How to define a permutation design?

Utility functions to describe unrestricted and restricted permutation designs for time series, line transects, spatial grids and blocking factors.

how(within = Within(), plots = Plots(), blocks = NULL,
    nperm = 199, complete = FALSE, maxperm = 9999,
    minperm = 5040, all.perms = NULL, make = TRUE,
    observed = FALSE)

Within(type = c("free","series","grid","none"),
       constant = FALSE, mirror = FALSE,
       ncol = NULL, nrow = NULL)

Plots(strata = NULL, type = c("none","free","series","grid"),
      mirror = FALSE, ncol = NULL, nrow = NULL)

Arguments

within, plots, blocks: Permutation designs for samples within the levels of plots (within), permutation of plots themselves, or for the definition of blocking structures which further restrict permutations (blocks). within and plots each require a named list as produced by Within and Plots respectively. blocks takes a factor (or an object coercible to a factor via as.factor), the levels of which define the blocking structure.
nperm: numeric; the number of permutations.
complete: logical; should complete enumeration of all permutations be performed?
type: character; the type of permutations required. One of "free", "series", "grid" or "none". See Details.
maxperm: numeric; the maximum number of permutations to perform. Currently unused.
minperm: numeric; the lower limit to the number of possible permutations at which complete enumeration is performed. When nperm is lower than minperm, sampling is performed from the set of complete permutations to avoid duplicate permutations. See argument complete and Details, below.
all.perms: an object of class allPerms, the result of a call to allPerms.
make: logical; should check generate all possible permutations? Useful if want to check permutation design but not produce the matrix of all permutations, or to circumvent the heuristics governing when complete enumeration is activated.
observed: logical; should the observed permutation be returned as part of the set of all permutations? Default is FALSE to facilitate usage in higher level functions.
constant: logical; should the same permutation be used within each level of strata? If FALSE a separate, possibly restricted, permutation is produced for each level of strata.
mirror: logical; should mirroring of sequences be allowed?
ncol, nrow: numeric; the number of columns and rows of samples in the spatial grid respectively.
strata: A factor, or an object that can be coerced to a factor via as.factor, specifying the strata for permutation.

Details

shuffle can generate permutations for a wide range of restricted permutation schemes. A small selection of the available combinations of options is provided in the Examples section below.

Argument type controls how samples are actually permuted; "free" indicates randomization, "series" indicates permutation via cyclic shifts (suitable for evenly-spaced line transect or time series data), "grid" indicates permutation via toroidal shifts (suitable for samples on a regular grid), and "none" indicates no permutation of samples. See the package vignette (browseVignettes("permute")) for additional information on each of these types of permutation.

Argument mirror determines whether grid or series permutations can be mirrored. Consider the sequence 1,2,3,4. The relationship between consecutive observations is preserved if we reverse the sequence to 4,3,2,1. If there is no inherent direction in your experimental design, mirrored permutations can be considered part of the Null model, and as such increase the number of possible permutations. The default is to not use mirroring so you must explicitly turn this on using mirror = TRUE in how.

To permute plots rather than the observations within plots (the levels of strata), use Within(type = "none") and Plots(type = foo), where foo is how you want the plots to be permuted. However, note that the number of observations within each plot must be equal!

For some experiments, such as BACI designs, one might wish to use the same permutation within each plot. This is controlled by argument constant. If constant = TRUE then the same permutation will be generated for each level of strata. The default is constant = FALSE.

Value

For how a list with components for each of the possible arguments.

References

shuffle() is modelled after the permutation schemes of Canoco 3.1 (ter Braak, 1990); see also Besag & Clifford (1989).

Besag, J. and Clifford, P. (1989) Generalized Monte Carlo significance tests. Biometrika 76; 633–642.

ter Braak, C. J. F. (1990). Update notes: CANOCO version 3.1. Wageningen: Agricultural Mathematics Group. (UR).

Author

Gavin Simpson

Examples

## Set up factors for the Plots and Blocks
plts <- gl(4, 10) ## 4 Plots of 10 samples each
blks <- gl(2, 20) ## 2 Blocks of 20 samples each

## permutation design
h1 <- how(within = Within(type = "series", mirror = TRUE),
          plots = Plots(strata = plts, type = "series"),
          blocks = blks)

## The design can be updated...
## ... remove the blocking:
update(h1, blocks = NULL)
#> 
#> Permutation Design:
#> 
#> Blocks:
#>   Defined by: none
#> 
#> Plots:
#>   Plots: plts
#>   Permutation type: series
#>   Mirrored?: No
#> 
#> Within Plots:
#>   Permutation type: series
#>   Mirrored?: Yes
#>   Different permutation within each Plot?: Yes
#> 
#> Permutation details:
#>   Number of permutations: 199
#>   Max. number of permutations allowed: 9999
#>   Evaluate all permutations?: No.  Activation limit: 5040

## ... or switch the type of shuffling at a level:
#update(h1, plots = update(getPlots(h1), type = "none"))
plots2 <- update(getPlots(h1), type = "none")
update(h1, plots = plots2)
#> 
#> Permutation Design:
#> 
#> Blocks:
#>   Blocks: blks
#> 
#> Plots:
#>   Plots: plts
#>   Permutation type: none
#>   Mirrored?: No
#> 
#> Within Plots:
#>   Permutation type: series
#>   Mirrored?: Yes
#>   Different permutation within each Plot?: Yes
#> 
#> Permutation details:
#>   Number of permutations: 199
#>   Max. number of permutations allowed: 9999
#>   Evaluate all permutations?: No.  Activation limit: 5040