Redundancy Analysis (RDA)

Redundancy analysis (RDA) is a constrained ordination that regresses a multivariate response matrix on explanatory variables and then applies principal component analysis to the fitted values.

중복분석(RDA)은 다변량 반응 행렬을 설명변수에 회귀한 다음, 그 적합값에 주성분분석을 적용하는 제약 서열화 기법입니다.

Which environmental variables explain the variation in my multivariate response, and how much do they explain after adjusting for the number of predictors?

어떤 환경변수가 다변량 반응의 변이를 설명하고, 설명변수 수를 보정하면 얼마나 설명하나요?

Redundancy analysis fits a multivariate linear regression of the response matrix, often Hellinger-transformed species data, on explanatory variables and summarizes the fitted part with ordination axes. It reports the explained variation as R² and adjusted R², and permutation tests assess the whole model, the first axis and each variable given the others.

When to use Redundancy Analysis (RDA)

• Relating a multivariate response to several explanatory variables with roughly linear relationships
• Analyzing species data after a Hellinger transformation
• Partitioning explained variation between two sets of explanatory variables

When to use something else

• Species responses are strongly unimodal along long gradients: use Canonical Correspondence Analysis (CCA)
• There are no explanatory variables and you only want to summarize the response: use PCA

Assumptions and requirements

• Linear relationships between transformed responses and explanatory variables
• Explanatory variables are not perfectly collinear (VIF is reported)
• Observations are exchangeable under the null hypothesis

What the analysis reports

• Constrained and unconstrained variance, R² and adjusted R²
• Permutation tests for all axes, the first axis and each term (Freedman-Lane)
• Optional forward selection with the double stopping rule
• Variation partitioning fractions when a partition of the explanatory variables is given
• Biplot correlations and a bar chart of constrained eigenvalues

How to report it

A redundancy analysis of [p] Hellinger-transformed response variables on [q] explanatory variables (N = [n]) explained [value]% of the variation (adjusted R² = [value]); the global permutation test gave F([q], [df]) = [value], p = [value].

Related methods

• Canonical Correspondence Analysis (CCA)
• Principal Component Analysis
• Mantel and Partial Mantel Tests

Run Redundancy Analysis (RDA) on Quorant