Table 2 Covariate structure applied in the simulation study. In particular, pairwise non-zero correlations between standard normal deviates Zk, the transformations defining Xk, measurement scale of covariates Xk and expected value of covariates E(Xk) are shown. [∙] denotes removal of the non-integer part of the argument and I is the indicator function
From: To tune or not to tune, a case study of ridge logistic regression in small or sparse datasets
Zk | Pairwise non-zero correlations of Zk | Transformation defining Xk | Scale of Xk | E(Xk) |
|---|---|---|---|---|
Z1 | Z2(0.5), Z3(0.5), Z7(0.5), Z14(0.5) | X1 = I(Z1 < 0.84) | binary | 0.80 |
Z2 | Z1(0.5), Z14(0.3) | X2 = I(Z2 < − 0.35) | binary | 0.36 |
Z3 | Z1(0.5), Z4(−0.5), Z5(−0.3) | X3 = I(Z3 < 0) | binary | 0.50 |
Z4 | Z3(−0.5), Z5(0.5), Z7(0.3), Z8(0.5), Z9(0.3), Z14(0.5) | X4 = I(Z4 < 0) | binary | 0.50 |
Z5 | Z3(−0.3), Z4(0.5), Z8(0.3), Z9(0.3) | X5 = I(Z5 ≥ − 1.2) + I(Z5 ≥ 0.75) | ordinal | 1.11 |
Z6 | Z7(−0.3), Z8(0.3), Z11(−0.5) | X6 = I(Z6 ≥ 0.5) + I(Z6 ≥ 1.5) | ordinal | 0.38 |
Z7 | Z1(0.5), Z4(0.3), Z6(−0.3) | X7 = [10Z7 + 55] | continuous | 54.5 |
Z8 | Z4(0.5), Z5(0.3), Z6(0.3), Z9(0.5), Z12(−0.3), Z14(0.5) | X8 = [max(0, 100 exp(Z8) − 20)] | continuous | 146 |
Z9 | Z4(0.3), Z5(0.3), Z8(0.5), Z14(0.3) | X9 = [max(0, 80 exp(Z9) − 20)] | continuous | 112 |
Z10 | – | X10 = [10Z10 + 55] | continuous | 54.5 |
Z11 | Z6(−0.5), Z12(0.3), Z15(0.5) | X11 = exp(0.4Z11 + 3) | continuous | 21.8 |
Z12 | Z8(−0.3), Z11(0.3), Z15(0.5) | X12 = exp(0.5Z12 + 1.5) | continuous | 5.1 |
Z13 | – | X13 = 0.01 ∗ [100(Z13 + 4)2] | continuous | 17 |
Z14 | Z1(0.5), Z2(0.3), Z4(0.5), Z8(0.5), Z9(0.3) | X14 = [10Z14 + 55] | continuous | 54.5 |
Z15 | Z11(0.5), Z12(0.5) | X15 = [10Z15 + 55] | continuous | 54.5 |