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Table 1 Illustration: coefficients and predictions estimated by Firth’s logistic regression with intercept-correction (FLIC) and ridge regression where complexity parameter is either tuned by leave one-out cross-validated deviance D or set according to some informative prior (IP)

From: To tune or not to tune, a case study of ridge logistic regression in small or sparse datasets

Method FLIC Ridge
D IP
Dataset 1 \( {\hat{\beta}}_1 \) 1.7 13.94 1.54
\( {\hat{\pi}}_{x=0} \) 0.02 0 0.03
\( {\hat{\pi}}_{x=1} \) 0.11 0.11 0.11
Dataset 2 \( {\hat{\beta}}_1 \) 0.55 0.06 0.65
\( {\hat{\pi}}_{x=0} \) 0.07 0.1 0.06
\( {\hat{\pi}}_{x=1} \) 0.11 0.1 0.11