# Redundancy analysis Computation of weighted or unweighted redundancy analysis of a samples-by-parts compositional data table, given a set of covariates. ```r RDA(data, cov=NA, nd = NA, weight = TRUE, suprow = NA, row.wt = NA) ``` ## Arguments - `data`: A data frame or matrix of interval-scale data, e.g. logratios (which are preferably in a list object with weights) - `cov`: List of covariates for constraining solution - `nd`: Number of dimensions for summary output, by default the number of constraining dimensions - `weight`: TRUE (default) when weights are in data list object, FALSE for unweighted analysis, or a vector of user-defined part weights - `suprow`: Indices of rows that are supplementary (passive) points (NOTE: this option is not implemented in this version) - `row.wt`: Optional user-defined set of positive weights for the rows (samples) (default: equal weights) ## Details The function `RDA` computes a redundancy analysis of a matrix of interval-scaled data, constrained by a matrix of covariates, using the singular value decomposition. By default weights are assumed in the data list object. For the unweighted logratio analysis, specify the option `weight=FALSE`. If `weight = TRUE` (the default) it is assumed that the weights are included in the data object, which comes from one of the logratio functions. User-specified part weights can be provided using the same `weight` option. Usually row weights are not specified, they are equal unless intentional weighting of the samples is desired. Supplementary rows can be declared (also known as passive points) -- these do not contribute to the solution but are positioned on the solution axes. This option will be available in the next release of the package. ## Returns - **sv**: Singular values - **nd**: Number of dimensions in the solution output - **rownames**: Row names - **rowmass**: Row weights - **rowdist**: Row distances to centroid - **rowinertia**: Row variances - **rowcoord**: Row standard coordinates - **rowpcoord**: Row principal coordinates - **rowsup**: Indices of row supplementary points - **colnames**: Column names - **colmass**: Column weights - **coldist**: Column logratio distances to centroid - **colinertia**: Column variances - **colcoord**: Column standard coordinates - **colpcoord**: Column principal coordinates - **covcoord**: Regression coordinates of constraining variables - **covnames**: Names of constraining variables - **N**: The data table (usually logratios in this package) - **cov**: The table of covariates ## References Van den Wollenbergh, A. (1977), Redundancy analysis. An alternative to canonical correlation analysis, Psychometrika 42, 207-219. Greenacre, M. (2013), Contribution biplots, Journal of Computational and Graphical Statistics 22, 107-122. ## Author(s) Michael Greenacre ## See Also `PLOT.RDA`, `CLR`, `LR`, `DUMMY` ## Examples ```r # Data frame fish has sex, habitat and mass in first columns, # then morphometric data in remaining columns data("fish") sex <- fish[,1] habitat <- fish[,2] mass <- fish[,3] fishm <- as.matrix(fish[,4:29]) # Convert to compositional data matrix fishm <- CLOSE(fishm) # Compute logarithm of mass and interaction of sex (F/M) and habitat (L/P) categories logmass <- log(mass) sexhab <- 2*(sex-1)+habitat sexhab.names <- c("FL","FP","ML","MP") rownames(fishm) <- sexhab.names[sexhab] # Create dummy variables for sexhab and create matrix of covariates sexhab.Z <- DUMMY(sexhab, catnames=sexhab.names) vars <- cbind(logmass, sexhab.Z) # Perform RDA on centred logratios require(ca) fish.rda <- RDA(CLR(fishm), cov=vars) # Plot results # (for more options see Appendix of Compositional Data Analysis in Practice) PLOT.RDA(fish.rda, map="contribution", rescale=0.05, indcat=2:5, colrows=rainbow(4, start=0.1, end=0.8)[sexhab], cexs=c(0.8,0.8,1)) ```

RDA function