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. If mtype"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, than 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 'bipartite'. First, a random matrix is generated by the r2dtable function retaining row and column sums. Than 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 'coda' package.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$orig ## note: original matrix is binarized!
summary(x3)
## Restricted permutation,
## check sums within strata:
x4 <- permatfull(m, strata=c(1,1,2,2))
summary(x4)
## Not sequential algorithm
data(BCI)
a <- permatswap(BCI, "quasiswap")
## Sequential algorithm
b <- permatswap(BCI, "abuswap", fixedmar="col",
burnin=0, thin=100, times=50)
opar <- par(mfrow=c(2,2))
plot(a, main="Not sequential")
plot(b, main="Sequential")
plot(a, "chisq")
plot(b, "chisq")
par(opar)
## Extract Bray-Curtis dissimilarities
## as time series
bc <- as.ts(b)
## Lag plot
lag.plot(bc)
## First order autoregressive model
mar <- arima(bc, c(1,0,0))
mar
## Ljung-Box test of residuals
Box.test(mar$residuals)
## Graphical diagnostics
tsdiag(mar)Run the code above in your browser using DataLab