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

• Published in: Methods in ecology and evolution Vol. 13; no. 4; pp. 782 - 788
• Main Authors: Lai, Jiangshan, Zou, Yi, Zhang, Jinlong, Peres‐Neto, Pedro R.
• Format: Journal Article
• Language: English
• Published: London John Wiley & Sons, Inc 01-04-2022
• Subjects: averaging over orderings; CCA; Commonality; commonality analysis; constrained ordination; db‐RDA; explained variation; Mathematical models; Partitioning; RDA; Regression analysis; Regression models; relative importance; Variation
• ISSN: 2041-210X; 2041-210X
• DOI: 10.1111/2041-210X.13800

Canonical analysis, a generalization of multiple regression to multiple‐response variables, is widely used in ecology. Because these models often involve many parameters (one slope per response per predictor), they pose challenges to model interpretation. Among these challenges, we lack quantitative frameworks for estimating the overall importance of single predictors in multi‐response regression models.
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.
In this application, we (a) demonstrate the mathematical links between commonality analysis, variation and hierarchical partitioning; (b) generalize these frameworks to allow the analysis of any number of predictor variables or groups of predictor variables as in the case of variation partitioning; and (c) introduce and demonstrate the implementation of these generalized frameworks in the R package rdacca.hp.
摘要
典范分析(RDA、dbRDA和CCA)作为多元回归应用于多响应变量的拓展，广泛应用于生态学数据分析。但由于典范分析通常涉及很多参数(即每个响应变量与每个解释变量之间都有一个系数)，因此在模型解读方面面临很多困难。其中有个尚未解决的挑战是缺乏定量的框架来评估解释变量相对重要性。
本研究中，我们证明了广泛用于估计多元回归模型解释变量重要性和提高模型解读性的共性分析(commonality analysis)和层次分割(hierarchical partitioning)是相关且互补的框架。我们也把层次分割框架扩展用于多响应变量的典范分析模型。
这里我们 a)展示了共性分析、变差分解(variation partitioning)和层次分割之间的数学联系；b)开发了不限制解释变量(组)数的变差分解和层次分割的R包rdacca.hp；c)使用Doubs鱼类数据演示rdacca.hp的使用和结果的解读。