Redundancy Analysis
Also known as: RDA
Redundancy Analysis (RDA) is a multivariate technique developed by van den Wollenberg (1977) that combines multiple regression and principal component analysis. RDA finds linear combinations of predictor variables that best predict variation in response variables, making it ideal for understanding how sets of predictors collectively explain multivariate outcomes.
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When to use it
Apply RDA when you have multiple response variables and want to understand how a set of predictors collectively influences them, when you need ordination (visualization) of multivariate relationships, or when you want to identify the most important linear combinations of predictors. Common in ecology, environmental science, and behavioral analysis.
Strengths & limitations
- Multivariate perspective: explains multiple outcomes, not just one
- Dimension reduction: identifies key predictor combinations that explain responses
- Interpretability: components have clear interpretation as weighted combinations of predictors
- Asymmetric modeling: naturally handles directional relationships (predictors cause responses)
- Visualization: component scores can be plotted to reveal patterns
- Assumes linearity: fits only linear relationships; non-linear patterns are missed
- Same space assumption: assumes predictors and responses operate in related linear space
- Sample size: needs sufficient sample relative to number of variables for stable estimation
- Correlation focus: optimizes correlation, not prediction per se (unlike PLS-SEM)
Frequently asked
How does RDA differ from canonical correlation?
Both analyze relationships between two sets of variables. RDA is asymmetric (predicting Y from X) and optimizes variance in Y. Canonical correlation is symmetric and maximizes correlation between X and Y composites.
What is the redundancy index?
It measures the proportion of variance in responses explained by extracted predictor components. Higher redundancy (0-1 scale) indicates predictors better explain response variation.
Can RDA handle categorical variables?
Standard RDA assumes continuous variables. Categorical predictors should be dummy-coded; categorical responses require extensions like redundancy analysis for correspondence analysis.
How many components should I extract?
Typically extract components that cumulatively explain 70-90% of variance in predictors, then check how much response variance they explain. Cross-validation helps avoid over-extraction.
Is RDA the same as PLS regression?
Similar goals but different optimization. RDA maximizes variance in predictors that correlates with responses. PLS regression maximizes covariance between predictor and response components. PLS is better for prediction; RDA for understanding variance patterns.
Sources
- van den Wollenberg, A. L. (1977). Redundancy analysis: An alternative for canonical correlation analysis. Psychometrika, 42(2), 207-219. DOI: 10.1007/BF02294050 ↗
- Legendre, P., & Legendre, L. (1998). Numerical Ecology (2nd ed.). Elsevier. ISBN: 9780444892546
- Knudsen, S., Andersen, T., & Hansen, J. (2007). Redundancy analysis of multivariate data using PLS. Chemometrics and Intelligent Laboratory Systems, 87(2), 264-272. link ↗
How to cite this page
ScholarGate. (2026, June 3). Redundancy Analysis. ScholarGate. https://scholargate.app/en/psychometrics/redundancy-analysis
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