Parsimonious and robust multivariate calibration with rational function Least Absolute Shrinkage and Selection...

Area of Science:

• Chemometrics
• Analytical Chemistry
• Statistical Modeling

Background:

• Multivariate calibration is crucial for analyzing complex chemical data.
• Existing methods may lack robustness or flexibility in model selection.
• The integration of regularization techniques with advanced function types is an area of active research.

Purpose of the Study:

• To present novel methods for multivariate calibration using rational functions.
• To explore the application of Least Absolute Shrinkage and Selection Operator (LASSO) and Elastic Net (ENET) in rational function modeling.
• To demonstrate the robustness and flexibility of the proposed approach.

Main Methods:

• Development of multivariate calibration models based on rational functions.
• Implementation of LASSO and ENET regularization techniques for coefficient shrinkage and variable selection.
• Automated model building and complexity reduction using cross-validation.
• Evaluation of model robustness, particularly in the context of collinearity and potential spectral interferences.

Main Results:

• Rational function modeling demonstrates inherent robustness.
• Cross-validation allows flexibility, occasionally reducing rational models to linear ones.
• LASSO and ENET effectively handle collinearity and enable parsimonious model construction.
• The combination of rational functions with ENET yields significant benefits, with LASSO solutions being a subset.

Conclusions:

• The proposed method offers a robust and flexible approach to multivariate calibration.
• ENET regularization is particularly beneficial when combined with rational function models.
• Automated model selection via cross-validation ensures parsimonious and potentially more robust models.