What is the difference between Logit and Probit models?



I am working on a classification problem and wanted to know how do I decide which model to use - Logit model or Probit model?

What are the differences between the two and how do we decide which one to use in which problem?




The difference between Logit and Probit models lies in the use of Link function. Logistic regression can be interpreted as modelling log odds and the co-efficients in the logistic regression can be interpreted as odds ratio.

Logistic has slightly flatter tails (as can be seen in the diagram below), hence you will find the models making different predictions on the outer side.

Link function used for Logistic regression: n(p) = ln(p/1-p)
Link function used for Probit regression: n(p) = f(p)

Could not type probit function here, but the actual form is irrelevant as it does not have a natural interpretation.

Typically logistic regression is more popular and people start modelling with Logit. You can compare the outcome of the two models using likelihood value and then decide which one to use.

Hope this helps.


I had a similar doubt. The link to this pdf was pretty helpful