# barley: Jenkyn's Data on Leaf-blotch on Barley In gnm: Generalized Nonlinear Models

 barley R Documentation

## 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.

`barley`

### Format

A data frame with 90 observations on the following 3 variables.

y

the proportion of leaf affected (values in [0,1])

site

a factor with 9 levels `A` to `I`

variety

a factor with 10 levels `c(1:9, "X")`

### Note

This dataset was used in Wedderburn's original paper (1974) on quasi-likelihood.

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Originally in an unpublished Aberystwyth PhD thesis by J F Jenkyn.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

```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 + instances(Mult(site, variety), 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?
```

gnm documentation built on April 29, 2022, 5:06 p.m.