Generalizing hierarchical and variation partitioning in multiple regression and canonical analyses using the rdacca.hp R package

Abstract Canonical analysis, a generalization of multiple regression to multiple‐response variables, is widely used in ecology. Here we demonstrate that commonality analysis and hierarchical partitioning, widely used for both estimating predictor importance and improving the interpretation of single‐response regression models, are related and complementary frameworks that can be expanded for the analysis of multiple‐response models.

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• 1 Because these models often involve many parameters (one slope per response per predictor), they pose challenges to model interpretation.
• 2 Among these challenges, we lack quantitative frameworks for estimating the overall importance of single predictors in multi‐response regression models.
• 3 Here we demonstrate that commonality analysis and hierarchical partitioning, widely used for both estimating predictor importance and improving the interpretation of single‐response regression models, are related and complementary frameworks that can be expanded for the analysis of multiple‐response models.

This work deepens our understanding of the fundamental laws governing the universe, from subatomic particles to cosmic structures.

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