ANOVA-Simultaneous Component Analysis (ASCA) is a powerful approach for analyzing multi-factorial experimental designs with multivariate responses. However, standard ASCA methods assume homogeneous variance across experimental groups, an assumption often violated in realworld data, particularly in biological and chemical studies. This paper introduces Variance Normalized ASCA (VNASCA), a novel extension that addresses heterogeneous variance through a weighted least squares framework. We provide a comprehensive mathematical derivation of the VNASCA methodology, including its weight calculation strategies, permutation-based significance testing, and variance partitioning approach. The method incorporates robust options for weight estimation, regularization for numerical stability, and automatic effect selection for enhanced interpretability. Practical implementation guidelines for parameter tuning are provided, and the method's performance is validated through both controlled simulations and application to real agricultural data from maize trials in Ghana. The experimental results demonstrate that VN-ASCA provides improved prediction accuracy in the presence of heterogeneous variance while maintaining interpretability. The application to multi-environment maize trials in Ghana (50 plots, 100 traits, 4 locations) demonstrates practical utility, with adaptive VN-ASCA showing measurable improvements in root mean squared error and substantially stronger statistical evidence for environmental effects. These findings suggest that accounting for variance heterogeneity can enhance the detection and interpretation of factorial effects in complex multivariate datasets.
Dwamena et al. (Sun,) studied this question.