Factorial experiment of potato, 3x3 with missing values

Factorial experiment of potato, 3x3 with missing values.

Format

A data frame with 80 observations on the following 3 variables.

trt: treatment factor, 8 levels
block: block, 10 levels
y: infection intensity
n: nitrogen treatment, 2 levels
p: phosphorous treatment, 2 levels
k: potassium treatment, 2 levels

Details

The response variable y is the intensity of infection of potato tubers innoculated with Phytophthora Erythroseptica.

There were 3 treatment factors:

2 nitrogen levels

2 phosphorous levels

2 potassium levels

Yates (1933) presents an iterative algorithm to estimate missing values in a matrix, using this data as an example.

Source

F. Yates (1933). The analysis of replicated experiments when the field results are incomplete. Emp. J. Exp. Agric., 1, 129–142.

References

Steel & Torrie (1980). Principles and Procedures of Statistics, 2nd Edition, page 212.

Examples

if (FALSE) { # \dontrun{

library(agridat)
data(yates.missing)
dat <- yates.missing

libs(lattice)
bwplot(y ~ trt, data=dat,
       xlab="Treatment", ylab="Infection intensity",
       main="yates.missing")

libs(reshape2)
mat0 <- acast(dat[, c('trt','block','y')], trt~block,
               id.var=c('trt','block'), value.var='y')

# Use lm to estimate missing values.  The estimated missing values
# are the same as in Yates (1933)
m1 <- lm(y~trt+block, dat)
dat$pred <- predict(m1, new=dat[, c('trt','block')])
dat$filled <- ifelse(is.na(dat$y), dat$pred, dat$y)
mat1 <- acast(dat[, c('trt','block','pred')], trt~block,
               id.var=c('trt','block'), value.var='pred')


# Another method to estimate missing values via PCA
libs("nipals")
m2 <- nipals(mat0, center=FALSE, ncomp=3, fitted=TRUE)
# mat2 <- m2$scores 
mat2 <- m2$fitted

  # See also pcaMethods::svdImpute
  
  # Compare
  ord <- c("0","n","k","p","nk","np","kp","nkp")
  print(mat0[ord,], na.print=".")
  round(mat1[ord,] ,2)
  round(mat2[ord,] ,2)
  
  # mat2 SVD with 3 components recovers original data better than
  # mat1 from lm()
  sum((mat0-mat1)^2, na.rm=TRUE)
  sum((mat0-mat2)^2, na.rm=TRUE) # Smaller SS => better fit
} # }