What is Redundancy Analysis?
Redundancy Analysis (RDA) was developed by Van den Wollenberg (1977) as an alternative to Canonical Correlation Analysis (CCorA). Redundancy Analysis allows studying the relationship between two tables of variables Y and X. While the Canonical Correlation Analysis is a symmetric method, Redundancy analysis is non-symmetric. In Canonical Correlation Analysis, the components extracted from both tables are such that their correlation is maximized. Redundancy Analysis, the components extracted from X are such that they are as much as possible correlated with the variables of Y. Then, the components of Y are extracted so that they are as much as possible correlated with the components extracted from X.
Figure 1. Redundancy analysis.
- If your response variables are not homogeneous in dimensionality (that is, if they have different basic measurement units), you can focus them on their averages, or standardize them using, for example, z-scores. However, it is not recommended to standardize the raw count data.
- Make sure that the number of explanatory variables is less than the number of objects (sites, samples, observations, etc.) in the data matrix. If this is not the case, your system cannot be sure.
- If your explanatory variables are not homogeneous in dimensionality (for example, they have different physical units), center them on their averages and standardize them.
- Check the distribution of each variable in the descriptive and response matrix.
Selection principle of RDA or model
First use species-sample data (97% similar sample OTU table) to do DCA analysis, see the size of the first axis of Lengths of gradient in the analysis result, if it is greater than 4.0, CCA should be selected If it is between 3.0-4.0, both RDA and CCA can be selected. If it is less than 3.0, the result of RDA is better than CCA.
Information about multiple constrained axes (RDA axis) and unconstrained axes (PCA axis) will be displayed in the RDA results.
- Each RDA axis has a characteristic value associated with it. Since the total variance of the solution is equal to the sum of all eigenvalues (constrained as unconstrained), the variance ratio explained by each axis is only the quotient of the given eigenvalue and the total variance of the solution.
- Sometimes, the ranking of the residuals and/or the correlation between the residuals may be more ecologically meaningful than well-characterized factors. By checking the non-normative (unconstrained) vectors of the RDA solution by sorting and relevance, insights into the behavior of these residuals can be obtained. Alternatively, you can perform PCA on the residual matrix after performing MLR on a set of response variables. Some implementations of RDA display the PCA axis together with the RDA axis. The PCA axis summarizes the unconstrained (residual) variance.
Software and algorithm
PC-ORD or CANOCO software for drawing.
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Magali Noval Rivas, PhD, Oliver T. Burton, et al. A microbita signature associated with experimental food allergy promotes allergic senitization and anaphylaxis. The Journal of Allergy and Clinical Immunology. 2013:131(1) , 201-212.
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