Both Logit and Probit models can be used to model a dichotomous dependent variable, e.g. yes/no, agree/disagree, like/dislike, etc. There are several problems in using Simple Linear Regression while modeling dichotomous dependent variable like: First, the regression line may lead to predictions outside the range of zero and one, but probability can only be between 0 and 1. Second assumptions like normal distribution of error and Homoscedasticity might be violated.
So if both logit and probit can be used in same situation then how do they differ:
The real difference lies in the link function been used is different for logit and probit. The major difference between logit and probit models lies in the assumption on the distribution of the error terms in the model. For the logit model, the errors are assumed to follow the standard logistic distribution while for the probit, the errors are assumed to follow a Normal distribution.
For Logit Model the link function used is:
For Probit Model the link function used is:
The distribution of Logit and Probit function is given below: