metaMDS performs Nonmetric
Multidimensional Scaling (NMDS), and tries to find a stable solution
using several random starts. In addition, it standardizes the
scaling in the result, so that the configurations are easier to
interpret, and adds species scores to the site ordination. The
metaMDS function does not provide actual NMDS, but it calls
another function for the purpose. Currently monoMDS is
the default choice, and it is also possible to call the
isoMDS (MASS package). metaMDS(comm, distance = "bray", k = 2, try = 20, trymax = 20, engine = c("monoMDS", "isoMDS"), autotransform =TRUE, noshare = (engine == "isoMDS"), wascores = TRUE, expand = TRUE, trace = 1, plot = FALSE, previous.best, ...)
"plot"(x, display = c("sites", "species"), choices = c(1, 2), type = "p", shrink = FALSE, ...)
"points"(x, display = c("sites", "species"), choices = c(1,2), shrink = FALSE, select, ...)
"text"(x, display = c("sites", "species"), labels, choices = c(1,2), shrink = FALSE, select, ...)
"scores"(x, display = c("sites", "species"), shrink = FALSE, choices, ...)
metaMDSdist(comm, distance = "bray", autotransform = TRUE, noshare = TRUE, trace = 1, commname, zerodist = "ignore", distfun = vegdist, ...)
metaMDSiter(dist, k = 2, try = 20, trymax = 20, trace = 1, plot = FALSE, previous.best, engine = "monoMDS", maxit = 200, parallel = getOption("mc.cores"), ...)
initMDS(x, k=2)
postMDS(X, dist, pc=TRUE, center=TRUE, halfchange, threshold=0.8, nthreshold=10, plot=FALSE, ...)
metaMDSredist(object, ...)dist structure or as a symmetric square matrix.
In the latter case all other stages are skipped except random
starts and centring and pc rotation of axes. vegdist.try has been reached, the
iteration will stop when two convergent solutions were found or
trymax was reached.autotransform = FALSE.stepacross. The
argument can be logical or a numerical value greater than zero
and less than one. If TRUE, extended dissimilarities are
used always when there are no shared species between some sites,
if FALSE, they are never used. If noshare is a
numerical value, stepacross is used when the
proportion of site pairs with no shared species exceeds
noshare. The number of pairs with no shared species is
found with no.shared function, and noshare
has no effect if input data were dissimilarities instead of
community data.wascores.wascores.trace = 2 or higher will be
more voluminous.par(ask = TRUE) with this option.metaMDS result (or a dissimilarity structure for
initMDS."p" for points, "t" for text, and
"n" for axes only."sites" or "species".TRUE for displayed items or a vector of indices
of displayed items.comm: should not be given if the
function is called directly.dist object and accepting argument method can be used
(but some extra arguments may cause name conflicts).clus), you must issue clusterEvalQ(clus,
library(vegan)) to make available internal vegan
functions. With parallel = 1 uses ordinary, non-parallel
processing. The parallel processing is done with parallel
package.TRUE when dissimilarities were evaluated within
metaMDS and the dissimilarity index has an upper limit of
$1$. If FALSE, the ordination dissimilarities are scaled
to the same range as the input dissimilarities.metaMDS.metaMDS passes all arguments to its component functions
metaMDSdist, metaMDSiter, postMDS, and to
distfun and engine.metaMDS returns an object of class
metaMDS. The final site ordination is stored in the item
points, and species ordination in the item species,
and the stress in item stress (NB, the scaling of the stress
depends on the engine: isoMDS uses
percents, and monoMDS proportions in the range $0
\ldots 1$). The other items store the information on the steps taken
and the items returned by the engine function. The object has
print, plot, points and text methods.
Functions metaMDSdist and metaMDSredist return
vegdist objects. Function initMDS returns a
random configuration which is intended to be used within
isoMDS only. Functions metaMDSiter and
postMDS returns the result of NMDS with updated
configuration. engine = "monoMDS" the function will
tabulate the stopping criteria used, so that you can see which
criterion should be made more stringent. The criteria can be given
as arguments to metaMDS and their current values are
described in monoMDS. In particular, if you reach
the maximum number of iterations, you should increase the value of
maxit. You may ask for a larger number of random starts
without losing the old ones giving the previous solution in
argument previous.best. In addition to too slack convergence criteria and too low number
of random starts, wrong number of dimensions (argument k)
is the most common reason for not finding convergent
solutions. NMDS is usually run with a low number dimensions
(k=2 or k=3), and for complex data increasing
k by one may help. If you run NMDS with much higher number
of dimensions (say, k=10 or more), you should reconsider
what you are doing and drastically reduce k. For very
heterogeneous data sets with partial disjunctions, it may help to
set stepacross, but for most data sets the default
weakties = TRUE is sufficient. Please note that you can give all arguments of other
metaMDS* functions and NMDS engine (default
monoMDS) in your metaMDS command,and you
should check documentation of these functions for details. metaMDS is a
wrapper function that calls several other functions to combine
Minchin's (1987) recommendations into one command. The complete
steps in metaMDS are:
wisconsin). If the values look
very large, the function also performs sqrt
transformation. Both of these standardizations are generally found
to improve the results. However, the limits are completely
arbitrary (at present, data maximum 50 triggers sqrt
and $>9$ triggers wisconsin). If you want to
have a full control of the analysis, you should set
autotransform = FALSE and standardize and transform data
independently. The autotransform is intended for community
data, and for other data types, you should set autotransform
= FALSE. This step is perfomed using metaMDSdist.
vegdist can be used. Function
rankindex can be used for finding the test winner
for you data and gradients. The default choice may be bad if you
analyse other than community data, and you should probably select
an appropriate index using argument distance. This step is
performed using metaMDSdist.
stepacross
dissimilarities, or flexible shortest paths among all sites. The
default NMDS engine is monoMDS which is able
to break tied values at the maximum dissimilarity, and this often
is sufficient to handle cases with no shared species, and
therefore the default is not to use stepacross with
monoMDS. Function isoMDS does
not handle tied values adequately, and therefore the default is to
use stepacross always when there are sites with no
shared species with engine = "isoMDS". The
stepacross is triggered by option noshare. If
you do not like manipulation of original distances, you should set
noshare = FALSE. This step is skipped if input data were
dissimilarities instead of community data. This step is performed
using metaMDSdist.
metaMDS is to first run NMDS starting with the
metric scaling (cmdscale which usually finds a good
solution but often close to a local optimum), or use the
previous.best solution if supplied, and take its solution
as the standard (Run 0). Then metaMDS starts NMDS
from several random starts (minimum number is given by try
and maximum number by trymax). These random starts are
generated by initMDS. If a solution is better (has a lower
stress) than the previous standard, it is taken as the new
standard. If the solution is better or close to a standard,
metaMDS compares two solutions using Procrustes analysis
(function procrustes with option
symmetric = TRUE). If the solutions are very similar in their
Procrustes rmse and the largest residual is very small, the
solutions are regarded as convergent and the better one is taken as
the new standard. The conditions are stringent, and you may have
found good and relatively stable solutions although the function is
not yet satisfied. Setting trace = TRUE will monitor the final
stresses, and plot = TRUE will display Procrustes overlay
plots from each comparison. This step is performed using
metaMDSiter. This is the only step performed if input data
(comm) were dissimilarities.
metaMDS will run postMDS
for the final result. Function postMDS provides the
following ways of “fixing” the indeterminacy of scaling and
orientation of axes in NMDS: Centring moves the origin to the
average of the axes; Principal components rotate the configuration
so that the variance of points is maximized on first dimension
(with function MDSrotate you can alternatively rotate
the configuration so that the first axis is parallel to an
environmental variable); Half-change scaling scales the
configuration so that one unit means halving of community
similarity from replicate similarity. Half-change scaling is
based on closer dissimilarities where the relation between
ordination distance and community dissimilarity is rather linear
(the limit is set by argument threshold). If there are
enough points below this threshold (controlled by the parameter
nthreshold), dissimilarities are regressed on distances.
The intercept of this regression is taken as the replicate
dissimilarity, and half-change is the distance where similarity
halves according to linear regression. Obviously the method is
applicable only for dissimilarity indices scaled to $0 \ldots
1$, such as Kulczynski, Bray-Curtis and Canberra indices. If
half-change scaling is not used, the ordination is scaled to the
same range as the original dissimilarities.
wascores with given value of parameter
expand. The expansion of weighted averages can be undone
with shrink = TRUE in plot or scores
functions, and the calculation of species scores can be suppressed
with wascores = FALSE.
Minchin, P.R. (1987) An evaluation of relative robustness of techniques for ecological ordinations. Vegetatio 69, 89--107.
monoMDS (and isoMDS),
decostand,
wisconsin,
vegdist, rankindex, stepacross,
procrustes, wascores, MDSrotate,
ordiplot.
## The recommended way of running NMDS (Minchin 1987)
##
data(dune)
# Global NMDS using monoMDS
sol <- metaMDS(dune)
sol
plot(sol, type="t")
## Start from previous best solution
sol <- metaMDS(dune, previous.best = sol)
## Local NMDS and stress 2 of monoMDS
sol2 <- metaMDS(dune, model = "local", stress=2)
sol2
## Use Arrhenius exponent 'z' as a binary dissimilarity measure
sol <- metaMDS(dune, distfun = betadiver, distance = "z")
sol
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