0

I know that it is not possible to run a fixed effects probit model, when fixed effects are at the individual level. In other words, it is not possible to estimate $\alpha_i$ for each individual $i$ in the sample.

However, is it possible to include fixed effects that are not at the individual level? For example, suppose I am estimating the impact of race on hiring probability, and I want to control for occupation. Can I include occupation fixed effects? I assume so but want to confirm. At what point can probit not handle fixed effects?

Durden
  • 1,171
eades
  • 1
  • 2
  • 1
    What's your source that you can't run a fixed effects probit model? You can run both fixed and random effects probit models. They are just GLMs and GLMMs respectively. – AdamO Apr 25 '23 at 19:00
  • I am not 100% sure on that, but that does seem to be the answer I'm seeing everywhere while googling about fixed effects probit models:

    https://stats.stackexchange.com/questions/521238/probit-with-fixed-effects

    https://www.statalist.org/forums/forum/general-stata-discussion/general/861508-probit-with-fixed-effects

    https://www.researchgate.net/post/How-STATA-can-use-probit-model-with-fixed-effects

     – eades Apr 25 '23 at 19:05
  • Yours is a problem of identification. – Durden Apr 25 '23 at 19:33

1 Answers1

1

  1. This question only matters if the design is actually panel data. It's no different from logistic regression on panel data in this respect as well.

  2. In short, you can absolutely fit fixed effects to panel data in a probit model. The main objective of the data modeling strategy is that the response data are mutually conditionally independent so that the standard statistical inferential approaches are accurate.

  3. Random effects are only one way of achieving number 2. Fixed effects do not necessarily mean that you adjust for a dummy variable for each subject in an analysis. You may, for instance, adjust for predictive effects - such as age, income, employment status, health history, etc. etc. A "random effect" is nothing more than a sum of all the unobserved patient-level variables.

  4. If the panel data contain clusters that are large enough and contain enough variability, you can still adjust for individual level fixed effects. The problem of course is that for a large number of sparse clusters, these fixed effect terms become unstable and it's desirable to employ an estimator with shrinkage properties, either REML GLMM (your random effect) or even a Ridge estimator (penalized regression with L2 penalty).

AdamO
  • 62,637