model RMSEP values using reveal that there is no statistical t-test Student’s difference in the prediction accuracies of the four models for this suite of 100 igneous rocks. These results are shown in Table 7, which gives both the p-values and the absolute differences in RMSEP for the model comparisons. MODEL SELECTION Partial Least Squares The number of components in the PLS model was constrained to 15 to prevent overfitting. The selected models for the ten major elemental oxides all used fewer than 15 components, as shown in Table 2. MgO had the most complex model with 14 components, while Na2O had the most parsimonious model with 3 components. The other elements had components numbering from 6 to 12, with SiO2 and Al2O3 on the lower end of that range, and TiO2 and Fe2O3 on the upper end. Lasso The tuning parameter, was constrained to 0.9 using the CRAN t, t 0.1 ≤ ≤ R package Larger values of would have permitted models with more caret. t coefficients. constrains to a maximum value of 0.9 because larger values do Caret not improve the predictions sufficiently to compensate for the lost model simplicity. These values, shown in Table 3, minimize the number of components t in the model and the model RMSEP values according to the one SE heuristic.
model RMSEP values using Student’s t-test reveal that there is no statistical difference in the prediction accuracies of the four models for this suite of 100 igneous rocks. These results are shown in Table 7, which gives both the p-values and the absolute differences in RMSEP for the model comparisons. MODEL SELECTION Partial Least Squares The number of components in the PLS model was constrained to 15 to prevent overfitting. The selected models for the ten major elemental oxides all used fewer than 15 components, as shown in Table 2. MgO had the most complex model with 14 components, while Na2O had the most parsimonious model with 3 components. The other elements had components numbering from 6 to 12, with SiO2 and Al2O3 on the lower end of that range, and TiO2 and Fe2O3 on the upper end. Lasso The tuning parameter, t, was constrained to 0.1 ≤ t ≤ 0.9 using the CRAN R package caret. Larger values of t would have permitted models with more coefficients. Caret constrains to a maximum value of 0.9 because larger values do not improve the predictions sufficiently to compensate for the lost model simplicity. These t values, shown in Table 3, minimize the number of components in the model and the model RMSEP values according to the one SE heuristic.