Naifei Zhao, Qingsong Xu, Man-lai Tang and Hong Wang* Pages 740 - 756 ( 17 )
Aim and Objective: Near Infrared (NIR) spectroscopy data are featured by few dozen to many thousands of samples and highly correlated variables. Quantitative analysis of such data usually requires a combination of analytical methods with variable selection or screening methods. Commonly-used variable screening methods fail to recover the true model when (i) some of the variables are highly correlated, and (ii) the sample size is less than the number of relevant variables. In these cases, Partial Least Squares (PLS) regression based approaches can be useful alternatives.
Materials and Methods: In this research, a fast variable screening strategy, namely the preconditioned screening for ridge partial least squares regression (PSRPLS), is proposed for modelling NIR spectroscopy data with high-dimensional and highly correlated covariates. Under rather mild assumptions, we prove that using Puffer transformation, the proposed approach successfully transforms the problem of variable screening with highly correlated predictor variables to that of weakly correlated covariates with less extra computational effort.
Results: We show that our proposed method leads to theoretically consistent model selection results. Four simulation studies and two real examples are then analyzed to illustrate the effectiveness of the proposed approach.
Conclusion: By introducing Puffer transformation, high correlation problem can be mitigated using the PSRPLS procedure we construct. By employing RPLS regression to our approach, it can be made more simple and computational efficient to cope with the situation where model size is larger than the sample size while maintaining a high precision prediction.
Puffer transformation, preconditioning, sure independence screening (SIS), ridge partial least squares regression, variable screening, near infrared (NIR) spectroscopy data.
School of Mathematics and Statistics, Changsha University of Science & Technology, Changsha, School of Mathematics and Statistics, Central South University Changsha, Hunan, Department of Mathematics and Statistics, Hang Seng University of Hong Kong, Hong Kong, School of Mathematics and Statistics, Central South University Changsha, Hunan