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I have a binary outcome variable which I'm testing other variables of my dataset against to determine which has a relationship with Y. My understanding is that probit and logit models should be giving me similar stats, but for some reason the logit coefficients are around double the probit ones.

Can anyone help me understand why this would happen?

(All have strong z values and low SEs, if that's pertinent.)

Also, is it generally an issue to test (binary ~ binary)? For gender I'm getting 0.3 (probit) and 0.5 (logit), whereas lm() gives 0.1.

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    $\begingroup$ Nothwithstanding @Ben Bolker's excellent answer, there are many relevant threads here e.g. stats.stackexchange.com/questions/20523/… $\endgroup$ Commented Apr 21 at 13:55
  • $\begingroup$ I'm not sure this is a duplicate: the topics covered by the linked question are very different (how does their meaning/application differ? vs. why is the scale different?) The scale difference is mentioned tangentially in one of the many answers in that thread, but probably wouldn't have solved the OP's question here. $\endgroup$ Commented Apr 22 at 2:35

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Probit and logit should give you very similar statistical conclusions ($p$-values, predictions, etc.), but the actual values of the coefficients differ by a scale factor. As mentioned on Wikipedia,

the logit and probit functions are extremely similar when the probit function is scaled [divided by a factor of $\sqrt{2 \pi}/4 = \sqrt{\pi/8} \approx 0.63$]

(emphasis added). The factor of 0.63 corresponds pretty closely to your reported difference of 0.3 (probit) vs 0.5 (logit).

Using binary predictors in a logistic/probit model is fine.

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    $\begingroup$ If this solved your problem you are encouraged to click the check-mark to accept it (although you are welcome to wait to see if a better answer is posted) $\endgroup$ Commented Apr 21 at 13:54

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