Interviewer fixed effects in probit regression

[Lisa Pr]

Hi everyone,

I am currently working on data which was gathered in a survey and I want to explore interviewer effects. My outcome variables are binary (yes/ no to a certain question). Until now I used "probit"- that was my initial model:

probit outcome enumerator1 enumerator2 enumerator3 enumerator4 ...

Then I explored differences between the interviewers (in comparison to the left out baseline-interviewer) using their coefficients. Now I searched for an interpretation and found articles stating that probit with fixed effects is not possible or leads to biased results.

Can I do it the way I did? If it is not possible to get correctly estimated interviewer effects, is it at least possible to conclude that there are some effects (or none)?

If it is not possible the way I did, could you help me? Would some non-binary controls help or if I had a second period to use xtprobit maybe?

I would appreciate any help, thank you so much!

Best, Lisa

[Carlo Lazzaro]

Lisa:
welcome to this forum.
If your data come from a survey and your dependent variable is binary, you may want to take a look at -svy:- prefix and -logit-.

[Lisa Pr]

Thank you, Carlo!

But I am still unsure whether or why I should not just stick with probit, at least to see that there are effects (even if the coefficients are potentially biased)?

[Carlo Lazzaro]

Lisa:
there's no a relevant difference between -probit- and -logit- (personally I would stick with the latter given a two-level categorical regressand).
You may investigate about the coefficients with both.

[Jeff Wooldridge]

Lisa: There are several considerations. First, are you including any variables other than the enumerator dummies? If not, then you should just use a linear regression because the estimated probabilities will be exactly the same. And you should be comparing differences in probabilities of Y = 1 across reviewers. I assume you have other controls, in which case you might want to use probit.

The key issue is (for probit or logit) is: How many observations do you have per interviewer? If it's nontrivial -- say, at least 50 each -- then it is fine to use probit or logit as you are. Even as low as 25 or so might work well. When people say "don't used fixed effects with probit" they're referring to unit fixed effects, as with longitudinal (panel) data, where you often have few observations per unit.

The term "fixed effects" is overused and can lead to confusion. It comes down to how many observations you have per "fixed effect."