Table 3

Model Comparisons between linear regression (standard least squares) and various techniques of optimisation (generalised regression) for predicting square root AEX-FV

Response distribution	Estimation method	AICc	BIC	Generalised R² (T)	Generalised R² (V)	RASE (T)	RASE (V)	Lambda (penalty, T)
Normal	Standard Least Squares	−5843.0	−5802.1	0.993	0.993	0.078	0.077	–
Normal	Ridge	−5843.0	−5802.1	0.993	0.993	0.078	0.077	0.000
Normal	Lasso	−5841.8	−5800.9	0.993	0.993	0.078	0.077	0.071
Normal	Adaptive Lasso	−5843.0	−5802.1	0.993	0.993	0.078	0.077	0.000
Normal	Elastic Net	−5842.2	−5801.3	0.993	0.993	0.078	0.077	0.050
Normal	Adaptive Elastic Net	−5843.0	−5802.1	0.993	0.993	0.078	0.077	0.000
Normal	Double Lasso	−5841.8	−5800.9	0.993	0.993	0.078	0.077	0.071
Normal	Adaptive Double Lasso	−5843.0	−5802.1	0.993	0.993	0.078	0.077	0.000
Gamma	Maximum Likelihood	−1812.5	−1771.5	0.969	0.968	–	–	–
Gamma	Ridge	−1793.6	−1752.7	0.969	0.969	–	–	10.708
Gamma	Lasso	−1808.3	−1767.4	0.969	0.968	–	–	38.550
Gamma	Adaptive Lasso	−1812.5	−1771.5	0.969	0.968	–	–	0.000
Gamma	Elastic Net	−1807.2	−1766.3	0.969	0.968	–	–	42.452
Gamma	Adaptive Elastic Net	−1812.5	−1771.5	0.969	0.968	–	–	0.000
Gamma	Double Lasso	−1808.3	−1767.4	0.969	0.968	–	–	38.550
Gamma	Adaptive Double Lasso	−1812.5	−1771.5	0.969	0.968	–	–	0.000
LogNormal	Maximum Likelihood	−1355.9	−1315.0	0.965	0.966	–	–	–
LogNormal	Ridge	−1339.8	−1298.9	0.965	0.966	–	–	8.279
LogNormal	Lasso	−1353.4	−1312.5	0.965	0.966	–	–	26.082
LogNormal	Adaptive Lasso	−1355.9	−1315.0	0.965	0.966	–	–	0.000
LogNormal	Elastic Net	−1352.4	−1311.5	0.965	0.966	–	–	30.105
LogNormal	Adaptive Elastic Net	−1355.9	−1315.0	0.965	0.966	–	–	0.000
LogNormal	Double Lasso	−1353.4	−1312.5	0.965	0.966	–	–	26.082
LogNormal	Adaptive Double Lasso	−1355.9	−1315.0	0.965	0.966	–	–	0.000

In both training (T, n=2577) and validation (V, n=1057) sets, the models’ R² was between 0.993 and 0.965 and RASE between 0.078 and 0.077. The lambda penalty coefficient was included, where appropriate.
AEX-FV, area under expiratory flow-volume curve; AICc, Akaike Information Criterion; BIC, Bayesian Information Criterion; RASE, root average square error.