Alternative Link Functions

Logistic functions

In some cases, including this one, more than one link function can be used with a given distribution in a GLM. In the case of the binomial GLM, two common alternatives to the logistic function are the wonderfully abbreviated cloglog complementary log-log function and the probit function. We can create alternative versions of model 1 by swapping the logistic link for the probit as follows:

m1_probit <- glm(cbind(killed, alive) ~ Dose, data = beetle, 
    binomial(link = "probit"))

As well as for the complementary log-log:

m1_cloglog <- glm(cbind(killed, alive) ~ Dose, data = beetle, 
    binomial(link = "cloglog"))

There are various ways in which we could compare these models, but we can take the opportunity to revisit the use of information criteria. In our example we’re using the AIC. The sample size is 471, or the number of beetles tested.