gnm (version 0.8-1)

barley: Jenkyn's Data on Leaf-blotch on Barley

Description

Incidence of R. secalis on the leaves of ten varieties of barley grown at nine sites.

Usage

data(barley)

source

Originally in an unpublished Aberystwyth PhD thesis by J F Jenkyn.

References

Gabriel, K R (1998). Generalised bilinear regression. Biometrika 85, 689--700.

McCullagh, P and Nelder, J A (1989) Generalized Linear Models (2nd ed). Chapman and Hall.

Wedderburn, R W M (1974). Quasilikelihood functions, generalized linear models and the Gauss-Newton method. Biometrika 61, 439--47.

Examples

data(barley)
set.seed(1)

##  Fit Wedderburn's logit model with variance proportional to [mu(1-mu)]^2
logitModel <- glm(y ~ site + variety, family = wedderburn, data = barley)
fit <- fitted(logitModel)
print(sum((barley$y - fit)^2 / (fit * (1-fit))^2))
##  Agrees with the chi-squared value reported in McCullagh and Nelder 
##  (1989, p331), which differs slightly from Wedderburn's reported value.

##  Fit the biplot model as in Gabriel (1998, p694)
biplotModel <- gnm(y ~ -1 + Mult(site, variety, multiplicity = 2),
                   family = wedderburn, data = barley)
barleySVD <- svd(matrix(biplotModel$predictors, 10, 9))
A <- sweep(barleySVD$v, 2, sqrt(barleySVD$d), "*")[, 1:2]
B <- sweep(barleySVD$u, 2, sqrt(barleySVD$d), "*")[, 1:2]
##  These are essentially A and B as in Gabriel (1998, p694), from which
##  the biplot is made by
plot(rbind(A, B), pch = c(levels(barley$site), levels(barley$variety)))

##  Fit the double-additive model as in Gabriel (1998, p697)
variety.binary <- factor(match(barley$variety, c(2,3,6), nomatch = 0) > 0,
                        labels = c("rest", "2,3,6"))
doubleAdditive <- gnm(y ~ variety + Mult(site, variety.binary),
                      family = wedderburn, data = barley)
##  It is unclear why Gabriel's chi-squared statistics differ slightly
##  from the ones produced in these fits.  Possibly Gabriel adjusted the
##  data somehow prior to fitting?