Extract results of a weighted redundancy analysis (wrda) or a cca0 object.

This function works very much like the vegan scores function, in particular scores.cca, but with regression coefficients for predictors.

Usage

# S3 method for class 'wrda'
scores(
  x,
  ...,
  choices = 1:2,
  display = "all",
  scaling = "sym",
  which_cor = "in model",
  normed = TRUE,
  tidy = FALSE
)

Arguments

x: object of class "wrda", i.e. result of wrda or cca0.
...: Other arguments passed to the function (currently ignored).
choices: integer vector of which axes to obtain. Default: all wrda axes.
display: a character vector, one or more of c("all", "species", "sites", "sp", "wa", "lc", "bp", "cor", "ic", "reg", "tval", "cn"). The most items are as in scores.cca, except "cor" and "ic", for inter-set and intra-set correlations, respectively, and "tval" for the (over-optimistic) t-values of the regression coefficients.
scaling: numeric (1,2 or 3) or character "sites", "species" or "symmetric". Default: "symmetric". Either site- (1) or species- (2) related scores are scaled by eigenvalues, and the other set of scores have unit weighted mean square or with 3 both are scaled symmetrically to weighted mean squares equal to the square root of eigenvalues. Negative values are treated as the corresponding positive ones by abs(scaling).
which_cor: character vector environmental variables names in the data frames for which inter-set correlations must calculated. Default: a character ("in_model") for all predictors in the model, including collinear variables and levels.
normed: logical (default TRUE) giving standardized regression coefficients and biplot scores. When FALSE, (regular) regression coefficients and (unstandardized) biplot scores.
tidy: Return scores that are compatible with ggplot2: all variable score, the names by variable label. See weights (in dc_CA are in variable weight. See scores.cca.

Value

A data frame if tidy = TRUE. Otherwise, a matrix if a single item is asked for and a named list of matrices if more than one item is asked for. The following names can be included: c("sites", "constraints_sites", "centroids", "regression", "t_values", "correlation", "intra_set_correlation", "biplot", "species"). Each matrix has an attribute "meaning" explaining its meaning. With tidy = TRUE, the resulting data frame has attributes "scaling" and "meaning"; the latter has two columns: (1) name of score type and (2) its meaning, usage and interpretation.

An example of the meaning of scores in scaling "symmetric" with display = "all":

sites: CMWs of the trait axes (constraints species) in scaling 'symmetric' optimal for biplots and, almost so, for inter-site distances.
constraints_sites: linear combination of the environmental predictors and the covariates (making the ordination axes orthogonal to the covariates) in scaling 'symmetric' optimal for biplots and, almost so, for inter-site distances.
regression: mean, sd, VIF, standardized regression coefficients and their optimistic t-ratio in scaling 'symmetric'.
t_values: t-values of the coefficients of the regression of the CWMs of the trait composite on to the environmental variables
correlation: inter set correlation, correlation between environmental variables and the sites scores (CWMs)
intra_set_correlation: intra set correlation, correlation between environmental variables and the dc-ca axis (constrained sites scores)
biplot: biplot scores of environmental variables for display with biplot-traits for fourth-corner correlations in scaling 'symmetric'.
centroids: environmental category means of the site scores in scaling 'symmetric' optimal for biplots and, almost so, for inter-environmental category distances.
species: SNC on the environmental axes (constraints sites) in scaling 'symmetric' optimal for biplots and, almost so, for inter-species distances.

The statements on optimality for distance interpretations are based on the scaling and the relative magnitude of the dc-CA eigenvalues of the chosen axes.

Details

The function is modeled after scores.cca.

An example of which_cor is: which_cor = c("acidity", "humidity")

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  0.012 *
#> 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 
#>