\( \newcommand{\bm}[1]{\boldsymbol{\mathbf{#1}}} \DeclareMathOperator{\tr}{tr} \DeclareMathOperator{\var}{var} \DeclareMathOperator{\cov}{cov} \DeclareMathOperator{\corr}{corr} \newcommand{\indep}{\perp\!\!\!\perp} \newcommand{\nindep}{\perp\!\!\!\perp\!\!\!\!\!\!/\;\;} \)

3.5 bliss data

bliss contains data on mortality of flour-beetles as a function of dose of a poison. To plot the death rates and fit a logistic regression model:

attach(bliss)
plot(log(dose), r/m, ylim = c(0, 1), ylab = "Proportion dead")
fit <- glm(cbind(r, m-r) ~ log(dose), binomial)
summary(fit)
points(log(dose), fitted(fit), pch = 3, col = 2)

Does the fit seem good to you? Try again with the probit and cloglog link functions, for example:

fit <- glm(cbind(r, m-r) ~ log(dose), binomial(cloglog))
points(log(dose), fitted(fit), pch = 3, col = 3)

Which fits best? Give a careful interpretation of the resulting model.

(Sections 10.1-10.4; Bliss, 1935)