Problem with Firth Logistic Regression

Hello all,

I am having some issues trouble shooting a Firth Logistic regression model I have run on municipal level data. So, I have a dataset on all municipalities under analysis and I am looking at an event with low frequency (81), while the number of non-events is more than 2000.

The issue I keep receiving an infinite estimate for the model intercept, while the IVs are ok (at least they look ok to me).

Any help troubleshooting this would be much appreciated. I could definitely use a fresh pair of eyes.

Here is the output I am stuck from R (logistf). I also attached the printout as the table below comes out a little convoluted. The covariances didn't strike me as particularly troublesome (though I'm all ears if someone disagrees). Also, I used the standardized option in the model for the IVs. All the variables are continuous.

Thanks in advance for any advice comments you have!

Model fitted by Penalized ML
Confidence intervals and p-values by Profile Likelihood Profile Likelihood Profile Likelihood Profile Likelihood

coef se(coef) lower 0.95 upper 0.95 Chisq p
(Intercept) -3.947938e+00 1.643859e-01 -4.283353e+00 -3.639557e+00 Inf 0.000000e+00
Total_Fixed_Ass 3.923257e-09 4.396373e-09 -3.774015e-09 1.342160e-08 0.9401887 3.322293e-01
Infrastructure 3.079252e-01 5.709936e-02 1.993128e-01 4.240471e-01 44.1480759 3.044509e-11
Salary_Rate 7.017842e-03 1.662845e-03 3.883563e-03 1.033340e-02 16.7389526 4.289128e-05

Likelihood ratio test=109.3604 on 3 df, p=0, n=2454
Wald test = 76.8872 on 3 df, p = 1.110223e-16

[,1] [,2] [,3] [,4]
[1,] 2.702274e-02 3.614560e-12 -8.852098e-04 -1.726696e-04
[2,] 3.614560e-12 1.932810e-17 -1.292892e-10 -1.467278e-12
[3,] -8.852098e-04 -1.292892e-10 3.260337e-03 -5.979337e-07
[4,] -1.726696e-04 -1.467278e-12 -5.979337e-07 2.765053e-06