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Penalized Maximum Likelihood Logistic Regression

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.

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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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