RT Journal Article
SR Electronic
T1 rdacca.hp: an R package for generalizing hierarchical and variation partitioning in multiple regression and canonical analysis
JF bioRxiv
FD Cold Spring Harbor Laboratory
SP 2021.03.09.434308
DO 10.1101/2021.03.09.434308
A1 Jiangshan Lai
A1 Yi Zou
A1 Jinlong Zhang
A1 Pedro Peres-Neto
YR 2021
UL http://biorxiv.org/content/early/2021/03/10/2021.03.09.434308.abstract
AB Canonical analysis, a generalization of multiple regression to multiple response variables, is widely used in ecology. Because these models often involve large amounts of parameters (one slope per response per predictor), they pose challenges to model interpretation. Currently, multi-response canonical analysis is constrained by two major challenges. Firstly, we lack quantitative frameworks for estimating the overall importance of single predictors. Secondly, although the commonly used variation partitioning framework to estimate the importance of groups of multiple predictors can be used to estimate the importance of single predictors, it is currently computationally constrained to a maximum of four predictor matrices.We established 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.In this application, we aim at: a) demonstrating the mathematical links between commonality analysis, variation and hierarchical partitioning; b) generalizing these frameworks to allow the analysis of any number of responses, predictor variables or groups of predictor variables in the case of variation partitioning; and c) introducing and demonstrating the usage of the R package rdacca.hp that implements these generalized frameworks.Competing Interest StatementThe authors have declared no competing interest.