douconca (version 1.2.3)

anova_sites: Utility function: community-level permutation test in Double Constrained Correspondence Analysis (dc-CA)

Description

anova_sites performs the community-level permutation test of dc-CA when site weights vary. The test uses residual predictor permutation (ter Braak 2022), which is robust against differences in site total abundance in the response in dc_CA (ter Braak & te Beest, 2022). The arguments of the function are similar to those of anova.cca, but more restricted. With equal site-totals as in dc_CA, anova(object$RDAonEnv) is much faster.

Usage

anova_sites(object, permutations = 999, rpp = TRUE, n_axes = "all", by = NULL)

Value

A list with two elements with names table and eigenvalues. The table is as from anova.cca and eigenvalues gives the dc-CA eigenvalues.

Arguments

object

an object from dc_CA.

permutations

a list of control values for the permutations as returned by the function how, or the number of permutations required (default 999), or a permutation matrix where each row gives the permuted indices.

rpp

Logical indicating residual predictor permutation (default TRUE). When FALSE, residual response permutation is used.

n_axes

number of axes used in the test statistic (default: "all"). Example, the test statistic is the sum of the first two eigenvalues, if n_axes=2. With a numeric n_axes and model ~X + Condition(Z), the residuals of X with respect to Z are permuted with a test statistic equal to the sum of the first n_axes eigenvalues of the fitted Y in the model Y ~ X + Z, with Y the response in the model. In the default "all", the test statistic is all eigenvalues of the model Y ~ X|Z, i.e. the effects of X after adjustment for the effects on Y of Z. If by = "axis", the setting of n_axes is ignored.

by

character "axis" which sets the test statistic to the first eigenvalue of the dc-CA model. Default: NULL which sets the test statistic to the inertia (sum of all double constrained eigenvalues; named constraintsTE in the inertia element of dc_CA). This is the trait constrained inertia explained by the environmental predictors (without covariates), which is equal to the environmentally-constrained inertia explained by the traits (without trait covariates). The default is quicker computationally as it avoids computation of an svd of permuted data sets.

Details

The algorithm is analogous to that of anova.wrda. The function is used in anova.dcca.

References

ter Braak, C.J.F. & te Beest, D.E. 2022. Testing environmental effects on taxonomic composition with canonical correspondence analysis: alternative permutation tests are not equal. Environmental and Ecological Statistics. 29 (4), 849-868. tools:::Rd_expr_doi("10.1007/s10651-022-00545-4")

ter Braak, C.J.F. (2022) Predictor versus response permutation for significance testing in weighted regression and redundancy analysis. Journal of statistical computation and simulation, 92, 2041-2059. tools:::Rd_expr_doi("10.1080/00949655.2021.2019256")

Examples

data("dune_trait_env")

# rownames are carried forward in results
rownames(dune_trait_env$comm) <- dune_trait_env$comm$Sites

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

a_species <- anova_species(mod)
a_species
# anova_species can be used for manual forward selection of
# trait variables, as done for environmental variables in the demo 
# dune_FS_dcCA.r, based on the first eigenvalue and its significance
# and adding the first axis of the constrained species scores from mod to 
# the Condition of a new mod.
(eig1_and_pval <- c(eig = a_species$eig[1], pval = a_species$table$`Pr(>F)`[1]))
a_species$eig
anova_sites(mod)