In generalized regression models for binary outcomes, the coefficients from the probit and logit models can be related, but they do not have a fixed multiplicative relationship. The coefficients of the probit and logit models reflect the effects of predictors on the probability of success, but they are interpreted differently due to the nature of the underlying distributions.
While there is no definitive rule that says one coefficient is a specific multiple of the other, it has been empirically observed that:
- The coefficients from a probit model are typically smaller than those from a logit model.
- A rough rule of thumb used in practice is that the coefficient from a probit model is approximately 1.6 times the coefficient from a logit model in some contexts, but this can vary depending on the specific data.
Therefore:
- The coefficient of the probit model is approximately 1.6 times the coefficient of the logit model (under certain assumptions).
- The coefficient of the logit model is approximately 0.625 times the coefficient of the probit model (as the inverse of 1.6).
These multipliers are not exact and should be used cautiously, as they may not hold in all cases. The specific transformation depends on the distributions of the error terms in the models.