Improving and Evaluating Resistant Alternatives to Procrustes Analysis for Multivariate Dataset Matching

ABSTRACT Procrustes analysis (PA) is a widely used method for aligning and comparing two or more multivariate data matrices and has been applied across various fields. However, PA is based on the least sum of squares, which has long been recognized as highly sensitive to outliers. This study proposes two new resistant alternatives to PA, advances five previously developed resistant PA methods, and provides accompanying R code for their implementation. The performance of PA and seven resistant PA methods in matching datasets containing outliers was compared and evaluated through simulation studies. We simulated 180 scenarios, including 36 scenarios without outliers and 144 scenarios varying in error variability, proportion of outliers, magnitude of outliers, sample size, reflection, and correlation structure. Results showed that in the presence of outliers, PA performed poorly in identifying outliers and matching datasets across all scenarios, while resistant PA methods, especially our proposed Improved Least Trimmed Squares, demonstrated strong robustness and practical utility. Key factors affecting methods' performance included error variability, proportion of outliers, magnitude of outliers, and sample size. These resistant PA methods have broad applicability in fields such as ecology and evolution, where robust comparison of multivariate datasets is essential.