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I have used penalized logistic regression (R package logistf) to predict probability of a rare event. 0.12% is the event rate i.e., only 35 occurrence of event in the total 29k+ data points.

What is the prediction equation for penalized logistic regression? Is it same has logistic regression i.e., $\frac{\exp(a+bX)}{1 + \exp(a+bX)}$?

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Yes. The penalty only affects the optimal parameters. Once the parameters are determined the structural form of the model is identical.

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  • $\begingroup$ thanks Matthew. Additionally, is it possible to provide some link or reference materials that explains your answer in detail. $\endgroup$ – Manohar Swamynathan May 29 '15 at 18:04
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    $\begingroup$ The primary source is freely available: stat.duke.edu/~scs/Courses/Stat376/Papers/GibbsFieldEst/…. But, in general, penalty methods only change the form of the loss function being optimized, not the functional form of the model itself. $\endgroup$ – Matthew Drury May 29 '15 at 18:08

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