**
****
**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

p

p

p

The corresponding graph is shown below:

model

{

for( i in 1 : N ) {

r[i] ~ dbin(p[i],n[i])

cloglog(p[i]) <- alpha.star + beta * (x[i] - mean(x[]))

rhat[i] <- n[i] * p[i]

cumulative.r[i] <- cumulative(r[i], r[i])

}

alpha <- alpha.star - beta * mean(x[])

beta ~ dnorm(0.0,0.001)

alpha.star ~ dnorm(0.0,0.001)

}

Results

A 1000 update burn in followed by a further 10000 updates gave the parameter estimates

Logit model

Probit model

Extreme value (cloglog) model