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

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Presentation on theme: "Penalized Maximum Likelihood Logistic Regression Joseph Coveney Cobridge Co., Ltd."— Presentation transcript:

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

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5 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

6 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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8 Approaches to Separation Remove predictors –Pool groups –Remove interaction terms Gather more data Use alternatives

9 Exact Logistic Regression

10 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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12 [19] D. Firth Bias reduction in maximum likelihood estimates. Biometrika 80:27–38.

13 firthlogit

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16 But... redux

17 But... redux, continued

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20 Profile Likelihood Ratio CIs

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22 Caveats Profile Penalized Likelihood CIs Small-sample Behavior

23 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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26 To-do’s Profile Penalized Likelihood CIs Modify ml d0


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