What is the difference between probit regression and logit regression?

Question

I looked online but I’m not exactly sure as to what exactly is the difference, apparently both take in binary variables (i think?) but one uses a cumulative distribution function while the other is logistic function? When would I use one or the other?

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Answer 1

There are minor differences in the technical assumptions underneath them, though IIRC these only become realistic-level concerns in extended models like multinomial logit vs multinomial probit.

Otherwise, there’s no pressing reason to use one or the other for a binary DV. –IF– you happen to think better with odds than probability, then you might favor logit because the coefficients map neatly to odds ratios. Similarly, –IF– for some reason you have to do a lot of manual processing of the results, then you might favor logit because exp(x)/(1+exp(x)) is simpler and harder to screw up than coding the cumulative normal by hand.