logit vs probit

[Olivia Johns]

My dependent variable takes on a value of 0 or 1.

So i should go ahead and run either probit or logit of which i prefer logit, just because of the interpretation it gives in terms of odds ratio.
I ran both and R^2 is about the same, and the log-likelihood is also about the same.

So my question is, i know probit assumes normality of its error term, and logit assumes logistic distribution of its error term.
Since i cannot observe how my error term is distributed, is it ok to just assume logistic distribution and go ahead with logit model?


Or is there any way to figure out which model is better?

Thanks in advance!

[Clyde Schechter]

Unless you have a theoretical reason to believe that one of the two distributions applies to your situation, the choice between logit and probit is largely one of taste or disciplinary tradition. The distinction between the logistic and normal distributions (appropriately scaled) is very slight, and only very large samples of data would enable you to distinguish them empirically.

I share your preference for the logistic model due to the convenience of the odds-ratio interpretation. But you should check if there is a traditional preference in your discipline before proceding.

[Carlo Lazzaro]

Olivia:
you may also be interested in the discussion on these two topics at http://stats.stackexchange.com/quest.../145265#145265

[Richard Williams]

As Carlo's excellent link points out the choice of link may matter more with more advanced methods. For example you can do a fixed effects logit but you can't do a fixed effects probit.

I also agree with Clyde that you should probably do whatever your field tends to do.

Whatever you use, I suggest you look at the margins command and see if it can help you make your results more interpretable.

[Enrique Pinzon (StataCorp)]

Based on some of the comments in this post and my own curiosity I started looking into the question of using logit or probit. I run some simulations and also looked a bit at the theory of quasilikelihood/pseudolikelihood. If you are interested here is an additional reference.

blog.stata.com/2016/01/07/probit-or-logit-ladies-and-gentlemen-pick-your-weapon/