douconca (version 1.2.3)

scores.dcca: Extract results of a double constrained correspondence analysis (dc-CA)

Description

This function works very much like the vegan scores function, in particular scores.cca, with the additional results such as regression coefficients and linear combinations of traits ('reg_traits', 'lc_traits'). All scores from CA obey the so called transition formulas and so do the scores of CCA and dc-CA. The differences are, for CCA, that the linear combinations of environmental variables (the constrained site scores) replace the usual (unconstrained) site scores, and for dc-CA, that the linear combinations of traits (the constrained species scores) also replace the usual (unconstrained) species scores in the transition formulas.

Usage

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

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", "constraints_species", "regression_traits", "t_values_traits", "correlation_traits", "intra_set_correlation_traits", "biplot_traits", "centroids_traits"). 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.

constraints_species

linear combination of the traits and the trait covariates (making the ordination axes orthogonal to the covariates) in scaling 'symmetric' optimal for biplots and, almost so, for inter-species distances.

regression_traits

mean, sd, VIF, standardized regression coefficients and their optimistic t-ratio in scaling 'symmetric'.

t_values_traits

t-values of the coefficients of the regression of the SNCs along a dc-CA axis on to the traits

correlation_traits

inter set correlation, correlation between traits and the species scores (SNCs)

intra_set_correlation_traits

intra set correlation, correlation between traits and the dc-ca axis (constrained species scores)

biplot_traits

biplot scores of traits for display with biplot scores for fourth-corner correlation in scaling 'symmetric'.

centroids_traits

trait category means of the species scores in scaling 'symmetric' optimal for biplots and, almost so, for inter-trait category 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.

Arguments

x

object of class "dcca", i.e. result of dc_CA.

...

Other arguments passed to the function (currently ignored).

choices

integer vector of which axes to obtain. Default: all dc-CA axes.

display

a character vector, one or more of c("all", "species", "sites", "sp", "wa", "lc", "bp", "cor", "ic", "reg", "tval", "cn", "lc_traits", "reg_traits", "tval_traits", "cor_traits", "ic_traits", "bp_traits", "cn_traits"). 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. The remaining scores are analogous scores for species and traits.

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 or list of trait and environmental variables names (in this order) in the data frames for which inter-set correlations must calculated. Default: a character ("in_model") for all traits and variables 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 scores are in a single data.frame, score type is identified by factor variable score, the names by variable label, and species weights (in dc_CA are in variable weight. See scores.cca.

Details

The function is modeled after scores.cca.

The t-ratios are taken from a multiple regression of the unconstrained species (or site) scores on to the traits (or environmental variables).

An example of which_cor is: which_cor = list(traits = "SLA", env = c("acidity", "humidity")).

Examples

data("dune_trait_env")

# rownames are carried forward in results
rownames(dune_trait_env$comm) <- dune_trait_env$comm$Sites
abun <- dune_trait_env$comm[, -1]  # must delete "Sites"
mod <- dc_CA(formulaEnv = abun ~ A1 + Moist + Mag + Use + Manure,
             formulaTraits = ~ SLA + Height + LDMC + Seedmass + Lifespan,
             dataEnv = dune_trait_env$envir,
             dataTraits = dune_trait_env$traits,
			 verbose = FALSE)

print(mod) # same output as with verbose = TRUE (the default of verbose).																		 
anova(mod, by = "axis")
# For more demo on testing, see demo dune_test.r

mod_scores <- scores(mod)
# correlation of axes with a variable that is not in the model
scores(mod, display = "cor", scaling = "sym", which_cor = list(NULL, "X_lot"))

cat("head of unconstrained site scores, with meaning\n")
print(head(mod_scores$sites))

mod_scores_tidy <- scores(mod, tidy = TRUE)
print("names of the tidy scores")
print(names(mod_scores_tidy))
cat("\nThe levels of the tidy scores\n")
print(levels(mod_scores_tidy$score))

cat("\nFor illustration: a dc-CA model with a trait covariate\n")
mod2 <- dc_CA(formulaEnv = abun ~ A1 + Moist + Mag + Use + Manure,
              formulaTraits = ~ SLA + Height + LDMC + Lifespan + Condition(Seedmass),
              dataEnv = dune_trait_env$envir,
              dataTraits = dune_trait_env$traits)

cat("\nFor illustration: a dc-CA model with both environmental and trait covariates\n")
mod3 <- dc_CA(formulaEnv = abun ~ A1 + Moist + Use + Manure + Condition(Mag),
              formulaTraits = ~ SLA + Height + LDMC + Lifespan + Condition(Seedmass),
              dataEnv = dune_trait_env$envir,
              dataTraits = dune_trait_env$traits, 
			  verbose = FALSE)

cat("\nFor illustration: same model but using dc_CA_object = mod2 for speed, ", 
    "as the trait model and data did not change\n")
mod3B <- dc_CA(formulaEnv = abun ~ A1 + Moist + Use + Manure + Condition(Mag),
               dataEnv = dune_trait_env$envir,
               dc_CA_object = mod2, 
			   verbose= FALSE)
cat("\ncheck on equality of mod3 (from data) and mod3B (from a dc_CA_object)\n",
    "the expected difference is in the component 'call'\n ")

print(all.equal(mod3[-c(5,12)], mod3B[-c(5,12)])) #  only the component call differs
print(mod3$inertia[-c(3,5),]/mod3B$inertia) #        and mod3 has two more inertia items