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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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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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**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 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**

[19] D. Firth 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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