permatfull(m, fixedmar = "both", shuffle = "both", strata = NULL,
mtype = "count", times = 99)
permatswap(m, method = "quasiswap", fixedmar="both", shuffle = "both",
strata = NULL, mtype = "count", times = 99, burnin = 0, thin = 1)
## S3 method for class 'permat':
print(x, digits = 3, ...)
## S3 method for class 'permat':
summary(object, ...)
## S3 method for class 'summary.permat':
print(x, digits = 2, ...)
## S3 method for class 'permat':
plot(x, type = "bray", ylab, xlab, col, lty,
lowess = TRUE, plot = TRUE, text = TRUE, ...)
## S3 method for class 'permat':
lines(x, type = "bray", ...)
## S3 method for class 'permat':
as.ts(x, type = "bray", ...)
## S3 method for class 'permat':
as.mcmc(x)"none", "rows", "columns", "both").nrow(m) for grouping rows within strata for restricted
permutations. Unique values or levels are used."count" for count data,
or "prab" for presence-absence type incidence data."swap", "tswap", "quasiswap",
"backtrack") as described for function
commsimulator."ind"), samples ("samp") or both ("both")
should be shuffled, see details."swap", "tswap") methods."swap", "tswap") methods."permat"plot
method."bray" for
Bray-Curtis dissimilarities, "chisq" for Chi-squared values.plot
method, whether a locally weighted regression curve should be drawn,
the plot should be drawn, and statistic values should be printed on
the plot.permatfull and permatswap return an
object of class "permat" containing the the function call
(call), the original data matrix used for permutations
(orig) and a list of permuted matrices with length times
(perm).
The summary method returns various statistics as a list
(including mean Bray-Curtis dissimilarities calculated pairwise among
original and permuted matrices, Chi-square statistics, and check
results of the constraints; see Examples). Note that when
strata is used in the original call, summary calculation may
take longer.
The plot creates a plot as a side effect.
The as.ts method returns an object of class "ts".permatfull is useful when matrix fill is
allowed to vary, and matrix type is count. The fixedmar
argument is used to set constraints for permutation. If none
of the margins are fixed, cells are randomised within the matrix. If
rows or columns are fixed, cells within rows or columns
are randomised, respectively. If both margins are fixed, the
r2dtable function is used that is based on Patefield's
(1981) algorithm. For presence absence data, matrix fill should be
necessarily fixed, and permatfull is a wrapper for the function
commsimulator. The r00, r0, c0, quasiswap
algorithms of commsimulator are used for "none",
"rows", "columns", "both" values of the fixedmar argument,
respectively
The shuffle argument only have effect if the mtype =
"count" and permatfull function is used with "none",
"rows", "columns" values of fixedmar. All other cases for
count data are individual based randomisations. The "samp" and
"both" options result fixed matrix fill. The "both"
option means that individuals are shuffled among non zero cells
ensuring that there are no cell with zeros as a result, then cell
(zero and new valued cells) are shuffled.
The function permatswap is useful when with matrix fill
(i.e. the proportion of empty cells) and row/columns sums should be
kept constant. permatswap uses different kinds of swap
algorithms, and row and columns sums are fixed in all cases. For
presence-absence data, the swap and tswap methods of
commsimulator can be used. For count data, a special
swap algorithm ('swapcount') is implemented that results in permuted
matrices with fixed marginals and matrix fill at the same time.
The 'quasiswapcount' algorithm (method="quasiswap" and
mtype="count") uses the same trick as Carsten Dormann's
swap.web function in the package
r2dtable function retaining row and column sums. Then
the original matrix fill is reconstructed by sequential steps to
increase or decrease matrix fill in the random matrix. These steps are
based on swapping 2x2 submatrices (see 'swapcount' algorithm for
details) to maintain row and column totals. This algorithm generates
independent matrices in each step, so burnin and thin
arguments are not considered. This is the default method, because this
is not sequential (as swapcount is) so independence of subsequent
matrices does not have to be checked.
The swapcount algorithm (method="swap" and
mtype="count") tries to find 2x2 submatrices (identified by 2
random row and 2 random column indices), that can be swapped in order
to leave column and row totals and fill unchanged. First, the
algorithm finds the largest value in the submatrix that can be swapped
($d$) and whether in diagonal or antidiagonal way. Submatrices
that contain values larger than zero in either diagonal or
antidiagonal position can be swapped. Swap means that the values in
diagonal or antidiagonal positions are decreased by $d$, while
remaining cells are increased by $d$. A swap is made only if fill
doesn't change. This algorithm is sequential, subsequent matrices are
not independent, because swaps modify little if the matrix is
large. In these cases many burnin steps and thinning is needed to get
independent random matrices. Although this algorithm is implemented in
C, large burnin and thin values can slow it down
considerably. WARNING: according to simulations, this algorithm seems
to be biased and non random, thus its use should be avoided!
The algorithm "swsh" in the function permatswap is a
hybrid algorithm. First, it makes binary quasiswaps to keep row and
column incidences constant, then non-zero values are modified
according to the shuffle argument (only "samp" and
"both" are available in this case, because it is applied only
on non-zero values).
The algorithm "abuswap" produces two kinds of null models
(based on fixedmar="columns" or fixedmar="rows") as
described in Hardy (2008; randomization scheme 2x and 3x,
respectively). These preserve column and row occurrences, and column
or row sums at the same time.
Constraints on row/column sums, matrix fill, total sum and sums within
strata can be checked by the summary method. plot method
is for visually testing the randomness of the permuted matrices,
especially for the sequential swap algorithms. If there are any
tendency in the graph, higher burnin and thin values can
help for sequential methods. New lines can be added to existing plot
with the lines method.
Unrestricted and restricted permutations: if strata is
NULL, functions perform unrestricted permutations. Otherwise,
it is used for restricted permutations. Each strata should contain at
least 2 rows in order to perform randomization (in case of low row
numbers, swap algorithms can be rather slow). If the design is not
well balanced (i.e. same number of observations within each stratum),
permuted matrices may be biased because same constraints are forced on
submatrices of different dimensions. This often means, that the number
of potential permutations will decrease with their dimensions. So the
more constraints we put, the less randomness can be expected.
The plot method is useful for graphically testing for trend and
independence of permuted matrices. This is especially important when
using sequential algorithms ("swap", "tswap", "abuswap").
The as.ts method can be used to extract Bray-Curtis
dissimilarities or Chi-squared values as time series. This can further
used in testing independence (see Examples). The method as.mcmc
is useful for accessing diagnostic tools available in the commsimulator.
Hardy, O. J. (2008) Testing the spatial phylogenetic structure of
local communities: statistical performances of different null models
and test statistics on a locally neutral community. Journal of Ecology
96, 914--926.
Patefield, W. M. (1981) Algorithm AS159. An efficient method of
generating r x c tables with given row and column totals.
Applied Statistics 30, 91--97.commsimulator, r2dtable,
sample, swap.web.
For the use of these permutation algorithms: oecosimu,
adipart, hiersimu.
For time-series diagnostics: Box.test,
lag.plot, tsdiag, ar,
arima## A simple artificial community data matrix.
m <- matrix(c(
1,3,2,0,3,1,
0,2,1,0,2,1,
0,0,1,2,0,3,
0,0,0,1,4,3
), 4, 6, byrow=TRUE)
## Using the quasiswap algorithm to create a
## list of permuted matrices, where
## row/columns sums and matrix fill are preserved:
x1 <- permatswap(m, "quasiswap")
summary(x1)
## Unrestricted permutation retaining
## row/columns sums but not matrix fill:
x2 <- permatfull(m)
summary(x2)
## Unrestricted permutation of presence-absence type
## not retaining row/columns sums:
x3 <- permatfull(m, "none", mtype="prab")
x3$orig ## note: original matrix is binarized!
summary(x3)
## Restricted permutation,
## check sums within strata:
x4 <- permatfull(m, strata=c(1,1,2,2))
summary(x4)
## NOTE: 'times' argument usually needs to be >= 99
## here much lower value is used for demonstration
## Not sequential algorithm
data(BCI)
a <- permatswap(BCI, "quasiswap", times=19)
## Sequential algorithm
b <- permatswap(BCI, "abuswap", fixedmar="col",
burnin=0, thin=100, times=19)
opar <- par(mfrow=c(2,2))
plot(a, main="Not sequential")
plot(b, main="Sequential")
plot(a, "chisq")
plot(b, "chisq")
par(opar)
## Extract Bray-Curtis dissimilarities
## as time series
bc <- as.ts(b)
## Lag plot
lag.plot(bc)
## First order autoregressive model
mar <- arima(bc, c(1,0,0))
mar
## Ljung-Box test of residuals
Box.test(mar$residuals)
## Graphical diagnostics
tsdiag(mar)Run the code above in your browser using DataLab