Performs a weighted redundancy analysis

wrda is formula-based implementation of weighted redundancy analysis.

Usage

wrda(
  formula,
  response = NULL,
  data,
  weights = rep(1/nrow(data), nrow(data)),
  traceonly = FALSE,
  cca_object = NULL,
  object4QR = NULL
)

Arguments

formula: one or two-sided formula for the rows (samples) with row predictors in data. The left hand side of the formula is ignored if it is specified in the next argument (response). Specify row covariates (if any ) by adding + Condition(covariate-formula) to formula as in rda. The covariate-formula should not contain a ~ (tilde).
response: matrix or data frame of the abundance data (dimension n x m). Rownames of response, if any, are carried through. Can be NULL if cca_object is supplied or if the response is formula is two-sided.
data: matrix or data frame of the row predictors, with rows corresponding to those in response (dimension n x p).
weights: row weights (a vector). If not specified unit weights are used.
traceonly: logical, default FALSE. If TRUE, only the explained variance of the predictors and the Condition() are returned, i.e without performing a singular value decompostion.
cca_object: a vegan-type cca-object of transposed response, from which centred abundance values and row and column weights can be obtained.
object4QR: a vegan-type cca-object with weighted QR's for formula, i.e. qr(Z) and qr(XZ) obtainable via get_QR(object4QR, model = "pCCA") and get_QR(object4QR, model = "CCA"), respectively.

Value

All scores in the wrda object are in scaling "sites" (1): the scaling with Focus on Case distances.

Details

The algorithm is a modified version of published R-code for weighted redundancy analysis (ter Braak, 2022).

Compared to rda, wrda does not have residual axes, i.e. no SVD or PCA of the residuals is performed.

References

ter Braak C.J.F. and P. Šmilauer (2018). Canoco reference manual and user's guide: software for ordination (version 5.1x). Microcomputer Power, Ithaca, USA, 536 pp.

Oksanen, J., et al. (2022) vegan: Community Ecology Package. R package version 2.6-4. https://CRAN.R-project.org/package=vegan.

Examples

data("dune_trait_env")

# rownames are carried forward in results
rownames(dune_trait_env$comm) <- dune_trait_env$comm$Sites
response <- dune_trait_env$comm[, -1]  # must delete "Sites"

w <- rep(1, 20) 
w[1:10] <- 8 
w[17:20] <- 0.5

object <- wrda(formula = response ~ A1 + Moist + Mag + Use + Condition(Manure),
               data = dune_trait_env$envir, 
               weights = w)
object # Proportions equal to those Canoco 5.15
#> 
#> Call: wrda(formula = response ~ A1 + Moist + Mag + Use + Condition(Manure),
#> data = dune_trait_env$envir, weights = w)
#> 
#>               Inertia Proportion Rank
#> Total         65.7007     1.0000     
#> Conditional    7.3839     0.1124    2
#> Constrained   36.4952     0.5555    6
#> Unconstrained 21.8217     0.3321   19
#> 
#> Inertia is weighted variance
#> 
#> Eigenvalues for constrained axes:
#>  wRDA1  wRDA2  wRDA3  wRDA4  wRDA5  wRDA6 
#> 18.133  8.233  4.047  3.155  2.238  0.689 
#> 
#> Eigenvalues for unconstrained axes:
#> wPCA1 wPCA2 wPCA3 wPCA4 wPCA5 wPCA6 wPCA7 wPCA8 
#>    NA    NA    NA    NA    NA    NA    NA    NA 
#> (Showing 8 of 19 unconstrained eigenvalues)
#> 
#> mean, sd, VIF and canonical coefficients with their optimistic [!] t-values:
#>           Avg    SDS     VIF   Regr1   tval1
#> Manure 2.4659 1.2056 10.5656 -0.2010 -0.1344
#> A1     4.1466 1.3786  1.4841  0.1013  0.1807
#> Moist  2.1761 1.4762  1.4883 -4.1077 -7.3195
#> MagBF  0.1932 0.3948  6.8216  0.7873  0.6553
#> MagHF  0.4545 0.4979  5.8054  1.8392  1.6594
#> MagNM  0.0455 0.2083  4.8878  0.1327  0.1304
#> Use    1.9205 0.7107  2.6787  0.2101  0.2791
#> 

mod_scores <- scores(object, display = "all")
scores(object, which_cor = c("A1", "X_lot"), display = "cor")
#>            wRDA1      wRDA2
#> A1    -0.2365172 -0.3510007
#> X_lot -0.4987793  0.4250562
#> attr(,"meaning")
#> [1] "inter set correlation, correlation between environmental variables and the sites scores (CWMs)"
anova(object)
#> $table
#> Permutation test for weighted reduncancy analysis
#> Model: wrda(formula = response ~ A1 + Moist + Mag + Use + Condition(Manure), data = dune_trait_env$envir, weights = w) 
#> Residualized predictor permutation
#> Permutation: free
#> Number of permutations: 999
#> 
#>          df Variance      R2      F Pr(>F)  
#> wRDA      6   36.495 0.62581 3.3449  0.014 *
#> Residual 12   21.822                        
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#> 
#> $eigenvalues
#>      wRDA1      wRDA2      wRDA3      wRDA4      wRDA5      wRDA6 
#> 18.1328543  8.2332883  4.0467247  3.1546579  2.2383295  0.6893052 
#>