Why choose probit or logit?

Specifically, the probit curve tends to approach the axes at a slower rate, indicating a more gradual transition from low to high probabilities. In contrast, the logit curve approaches the axes more quickly, reflecting a steeper increase or decrease in predicted probabilities.

The primary distinction between the two models lies in their linking functions, which govern the relationship between the dependent variable and the explanatory variables.

Logistic regression exhibits a slightly flatter tail characteristic, meaning that as the values of the explanatory variables approach extreme limits, the probability predicted by the model changes more gradually compared to the probit model.

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When it comes to interpretability, the logit model offers a simpler and more intuitive interpretation. The logit coefficients can be directly interpreted as the change in the log-odds of the dependent variable occurring for a one-unit increase in the explanatory variable, holding all other variables constant.