Wheat experiment with diagonal checks

Description

Wheat experiment augmented with two check varieties in diagonal strips.

Format

A data frame with 180 observations on the following 4 variables.

row

Row

col

Column

gen

Genotype factor, 120 levels

yield

Yield

Details

This experiment was conducted by Matthew Reynolds, CIMMYT. There are 180 plots in the field, 60 for the diagonal checks (G121 and G122) and 120 for new varieties.

Federer used this data in multiple papers to illustrate the use of orthogonal polynomials to model field trends that are not related to the genetic effects.

Note: Federer and Wolfinger (2003) provide a SAS program for analysis of this data. However, when the SAS program is used to analyze this data, the results do not match the results given in Federer (1998) nor Federer and Wolfinger (2003). The differences are slight, which suggests a typographical error in the presentation of the data.

The R code below provides results that are consistent with the SAS code of Federer & Wolfinger (2003) when both are applied to this version of the data.

Source

Federer, Walter T. 1998. Recovery of interblock, intergradient, and intervariety information in incomplete block and lattice rectangle design experiments. Biometrics, 54, 471–481.

References

Walter T Federer and Russell D Wolfinger, 2003. Augmented Row-Column Design and Trend Analysis, chapter 28 of Handbook of Formulas and Software for Plant Geneticists and Breeders, Haworth Press.

Examples

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data(federer.diagcheck)
dat <- federer.diagcheck

# Show the layout as in Federer 1998.
dat$check <- ifelse(dat$gen == "G121" | dat$gen=="G122", "C","N")
desplot(yield ~ col*row, dat, text=gen, show.key=FALSE,
      main="federer.diagcheck",
      shorten='no', col=check, cex=.8, col.text=c("yellow","gray"))

# Now reproduce the analysis of Federer 2003.

# Only to match SAS results
dat$row <- 16 - dat$row
dat <- dat[order(dat$col, dat$row), ]

# Add row / column polynomials to the data.
# The scaling factors sqrt() are arbitrary, but used to match SAS
nr <- length(unique(dat$row))
nc <- length(unique(dat$col))
rpoly <- poly(dat$row, degree=10) * sqrt(nc)
cpoly <- poly(dat$col, degree=10) * sqrt(nr)
dat <- transform(dat,
                 c1 = cpoly[,1], c2 = cpoly[,2], c3 = cpoly[,3],
                 c4 = cpoly[,4], c6 = cpoly[,6], c8 = cpoly[,8],
                 r1 = rpoly[,1], r2 = rpoly[,2], r3 = rpoly[,3],
                 r4 = rpoly[,4], r8 = rpoly[,8], r10 = rpoly[,10])
dat$trtn <- ifelse(dat$gen == "G121" | dat$gen=="G122", dat$gen, "G999")
dat$new <- ifelse(dat$gen == "G121" | dat$gen=="G122", "N", "Y")
dat <- transform(dat, trtn=factor(trtn), new=factor(new))

m1 <- lm(yield ~ c1 + c2 + c3 + c4 + c6 + c8
         + r1 + r2 + r4 + r8 + r10
         + c1:r1 + c2:r1 + c3:r1 + gen, data = dat)
# To get Type III SS use the following
if(require(car)) {
Anova(m1, type=3) # Matches PROC GLM output
}

# lmer
if(require(lme4) & require(lucid)){

dat$one <- factor(rep(1, nrow(dat)))

# lmer with bobyqa (default)
m2b <- lmer(yield ~ trtn + (0 + r1 + r2 + r4 + r8 + r10 +
            c1 + c2 + c3 + c4 + c6 + c8 + r1:c1 + r1:c2 + r1:c3 || one) +
            (1|new:gen)
            , data = dat, control=lmerControl(check.nlev.gtr.1="ignore"))
vc(m2b)
##      grp        var1 var2     vcov  sdcor
##  new.gen (Intercept) <NA>   2869    53.57
##      one       r1:c3 <NA>   5532    74.37
##    one.1       r1:c2 <NA>  58230   241.3
##    one.2       r1:c1 <NA> 128000   357.8
##    one.3          c8 <NA>   6456    80.35
##    one.4          c6 <NA>   1400    37.41
##    one.5          c4 <NA>   1792    42.33
##    one.6          c3 <NA>   2549    50.49
##    one.7          c2 <NA>   5942    77.08
##    one.8          c1 <NA>      0     0
##    one.9         r10 <NA>   1133    33.66
##   one.10          r8 <NA>   1355    36.81
##   one.11          r4 <NA>   2269    47.63
##   one.12          r2 <NA>    241.8  15.55
##   one.13          r1 <NA>   9200    95.92
## Residual        <NA> <NA>   4412    66.42

## lmer with Nelder_Mead gives 'wrong' results
## m2n <- lmer(yield ~ trtn + (0 + r1 + r2 + r4 + r8 + r10 +
##             c1 + c2 + c3 + c4 + c6 + c8 + r1:c1 + r1:c2 + r1:c3 || one) +
##             (1|new:gen)
##             , data = dat,
##             control=lmerControl(optimizer="Nelder_Mead",check.nlev.gtr.1="ignore"))
## vc(m2n)
##    groups        name variance   stddev
##  new.gen  (Intercept)   3228    56.82
##  one      r1:c3         7688    87.68
##  one.1    r1:c2        69750   264.1
##  one.2    r1:c1       107400   327.8
##  one.3    c8            6787    82.38
##  one.4    c6            1636    40.45
##  one.5    c4           12270   110.8
##  one.6    c3            2686    51.83
##  one.7    c2            7645    87.43
##  one.8    c1               0     0.0351
##  one.9    r10           1976    44.45
##  one.10   r8            1241    35.23
##  one.11   r4            2811    53.02
##  one.12   r2             928.2  30.47
##  one.13   r1           10360   101.8
##  Residual               4127    64.24

}


## Not run: 

# asreml
require(asreml)
require(lucid)
m3 <- asreml(yield ~ -1 + trtn, data=dat,
             random = ~ r1 + r2 + r4 + r8 + r10 +
             c1 + c2 + c3 + c4 + c6 + c8 + r1:c1 + r1:c2 + r1:c3 + new:gen)
coef(m3)
# REML cultivar means.  Very similar to Federer table 2.
rev(sort(round(coef(m3)$fixed[3] + coef(m3)$random[137:256,],0)))
## gen_G060 gen_G021 gen_G011 gen_G099 gen_G002
##      974      949      945      944      942
## gen_G118 gen_G058 gen_G035 gen_G111 gen_G120
##      938      937      937      933      932
## gen_G046 gen_G061 gen_G082 gen_G038 gen_G090
##      932      931      927      927      926

vc(m3)
##           effect component std.error z.ratio constr
##        r1!r1.var   9201        13720    0.67    pos
##        r2!r2.var    241.7       1059    0.23    pos
##        r4!r4.var   2269         3915    0.58    pos
##        r8!r8.var   1355         2627    0.52    pos
##      r10!r10.var   1133         2312    0.49    pos
##        c1!c1.var      0.01         0    4.8   bound
##        c2!c2.var   5942         8969    0.66    pos
##        c3!c3.var   2549         4177    0.61    pos
##        c4!c4.var   1792         3106    0.58    pos
##        c6!c6.var   1400         2551    0.55    pos
##        c8!c8.var   6456         9702    0.67    pos
##     r1:c1!r1.var 128000       189700    0.67    pos
##     r1:c2!r1.var  58230        90820    0.64    pos
##     r1:c3!r1.var   5531        16550    0.33    pos
##  new:gen!new.var   2869         1367    2.1     pos
##       R!variance   4412          915    4.8     pos


## End(Not run)

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