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 | |