Redundancy analysis

Redundancy analysis with your own predictors

Redundancy analysis asks a direct question: how much of the variation in one matrix is explained by another? Magic Stat runs it from two spreadsheet blocks — the response matrix and the predictors — and gives you the constrained ordination, R² and the biplot.

The honest part

What RDA is, and the question it answers

Redundancy analysis is a constrained ordination. It regresses each response variable on the explanatory variables, then does a PCA of the fitted values. The axes are therefore linear combinations of your predictors, chosen to explain as much of the response matrix as they can.

The number to read is not the picture but the R², and its adjusted version. R² says how much of the response variation the constrained axes carry; the adjusted R² penalises that figure for the number of predictors, which matters as soon as you have more than a handful.

RDA assumes a linear response of the response variables to the predictors. That is a real assumption, not a formality: on long ecological gradients, or with abundance data full of zeros and unimodal responses, CCA is the appropriate method and RDA will understate the structure. A Hellinger or chord transformation before RDA is a common and defensible compromise.

If you have no predictors at all, you want an unconstrained ordination — PCA or PCoA — not RDA.

What it does

What Magic Stat gives you for RDA

How it works

Two blocks to a constrained ordination

  1. Load the data. responses in matrix X, explanatory variables in matrix Y, on the same rows.
  2. Pick RDA. Statistics → Multivariate → RDA.
  3. Select X and Y. the response variables and at least one non-overlapping explanatory variable; the dialog keeps the two matrices aligned by row.
  4. Choose the scaling. standardise the response variables if their scales differ; apply a transformation if the responses need one.
  5. Run and read. constrained axes and R² in the results table, the biplot in the figure, both in the report.
Options

The settings, in the dialog

Two matrices: X (responses) and Y (explanatory). Y must contain at least one variable that is not in X; rows are matched across both.

Standardise response variables (checkbox, matching the scaling you would use in R) and the shared transformation list: None · Z-score (standardise) · ln(1+x) · ln(x) · Hellinger · Chord · Chi-square · Square root · Range 0–1. Hellinger is the usual starting point for abundance responses.

Frequently asked

RDA questions, answered honestly

RDA or CCA?

RDA assumes linear responses; CCA assumes unimodal responses. On short gradients the two agree closely and RDA is simpler to explain. On long gradients, or with clear unimodal species responses, CCA is the more honest model.

RDA or PCA?

PCA is unconstrained: it finds the main axes of the response matrix with no predictors. RDA constrains those axes to be combinations of your explanatory variables. If you only want to describe the responses, use PCA.

How do I test whether the constraints are significant?

This dialog reports the constrained ordination, R² and the adjusted R², but it does not run a per-term permutation test of the constraints. When you need tests of individual terms or axes, or partial RDA, vegan in R is the appropriate tool.

Which transformation should I use?

For abundance responses, Hellinger or chord usually behave better than raw counts because they reduce the weight of the largest values. For standardised continuous responses with comparable units, None or Z-score. Whatever you choose, report it — the transformation is part of the method.

Is my data uploaded somewhere?

No. The analysis runs on your computer. The only automatic signal is an anonymous installation counter, with no data in it.

Canonical correspondence analysis → PCA analysis → Correspondence analysis →