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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