01-10-2018 08:46 AM - edited 08-03-2021 03:46 PM
When the target (dependent) variable of a regression is dichotomous (has only two possible values), a traditional linear (OLS) regression is not appropriate. This is because:
Logit, probit and cloglog models account for these problems by fitting the data to a Cumulative Density Function (CDF), which is an S-shaped curve that falls within the range of the dependent variable, and allows for different rates of change at the low and high ends of the predictor variable. These three models differ from one another because they perform Maximum Likelihood Estimation (MLE) using different CDFs (link functions).
So... Which option to choose?
Note: Both the Logit and the Probit models will yield similar, but not necessarily the same results.
When in doubt:
Logit tends to be the default link function to use when you have no particular reason to use another one. However, in some fields using probit is standard. Unless you have a good reason to deviate, it is probably your best bet to select the model your target audience is most familiar with.
If you would like more detail, here are some additional resources:
http://bayesium.com/wp-content/uploads/2015/08/logit-probit-cloglog.pdf