A comparison of procedures to select important variables for describing datasets

Area of Science:

• Chemometrics
• Data Analysis
• Multivariate Statistics

Background:

• Variable selection is crucial for simplifying complex datasets and improving model interpretability.
• Procrustes rotation is a known method for dimensionality reduction and variable selection.
• Evaluating different preprocessing and matching criteria is essential for optimizing Procrustes rotation.

Purpose of the Study:

• To investigate the effectiveness of Procrustes rotation for variable selection under various preprocessing and matching criteria.
• To introduce and compare a novel variable selection procedure, DROPCORA, against Procrustes rotation.
• To assess the robustness and multicollinearity of variables selected by different methods.

Main Methods:

• Procrustes rotation applied with autoscaling and 'minone' preprocessing.
• Four distinct criteria for matching original and reduced subspaces in Procrustes rotation.
• Development and application of the DROPCORA procedure based on correlation coefficients.
• Analysis of robustness and multicollinearity for selected variables.

Main Results:

• The number of variables selected by both methods consistently matched the number of important dataset dimensions.
• Variable selection outcomes differed between Procrustes rotation and DROPCORA.
• The DROPCORA procedure, utilizing correlation coefficients, yielded the best results in terms of robustness and multicollinearity.

Conclusions:

• The DROPCORA procedure offers an effective alternative for variable selection, outperforming Procrustes rotation in key statistical measures.
• Variable selection strategies significantly impact data robustness and multicollinearity.
• The choice of variable selection method is critical for accurate characterization of object sets.