin: Comparison of predicted values")
  ## text(pred.rcb$pvals[,2],pred.sp$pvals[,2],
  ##      as.character(pred.rcb$pvals[,1]),cex=0.5)
  ## abline(0,1)
  
# }
# NOT RUN {
# ----------------------------------------------------------------------------

# }