Partial least squares methods: partial least squares correlation and partial least square regression.

Area of Science:

• Multivariate statistical analysis
• Data mining and machine learning

Background:

• Partial least square (PLS) methods, also known as projection to latent structures, are designed to relate information from two datasets measuring the same observations.
• PLS methods derive latent variables, which are optimal linear combinations of variables within a data table, to capture underlying structures.

Purpose of the Study:

• To present and illustrate partial least square correlation (PLSC) and partial least square regression (PLSR).
• To demonstrate the extension of these descriptive multivariate analysis techniques to address inferential questions.

Main Methods:

• Partial least square correlation (PLSC) identifies shared information between two tables by maximizing covariance between two sets of latent variables.
• Partial least square regression (PLSR) predicts one data table from another using latent variables derived from the predictor table to optimize prediction accuracy.
• Cross-validation techniques, including bootstrap and permutation tests, are employed to extend PLSC and PLSR for inferential analyses.

Main Results:

• The study illustrates the application and interpretation of PLSC for finding shared information and PLSR for predictive modeling between datasets.
• The effectiveness of cross-validation methods in enabling inferential statistical questions using PLS techniques is demonstrated.

Conclusions:

• Partial least square methods offer robust approaches for exploring relationships in complex datasets.
• The integration of cross-validation with PLS techniques expands their utility from descriptive to inferential statistical analysis.