1. Penalized Maximum Likelihood Logistic Regression
Joseph Coveney
Cobridge Co., Ltd.

2. Topics Separation in Logistic Regression Approaches to Separation
Firth’s Bias-reduced GLMs
firthlogit: syntax and examples
Caveats and to-do’s

3. Separation in Logistic Regression

5. Complete Separation
Dataset adapted from D. W. Hosmer and S. Lemeshow, Applied Logistic Regression Second Edition. (New York: John Wiley & Sons, 2000), pp. 138–39.

6. Quasi-complete Separation
Dataset adapted from D. W. Hosmer and S. Lemeshow, Applied Logistic Regression Second Edition. (New York: John Wiley & Sons, 2000), pp. 138–39.

8. Approaches to Separation
Remove predictors
Pool groups
Remove interaction terms
Gather more data
Use alternatives

9. Exact Logistic Regression

10. But . . .
Dataset from D. M. Potter A permutation test for inference in logistic regression with small- and moderate-sized data sets. Statistics in Medicine 24:693–708.

12. [19] D. Firth. 1993. Bias reduction in maximum likelihood estimates
[19] D. Firth Bias reduction in maximum likelihood estimates. Biometrika 80:27–38.

13. firthlogit

16. But redux

17. But redux, continued

20. Profile Likelihood Ratio CIs

22. Caveats
Profile Penalized Likelihood CIs
Small-sample Behavior

23. G. Heinze and M. Ploner, A SAS macro, S-PLUS library and R package to perform logistic regression without convergence problems. Technical Report 2/2004. Medical University of Vienna. p. 36.

26. To-do’s
Profile Penalized Likelihood CIs
Modify ml d0