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 with pseudo-F ratios.
adonis2(formula, data, permutations = 999, method = "bray", sqrt.dist = FALSE, add = FALSE, by = "terms", parallel = getOption("mc.cores"), na.action = na.fail, strata = NULL, ...)
Model formula. The left-hand side (LHS) of the formula
must be either a community data matrix or a dissimilarity matrix,
the data frame for the independent variables.
a list of control values for the permutations
as returned by the function
the name of any method used in
Take square root of dissimilarities. This often euclidifies dissimilarities.
Add a constant to the non-diagonal dissimilarities such
that all eigenvalues are non-negative in the underlying Principal
Co-ordinates Analysis (see
Number of parallel processes or a predefined socket
Handling of missing values on the right-hand-side
of the formula (see
Groups within which to constrain permutations. The traditional non-movable strata are set as Blocks in the permute package, but some more flexible alternatives may be more appropriate.
Other arguments passed to
adonis2 is a function for the analysis and partitioning sums of
squares using dissimilarities. The function is based on the principles
of McArdle & Anderson (2001) and can perform sequential, marginal and
overall tests. The function also allows using additive constants or
squareroot of dissimilarities to avoid negative eigenvalues, but can
also handle semimetric indices (such as Bray-Curtis) that produce
negative eigenvalues. The
adonis2 tests are identical to
dbrda. With Euclidean
distances, the tests are also identical to
The function partitions sums of squares of a multivariate data set, and
they are directly analogous to MANOVA (multivariate analysis of
variance). McArdle and Anderson (2001) and Anderson (2001) refer to the
method as “permutational MANOVA” (formerly “nonparametric
MANOVA”). Further, as the inputs are linear predictors, and a response
matrix of an arbitrary number of columns, they are a robust alternative
to both parametric MANOVA and to ordination methods for describing how
variation is attributed to different experimental treatments or
uncontrolled covariates. The method is also analogous to distance-based
redundancy analysis in functions
capscale (Legendre and Anderson 1999), and provides
an alternative to AMOVA (nested analysis of molecular variance,
Excoffier, Smouse, and Quattro, 1992;
amova in the
ade4 package) for both crossed and nested factors.
The function returns an
anova.cca result object with a
new column for partial R-squared: This is the proportion
of sum of squares from the total, and in marginal models
by = "margin") the R-squared terms do not add up to
Anderson (2001, Fig. 4) warns that the method may confound
location and dispersion effects: significant differences may be caused
by different within-group variation (dispersion) instead of different
mean values of the groups (see Warton et al. 2012 for a general
analysis). However, it seems that
adonis2 is less sensitive to
dispersion effects than some of its alternatives (
betadisper is a sister
adonis2 to study the differences in dispersion
within the same geometric framework.
Martin Henry H. Stevens and Jari Oksanen.
Anderson, M.J. 2001. A new method for non-parametric multivariate analysis of variance. Austral Ecology, 26: 32–46.
Excoffier, L., P.E. Smouse, and J.M. Quattro. 1992. Analysis of molecular variance inferred from metric distances among DNA haplotypes: Application to human mitochondrial DNA restriction data. Genetics, 131:479–491.
Legendre, P. and M.J. Anderson. 1999. Distance-based redundancy analysis: Testing multispecies responses in multifactorial ecological experiments. Ecological Monographs, 69:1–24.
McArdle, B.H. and M.J. Anderson. 2001. Fitting multivariate models to community data: A comment on distance-based redundancy analysis. Ecology, 82: 290–297.
Warton, D.I., Wright, T.W., Wang, Y. 2012. Distance-based multivariate analyses confound location and dispersion effects. Methods in Ecology and Evolution, 3, 89–101.
data(dune) data(dune.env) ## default test by terms adonis2(dune ~ Management*A1, data = dune.env) ## overall tests adonis2(dune ~ Management*A1, data = dune.env, by = NULL) ### Example of use with strata, for nested (e.g., block) designs. dat <- expand.grid(rep=gl(2,1), NO3=factor(c(0,10)),field=gl(3,1) ) dat Agropyron <- with(dat, as.numeric(field) + as.numeric(NO3)+2) +rnorm(12)/2 Schizachyrium <- with(dat, as.numeric(field) - as.numeric(NO3)+2) +rnorm(12)/2 total <- Agropyron + Schizachyrium dotplot(total ~ NO3, dat, jitter.x=TRUE, groups=field, type=c('p','a'), xlab="NO3", auto.key=list(columns=3, lines=TRUE) ) Y <- data.frame(Agropyron, Schizachyrium) mod <- metaMDS(Y, trace = FALSE) plot(mod) ### Ellipsoid hulls show treatment with(dat, ordiellipse(mod, field, kind = "ehull", label = TRUE)) ### Spider shows fields with(dat, ordispider(mod, field, lty=3, col="red")) ### Incorrect (no strata) adonis2(Y ~ NO3, data = dat, permutations = 199) ## Correct with strata with(dat, adonis2(Y ~ NO3, data = dat, permutations = 199, strata = field))
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