I know that there is a very good explanation of the technical differences of probit and logit model in this question. However, I would appreciate some common sense clarifications which can be very helpful when deciding which model to use.
So let's consider this model: $$ Prob(y=1|x) = G(\beta_0 + x\beta) $$
where $G(z)$ is the respective link function.
Do I get it right that when the inner linear model yields
z=0then both the probit and logit predict 50% probability that
y=1and 50% that
I know that there isn't any general rule which model to choose, however one of the differences which should be considered are the slightly different shapes of the curves (the tails). So again, am I right if I say that the logit model "spreads" probability across wider range of values of
z? That is, the probit will predict lower probabilities for negative values and higher probabilities for positive values of