Penalized Maximum Likelihood for Mixed Effects Models-firthlogit

[Buki Peters]

I have a sample size of 308 retail stores clustered in 31 municipalities. My dependent variable is a 0-1 measure of compliance with 283 compliant and 25 non-compliant, so I used a mixed-effects logistic regression model for my analysis. My analysis has been reviewed and I've been informed to do a penalized maximum likelihood regression because 25 stores may pass as 'rare events'. I reran the analysis using firthlogit. but firthlogit does not take clusters into consideration.

Does anyone know a code for penalized maximum likelihood for mixed-effects models? I've pored through the posts here and I can't find any.

On the other hand, is it possible to run the two models; melogit and firthlogit, and select the one with a better fit (AIC/ BIC) to be used in my paper. While the both models produced similar estimates, they have completely different p-values, so I won't be able to include both models in one paper.

[Joseph Coveney]

I have a sample size of 308 retail stores clustered in 31 municipalities . . . I've been informed . . . 25 stores may pass as 'rare events'.

A nearly 10% rate doesn't strike me as particularly rare. To me, the 31 municipalities is the bigger problem for use of maximum likelihood estimation.

Does anyone know a code for penalized maximum likelihood for mixed-effects models?

You could use Stata's Bayesian commands or command prefixes to "penalize" a hierarchical logistic regression model.

help bayes_melogit

is it possible to run the two models; melogit and firthlogit, and select the one with a better fit (AIC/ BIC) to be used in my paper.

-firthlogit- is just the wrong command to model clustered data. I recommend instead to simulate under circumstances like what you observe and see just how bad the maximum likelihood estimates are. If they are adequate for your purposes, then show that to the referee.

help simulate

[Buki Peters]

This is super helpful. Thank you!