wedderburn.barley {agridat} | R Documentation

## Multi-environment trial of barley, percent of leaves affected by leaf blotch

### Description

Percent of leaf area affected by leaf blotch on 10 varieties of barley at 9 sites.

### Format

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

`y`

  Percent of leaf area affected, 0-100.

`site`

  Site factor, 9 levels

`gen`

  Variety factor, 10 levels

### Details

Incidence of Rhynchosporium secalis (leaf blotch) on the leaves of 10 varieties of barley grown at 9 sites in 1965.

### Source

Wedderburn, R W M (1974). Quasilikelihood functions, generalized linear models and the Gauss-Newton method. Biometrika, 61, 439–47. http://doi.org/10.2307/2334725

Wedderburn credits the original data to an unpublished thesis by J. F. Jenkyn.

### References

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

R. B. Millar. Maximum Likelihood Estimation and Inference: With Examples in R, SAS and ADMB. Chapter 8.

### Examples

    data(wedderburn.barley)
    dat <- wedderburn.barley
    dat$y <- dat$y/100

    require(lattice)
    dotplot(gen~y|site, dat, main="wedderburn.barley")

    # Use the variance function mu(1-mu).  McCullagh page 330
    # Note, 'binomial' gives same results as 'quasibinomial', but also a warning
    m1 <- glm(y ~ gen + site, data=dat, family="quasibinomial")
    summary(m1)

    # Same shape (different scale) as McCullagh fig 9.1a
    plot(m1, which=1, main="wedderburn.barley")

    # Compare data and model
    dat$pbin <- predict(m1, type="response")
    dotplot(gen~pbin+y|site, dat, main="wedderburn.barley: observed/predicted")

    # Wedderburn suggested variance function: mu^2 * (1-mu)^2
    # Millar shows how to do this explicitly.
    wedder <- list(varfun=function(mu) (mu*(1-mu))^2,
                 validmu=function(mu) all(mu>0) && all(mu<1),
                 dev.resids=function(y,mu,wt) wt * ((y-mu)^2)/(mu*(1-mu))^2,
                 initialize=expression({
                   n <- rep.int(1, nobs)
                   mustart <- pmax(0.001, pmin(0.99,y)) }),
                 name="(mu(1-mu))^2")
    m2 <- glm(y ~ gen + site, data=dat, family=quasi(link="logit", variance=wedder))
    #plot(m2)

    ## Not run:
    # Alternatively, the 'gnm' package has the 'wedderburn' family.
    require(gnm)
    m3 <- glm(y ~ gen + site, data=dat, family="wedderburn")
    summary(m3)
    # Similar to McCullagh fig 9.2
    plot(m3, which=1)

    # Compare data and model
    dat$pwed <- predict(m3, type="response")
    dotplot(gen~pwed+y|site, dat)

    ## End(Not run)

[Package agridat version 1.16 Index]