Analysis of variance using distance matrices --- for partitioning distance matrices among sources of variation and fitting linear models (e.g., factors, polynomial regression) to distance matrices; uses a permutation test (Freedman-Lane permutation) with pseudo-\(F\) ratios.
adonis3(formula, data, permutations = 999, method = "bray",
strata = NULL, contr.unordered = "contr.sum",
contr.ordered = "contr.poly", parallel = getOption("mc.cores"), ...)Function adonis3 returns an object of class "adonis" with
following components:
typical AOV table showing sources of variation, degrees of freedom, sequential sums of squares, mean squares, \(F\) statistics, partial \(R^2\) and \(P\) values, based on \(N\) permutations.
matrix of coefficients of the linear model, with rows representing sources of variation and columns representing species; each column represents a fit of a species abundance to the linear model. These are what you get when you fit one species to your predictors. These are NOT available if you supply the distance matrix in the formula, rather than the site x species matrix
matrix of coefficients of the linear model, with rows representing sources of variation and columns representing sites; each column represents a fit of a sites distances (from all other sites) to the linear model. These are what you get when you fit distances of one site to your predictors.
an \(N\) by \(m\) matrix of the null \(F\)
statistics for each source of variation based on \(N\)
permutations of the data. The permutations can be inspected with
permustats and its support functions.
the model.matrix for the right hand
side of the formula.
the terms component of the model.
model formula. The LHS must be either a community
data matrix or a dissimilarity matrix, e.g., from
vegdist or dist. If the LHS is a data
matrix, function vegdist will be used to find the
dissimilarities. The RHS defines the independent variables. These
can be continuous variables or factors, they can be transformed
within the formula, and they can have interactions as in a typical
formula.
the data frame for the independent variables.
a list of control values for the permutations
as returned by the function how, or the
number of permutations required, or a permutation matrix where each
row gives the permuted indices.
the name of any method used in vegdist to
calculate pairwise distances if the left hand side of the
formula was a data frame or a matrix.
groups (strata) within which to constrain permutations.
contrasts used for the design matrix (default in R is dummy or treatment contrasts for unordered factors).
number of parallel processes or a predefined socket
cluster. With parallel = 1 uses ordinary, non-parallel
processing. The parallel processing is done with parallel
package.
Other arguments passed to vegdist.
Martin Henry H. Stevens (adonis) and Jun Chen
(adonis3).
adonis3 is the re-implementation of the adonis function in
the vegan package based on the Freedman-Lane permutation scheme
(Freedman & Lane (1983), Hu & Satten (2020)). The original
implementation in the vegan package is directly based on the algorithm of Anderson (2001) and
performs a sequential test of terms. Statistical significance is assessed
based on permuting the distance matrix. We found that such permutation
will lead to power loss in testing the effect of a covariate of interest while adjusting
for other covariates (confounders). The power loss is more evident when the confounders' effects
are strong, the correlation between the covariate of interest and the confounders is high, and
the sample size is small. When the sample size is large than 100, the difference is usually small.
The new implementation is revised on the adonis function with the same interface.
Anderson, M.J. 2001. A new method for non-parametric multivariate analysis of variance. Austral Ecology, 26: 32--46.
Freedman D. & Lane D. 1983. A nonstochastic interpretation of reported significance levels. Journal of Business and Economic Statistics, 1292--298.
Hu, Y. J. & Satten, G. A. 2020. Testing hypotheses about the microbiome using the linear decomposition model (LDM). JBioinformatics, 36(14) : 4106-4115.
if (FALSE) {
data(throat.otu.tab)
data(throat.tree)
data(throat.meta)
groups <- throat.meta$SmokingStatus
# Rarefaction
otu.tab.rff <- Rarefy(throat.otu.tab)$otu.tab.rff
# Calculate the UniFrac distance
unifracs <- GUniFrac(otu.tab.rff, throat.tree, alpha=c(0, 0.5, 1))$unifracs
# Test the smoking effect based on unweighted UniFrac distance, adjusting sex
adonis3(as.dist(unifracs[, , 'd_UW']) ~ Sex + SmokingStatus, data = throat.meta)
}
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