The main idea ...
Like other partial methods (e.g. partial CCA), partial redundancy analysis (pRDA) seeks to remove the effect of one or more explanatory variables on a set of response variables prior to a standard RDA. This may be useful when well-characterised variables with strong effects obscure the effects of more interesting explanatory variables.
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Figure 1: An illustration of "partialling out" a set of variables (W) from a model. a) Both the explanatory variable(s) in matrices X and Y explain a portion of the variation in the response data (Y). b) After the partialling out the effect of W (which may be a single variable or a set of variables), only the variance in the response variables (Y) which can be exclusively explained by the variance in one set of explanatory variables (X) is retained.
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When partialling out the effects of time or space, it is important to consider what the best representation of temporal/spatial difference between objects is. Complex surfaces or non-linear representations of time may not be partialled out in a meaningful way and may adversely effect the analysis.
The method can also be applied to examine the effect of a single variable in a matrix of explanatory variables using pRDA, while controlling for the other variables. This is done by placing all other explanatory variables in a matrix of control variables. Their effects may then be partialled out. A single canonical axis and eigenvalue will be generated which express the variation that the variable of interest is responsible for.
Implementations
- R
- The function rda() in the vegan package can be used to perform pRDA by adding a conditioning matrix (i.e. the matrix containing the variables whose effects are to be partialled out) via the "Condition()" argument. For example: rda(Y ~ X + Condition(Z))" will perform an RDA of a response matrix "Y" and an explanatory matrix "X" after partialling out the effects of a conditioning matrix "Z".
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