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Penalized Maximum Likelihood Logistic Regression

Explore separation in logistic regression, Firth's Bias-reduced GLMs, practical firthlogit syntax, examples, and addressing caveats. Learn from complete & quasi-complete separation datasets, exact logistic regression, profile likelihood ratio CIs, and profile penalized likelihood CIs. Uncover strategies to deal with separation such as removing predictors, pooling groups, avoiding interaction terms, gathering more data, and utilizing alternatives. Keep up to date with small-sample behavior, bias reduction in maximum likelihood estimates, and tools like the firthlogit and profile penalized likelihood CIs. Discover insights on avoiding convergence problems and considerations for modifying ml.d0.

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Penalized Maximum Likelihood Logistic Regression

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  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

  4. 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.

  5. 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.

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

  7. Exact Logistic Regression

  8. 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.

  9. [19] D. Firth. 1993. Bias reduction in maximum likelihood estimates. Biometrika80:27–38.

  10. firthlogit

  11. But . . . redux

  12. But . . . redux, continued

  13. Profile Likelihood Ratio CIs

  14. Caveats • Profile Penalized Likelihood CIs • Small-sample Behavior

  15. 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.

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

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