What is the difference between probit and logit in R?

Despite these differing assumptions, empirical studies have consistently shown that the probit and logit models tend to yield highly similar marginal effects. Marginal effects represent the change in the dependent variable caused by a unit change in one of the independent variables, holding all other variables constant.

This similarity in marginal effects suggests that, in many practical applications, the choice between the logit and probit models may not significantly impact the interpretation of results. However, the choice of model should still be guided by the specific assumptions and characteristics of the data at hand.

The fundamental distinction between the logit and probit models revolves around the assumed distribution of errors within their respective frameworks. The logit model operates under the premise of a standard logistic distribution of errors, which is characterized by a sigmoid-shaped curve.

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In contrast, the probit model adopts a Normal distribution of errors, more commonly known as the bell-shaped curve. This difference in the underlying error distribution is crucial in determining the suitability of each model for specific analytical purposes.