Function simulates a response data frame so that it adds
Gaussian error to the fitted responses of Redundancy Analysis
(rda
), Constrained Correspondence Analysis
(cca
) or distance-based RDA (capscale
).
The function is a special case of generic simulate
, and
works similarly as simulate.lm
.
# S3 method for rda
simulate(object, nsim = 1, seed = NULL, indx = NULL,
rank = "full", correlated = FALSE, ...)
If nsim = 1
, returns a matrix or dissimilarities (in
capscale
) with similar additional arguments on random
number seed as simulate
. If nsim > 1
, returns a
similar array as returned by simulate.nullmodel
with
similar attributes.
an object representing a fitted rda
,
cca
or capscale
model.
number of response matrices to be simulated. Only one
dissimilarity matrix is returned for capscale
, and
larger nsim
is an error.
an object specifying if and how the random number
generator should be initialized (‘seeded’). See
simulate
for details.
Index of residuals added to the fitted values, such as
produced by shuffleSet
or
sample
. The index can have duplicate entries so
that bootstrapping is allowed. If nsim
\(>1\), the output
should be compliant with shuffleSet
with
one line for each simulation. If nsim
is missing, the
number of rows of indx
is used to define the number of
simulations, but if nsim
is given, it should match number
of rows in indx
. If null, parametric simulation is used and
Gaussian error is added to the fitted values.
The rank of the constrained component: passed to
predict.rda
or predict.cca
.
Are species regarded as correlated in parametric
simulation or when indx
is not given? If
correlated = TRUE
, multivariate Gaussian random error is
generated, and if FALSE
, Gaussian random error is generated
separately for each species. The argument has no effect in
capscale
which has no information on species.
additional optional arguments (ignored).
Jari Oksanen
The implementation follows "lm"
method of
simulate
, and adds Gaussian (Normal) error to the fitted
values (fitted.rda
) using function rnorm
if correlated = FALSE
or mvrnorm
if
correlated = TRUE
. The standard deviations (rnorm
)
or covariance matrices for species (mvrnorm
) are
estimated from the residuals after fitting the constraints.
Alternatively, the function can take a permutation index that is used
to add permuted residuals (unconstrained component) to the fitted
values. Raw data are used in rda
. Internal Chi-square
transformed data are used in cca
within the function,
but the returned matrix is similar to the original input data. The
simulation is performed on internal metric scaling data in
capscale
, but the function returns the Euclidean
distances calculated from the simulated data. The simulation uses
only the real components, and the imaginary dimensions are ignored.
data(dune)
data(dune.env)
mod <- rda(dune ~ Moisture + Management, dune.env)
## One simulation
update(mod, simulate(mod) ~ .)
## An impression of confidence regions of site scores
plot(mod, display="sites")
for (i in 1:5) lines(procrustes(mod, update(mod, simulate(mod) ~ .)), col="blue")
## Simulate a set of null communities with permutation of residuals
simulate(mod, indx = shuffleSet(nrow(dune), 99))
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