A new strategy to prevent over-fitting in partial least squares models based on model population analysis

Area of Science:

• Chemometrics
• Data analysis
• Statistical modeling

Background:

• Partial Least Squares (PLS) is a widely used method in chemical modeling.
• PLS models are prone to over-fitting, necessitating optimal selection of the number of latent variables (nLVs).
• Cross-validation (CV) is common for PLS model selection but can present challenges in identifying a clear minimum for prediction errors.

Purpose of the Study:

• To propose a novel strategy for selecting the optimal number of latent variables (nLVs) in Partial Least Squares (PLS) models.
• To enhance the reliability of PLS model selection by addressing the limitations of traditional cross-validation (CV).
• To improve the balance between prediction ability and model stability in PLS modeling.

Main Methods:

• A new strategy for PLS model selection was developed, integrating cross-validated coefficient of determination (Qcv(2)) with model stability (S).
• Model stability (S) was quantified using model population analysis (MPA) of PLS regression vectors.
• The proposed method was compared against other indicators like Euclidean 2-norm (B2), Durbin Watson statistic (DW), and jaggedness (J).

Main Results:

• The combined strategy of Qcv(2) and S provides additional insights into over-fitting when a clear Qcv(2) maximum is not observed.
• Model stability (S) proved more sensitive to over-fitting than B2, DW, and J.
• The proposed method successfully identified PLS models with both good prediction ability and enhanced stability.

Conclusions:

• The novel strategy effectively aids in selecting the optimal number of latent variables (nLVs) for PLS models, particularly when CV results are ambiguous.
• Integrating model stability (S) with Qcv(2) offers a more robust approach to mitigate over-fitting in PLS.
• The selected models demonstrate superior prediction performance and stability, advancing chemometric modeling practices.