Penalized Maximum Likelihood Logistic Regression Joseph Coveney Cobridge

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

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

Separation in Logistic Regression

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.

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.

Approaches to Separation • Remove predictors – Pool groups – Remove interaction terms • Gather more data • Use alternatives

Exact Logistic Regression

But. . . Dataset from D. M. Potter. 2005. A permutation test for inference in logistic regression with small- and moderate-sized data sets. Statistics in Medicine 24: 693– 708.

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

firthlogit

But. . . redux

But. . . redux, continued

Profile Likelihood Ratio CIs

Caveats • Profile Penalized Likelihood CIs • Small-sample Behavior

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.

To-do’s • Profile Penalized Likelihood CIs • Modify ml d 0