agridat (version 1.12)

hanks.sprinkler: Wheat yields in a line-source sprinkler experiment

Description

Three wheat varieties planted in 3 blocks, with a line sprinkler crossing all whole plots.

Format

A data frame with 108 observations on the following 7 variables.

block

Block factor

row

Row ordinate

subplot

Column ordinate

gen

Genotype factor, 3 levels

yield

Yield (tons/ha)

irr

Irrigation level, 1..6

dir

Factor for direction from sprinkler, N/S

Details

A line-source sprinkler is placed through the middle of the experiment (between subplots 6 and 7). Subplots closest to the sprinkler receive the most irrigation. Subplots far from the sprinkler (near the edges) have the lowest yields.

One data value was modified from the original (following the example of other authors).

References

Johnson, D. E., Chaudhuri, U. N., and Kanemasu, E. T. (1983). Statistical Analysis of Line-Source Sprinkler Irrigation Experiments and Other Nonrandomized Experiments Using Multivariate Methods. Soil Science Society American Journal, 47, 309-312.

Stroup, W. W. (1989). Use of Mixed Model Procedure to Analyze Spatially Correlated Data: An Example Applied to a Line-Source Sprinkler Irrigation Experiment. Applications of Mixed Models in Agriculture and Related Disciplines, Southern Cooperative Series Bulletin No. 343, 104-122.

SAS Stat User's Guide. http://support.sas.com/documentation/cdl/en/statug/63347/HTML/default/viewer.htm#statug_mixed_sect038.htm

Examples

# NOT RUN {
data(hanks.sprinkler)
dat <- hanks.sprinkler

# The line sprinkler is vertical between subplots 6 & 7
desplot(yield~subplot*row, dat, out1=block, out2=irr, cex=1,
        num=gen, main="hanks.sprinkler")

require(lattice)
xyplot(yield~subplot|block, dat, type=c('b'), group=gen,
       layout=c(1,3), auto.key=TRUE,
       main="hanks.sprinkler",
       panel=function(x,y,...){
         panel.xyplot(x,y,...)
         panel.abline(v=6.5, col='wheat')
       })

# }
# NOT RUN {
## This is the model from the SAS documentation
## proc mixed;
## class block gen dir irr;
## model yield = gen|dir|irr@2;
## random block block*dir block*irr;
## repeated / type=toep(4) sub=block*gen r;

dat <- transform(dat, subf=factor(subplot),
                 irrf=factor(irr))
dat <- dat[order(dat$block, dat$gen, dat$subplot),]

# Reproduced with asreml
require(asreml)
m1 <- asreml(yield ~ gen + dir + irrf + gen:dir + gen:irrf + dir:irrf,
             data=dat,
             random= ~ block + block:dir + block:irrf,
             rcov= ~ block:gen:corb(subf, k=3))

require(lucid)
vc(m1)
##                effect component std.error z.ratio constr
##       block!block.var  0.2194     0.2393     0.92    pos
##   block:dir!block.var  0.01768    0.03154    0.56    pos
##  block:irrf!block.var  0.03539    0.03617    0.98    pos
##            R!variance  0.285      0.05086    5.6     pos
##                R!cor1  0.02802    0.1143     0.25  uncon
##                R!cor2  0.005095   0.1278     0.04  uncon
##                R!cor3 -0.3246     0.0905    -3.6   uncon

## # convert asreml correlations to SAS covariances
## round(.2850 * c(1, .02802, .005095, -.3246),4) # res var * (cor1, cor2, cor3)
## [1]  0.2850  0.0080  0.0015 -0.0925

# }