Elastic Net For the elastic net models, the tuning parameters were constrained such that 0.1 3.0 and = {0.1, 1.0} using the CRAN R package Models t caret. ≤ ≤ α were selected according to the one SE heuristic. Most elemental oxide models selected = 0.1, which represents 10% L1-penalty and 90% L2-penalty. The α exception was SiO2, which selected = 1.0. This is equivalent to a lasso penalty α because it is 100% L1-penalty. The MnO model had the smallest value (t = 0.1); t Al2O3, Fe2O3, MgO, and CaO had the largest value (t = 3.0). The latter four t models had the most coefficients. Sparse Partial Least Squares For the SPLS models, tuning parameters were constrained using = caret: η {0.1, 0.3, 0.5, 0.7, 0.9} and = {1, 2, 3, 4, 5}. The parameter is a combination K η of the and parameters; it controls the sparsity of the model. The sparser t1 t2 models are for Al2O3, TiO2, and MgO. TiO2 has the largest number of hidden components (K = 4). The third parameter was = 0.5, which simply dictates the κ starting point for the SPLS algorithm.
Elastic Net For the elastic net models, the tuning parameters were constrained such that 0.1 ≤ t ≤ 3.0 and α = {0.1, 1.0} using the CRAN R package caret. Models were selected according to the one SE heuristic. Most elemental oxide models selected α = 0.1, which represents 10% L1-penalty and 90% L2-penalty. The exception was SiO2, which selected α = 1.0. This is equivalent to a lasso penalty because it is 100% L1-penalty. The MnO model had the smallest t value (t = 0.1); Al2O3, Fe2O3, MgO, and CaO had the largest t value (t = 3.0). The latter four models had the most coefficients. Sparse Partial Least Squares For the SPLS models, tuning parameters were constrained using caret: η = {0.1, 0.3, 0.5, 0.7, 0.9} and K = {1, 2, 3, 4, 5}. The η parameter is a combination of the t1 and t2 parameters; it controls the sparsity of the model. The sparser models are for Al2O3, TiO2, and MgO. TiO2 has the largest number of hidden components (K = 4). The third parameter was κ = 0.5, which simply dictates the starting point for the SPLS algorithm.