Model averaging in calibration of near-infrared instruments with correlated high-dimensional data.

Model averaging (MA) is a modelling strategy where the uncertainty in the configuration of selected variables is taken into account by weight-combining each estimate of the so-called 'candidate model'. Some studies have shown that MA enables better prediction, even in high-dimensional cases. However, little is known about the model prediction performance at different types of multicollinearity in high-dimensional data. Motivated by calibration of near-infrared (NIR) instruments,we focus on MA prediction performance in such data. The weighting schemes that we consider are based on the Akaike's information criterion (AIC), Mallows' C(p), and cross-validation. For estimating the model parameters, we consider the standard least squares and the ridge regression methods. The results indicate that MA outperforms model selection methods such as LASSO and SCAD in high-correlation data. The use of Mallows' C(p) and cross-validation for the weights tends to yield similar results in all structures of correlation, although the former is generally preferred. We also find that the ridge model averaging outperforms the least-squares model averaging. This research suggests ridge model averaging to build a relatively better prediction of the NIR calibration model.