Data Adequacy Testing for Partial Least Squares Discriminant Analysis Using Raman Spectra.

Area of Science:

• Statistical modeling
• Chemometrics
• Data analysis

Background:

• Partial Least Squares Discriminant Analysis (PLS-DA) is prone to false conclusions with high-dimensional data.
• Existing methods lack data adequacy testing, necessitating new approaches.
• Chance correlations can arise in datasets with numerous predictors and limited observations.

Purpose of the Study:

• To propose a novel data adequacy testing method for PLS-DA.
• To address the need for pre-model building assessment in high-dimensional datasets.
• To provide a framework for determining sufficient sample sizes for predictive modeling.

Main Methods:

• Utilized random permutations to disrupt predictor-response correlations and establish chance distributions.
• Defined novel null hypotheses to control Type I and Type II errors.
• Applied predictor-based Bonferroni corrections and analyzed distribution tails to adjust significance levels.

Main Results:

• The proposed method significantly reduced false positives compared to standard PLS-DA (12x error rate reduction).
• The method exhibited a higher rate of false negatives (4.5x increase) than PLS-DA.
• Demonstrated successful application to real-world Raman spectroscopy data, validating its practical utility.

Conclusions:

• The developed method effectively assesses data adequacy for PLS-DA, enhancing model reliability.
• It provides guidance on sample size requirements for datasets with many predictors.
• This approach aids researchers in deciding whether to proceed with model building, especially with spectroscopic data.