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

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

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Separation in Logistic Regression

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

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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.

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

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Exact Logistic Regression

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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.

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

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firthlogit

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But... redux

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But... redux, continued

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Profile Likelihood Ratio CIs

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Caveats Profile Penalized Likelihood CIs Small-sample Behavior

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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.

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

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