Beetles: choice of link function
Dobson (1983) analyses binary dose-response data published by Bliss (1935), in which the numbers of beetles killed after 5 hour exposure to carbon disulphide at N = 8 different concentrations are recorded:

We assume that the observed number of deaths r i at each concentration x i is binomial with sample size n i and true rate p i . Plausible models for pi include the logistic, probit and extreme value (complimentary log-log) models, as follows
p i = exp( a + b x i ) / (1 + exp( a + b x i )
p i = Phi( a + b x i )
p i = 1 - exp(-exp( a + b x i ))
The corresponding graph is shown below:
model
{
for( i in 1 : N ) {
r[i] ~ dbin(p[i],n[i])
logit(p[i]) <- alpha.star + beta * (x[i] - mean(x[]))
rhat[i] <- n[i] * p[i]
culmative.r[i] <- culmative(r[i], r[i])
}
alpha <- alpha.star - beta * mean(x[])
beta ~ dnorm(0.0,0.001)
alpha.star ~ dnorm(0.0,0.001)
}
Data ( click to open )
Inits ( click to open )
Results
A 1000 update burn in followed by a further 10000 updates gave the parameter estimates
Logit model
Probit model
Extreme value (cloglog) model