# Link functions for Binomial Regression

So I have a dataset of presence (1) and absence (0) data, but it mainly consists of 0's (~80% of the 5200 observations). Now while constructing my binomial logistic model I am reading (Zuurt et al. 2009) as a guide. There is only a short description about the different link-choices for a binomial model and throughout the examples the standard logit-link is used. But the book also states that if you have more 0's than 1's, the cloglog-link is also an option.

How can I find out which model is better (just by comparing the AIC?) and is there any good description of the selection proces of these link-functions? Or maybe somebody here can give some advice.

• I do not have sufficient reputation to comment or flag, but this is a duplicate. Read this thread: stats.stackexchange.com/questions/20523/… Jul 20, 2016 at 17:23
• Actually it is not, as I am more interested in the difference between legit/probit and cloglog (complementary log log). Jul 20, 2016 at 18:38
• If you can get a hold on Julian Faraway's "Extending Linear Model with R" book, it contains a very enlightening discussion on that subject. In the first chapter it is illustrated with examples how, despite the similar overall shape, the three link functions differ in estimation of tail probabilities. There is also an explanation of how each of the link functions can be interpreted in terms of a latent variable with different distribution. This can matter - I've worked on problems where probit was a natural choice since the aim was recovering the parameters of a hidden Gaussian variable. Jul 20, 2016 at 20:47
• @Guido167, Actually, that link does discuss cloglog as well. Do a word search for "cloglog" and you'll find some useful commentary. Jul 20, 2016 at 22:07
• @JacekPodlewski, thank you very much for the recommendation. Will read through the book! Jul 21, 2016 at 10:49