Generate a set of permutations from the specified design.

shuffleSet returns a set of nset permutations from the specified design. The main purpose of the function is to circumvent the overhead of repeatedly calling shuffle to generate a set of permutations.

shuffleSet(n, nset, control = how(), check = TRUE, quietly = FALSE)

# S3 method for class 'permutationMatrix'
as.matrix(x, ...)

Arguments

n: numeric; the number of observations in the sample set. May also be any object that nobs knows about; see nobs-methods.
nset: numeric; the number of permutations to generate for the set. Can be missing, the default, in which case nset is determined from control.
control: an object of class "how" describing a valid permutation design.
check: logical; should the design be checked for various problems via function check? The default is to check the design for the stated number of observations and update control accordingly. See Details.
quietly: logical; should messages by suppressed?
x: an object of class "permutationMatrix", as returned by shuffleSet.
...: arguments passed to other methods. For the as.matrix method only.

Details

shuffleSet is designed to generate a set of nset permutation indices over which a function can iterate as part of a permutation test. It is only slightly more efficient than calling shuffle nset times, but it is far more practical than the simpler function because a set of permutations can be worked on by applying a function to the rows of the returned object. This simplifies the function applied, and facilitates the use of parallel processing functions, thus enabling a larger number of permutations to be evaluated in reasonable time.

By default, shuffleSet will check the permutations design following a few simple heuristics. See check for details of these. Whether some of the heuristics are activiated or not can be controlled via how, essentialy via its argument minperm. In particular, if there are fewer than minperm permutations, shuffleSet will generate and return all possible permutations, which may differ from the number requested via argument nset.

The check argument to shuffleSet controls whether checking is performed in the permutation design. If you set check = FALSE then exactly nset permutations will be returned. However, do be aware that there is no guarantee that the set of permutations returned will be unique, especially so for designs and data sets where there are few possible permutations relative to the number requested.

The as.matrix method sets the control and seed attributes to NULL and removes the "permutationMatrix" class, resulting in a standard matrix object.

Value

Returns a matrix of permutations, where each row is a separate permutation. As such, the returned matrix has nset rows and n columns.

Author

Gavin L. Simpson

References

shuffleSet() 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).

Examples

set.seed(1)
## simple random permutations, 5 permutations in set
shuffleSet(n = 10, nset = 5)
#> No. of Permutations: 5
#> No. of Samples: 10 (Randomised)
#> 
#>     1 2 3  4  5  6 7 8  9 10
#> p1  3 4 5  7  2  8 9 6 10  1
#> p2  3 2 6 10  5  7 8 4  1  9
#> p3 10 2 6  1  9  8 7 5  3  4
#> p4  5 6 4  2 10  8 9 1  7  3
#> p5  9 6 7  4  8 10 1 2  3  5

## series random permutations, 5 permutations in set
shuffleSet(10, 5, how(within = Within(type = "series")))
#> Set of permutations < 'minperm'. Generating entire set.
#> No. of Permutations: 5
#> No. of Samples: 10 (Sequence)
#> 
#>    1 2  3 4  5  6 7  8  9 10
#> p1 6 7  8 9 10  1 2  3  4  5
#> p2 8 9 10 1  2  3 4  5  6  7
#> p3 5 6  7 8  9 10 1  2  3  4
#> p4 3 4  5 6  7  8 9 10  1  2
#> p5 2 3  4 5  6  7 8  9 10  1

## series random permutations, 10 permutations in set,
## with possible mirroring
CTRL <- how(within = Within(type = "series", mirror = TRUE))
shuffleSet(10, 10, CTRL)
#> Set of permutations < 'minperm'. Generating entire set.
#> No. of Permutations: 10
#> No. of Samples: 10 (Sequence; mirrored)
#> 
#>      1 2  3  4  5  6  7  8 9 10
#> p1   3 4  5  6  7  8  9 10 1  2
#> p2   7 8  9 10  1  2  3  4 5  6
#> p3  10 1  2  3  4  5  6  7 8  9
#> p4   2 1 10  9  8  7  6  5 4  3
#> p5   8 9 10  1  2  3  4  5 6  7
#> p6   4 3  2  1 10  9  8  7 6  5
#> p7   5 6  7  8  9 10  1  2 3  4
#> p8   9 8  7  6  5  4  3  2 1 10
#> p9   5 4  3  2  1 10  9  8 7  6
#> p10  6 5  4  3  2  1 10  9 8  7

## Permuting strata
## 4 groups of 5 observations
CTRL <- how(within = Within(type = "none"),
            plots = Plots(strata = gl(4,5), type = "free"))
shuffleSet(20, 10, control = CTRL)
#> Set of permutations < 'minperm'. Generating entire set.
#> No. of Permutations: 10
#> No. of Samples: 20 (Nested in: plots; )
#> Restricted by Plots: gl(4, 5) (4 plots; Randomised)
#> 
#>      1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 16 17 18 19 20
#> p1   6  7  8  9 10  1  2  3  4  5 11 12 13 14 15 16 17 18 19 20
#> p2   6  7  8  9 10 16 17 18 19 20 11 12 13 14 15  1  2  3  4  5
#> p3  11 12 13 14 15 16 17 18 19 20  6  7  8  9 10  1  2  3  4  5
#> p4   1  2  3  4  5 11 12 13 14 15  6  7  8  9 10 16 17 18 19 20
#> p5  16 17 18 19 20  6  7  8  9 10 11 12 13 14 15  1  2  3  4  5
#> p6   6  7  8  9 10  1  2  3  4  5 16 17 18 19 20 11 12 13 14 15
#> p7  11 12 13 14 15  6  7  8  9 10 16 17 18 19 20  1  2  3  4  5
#> p8  16 17 18 19 20 11 12 13 14 15  6  7  8  9 10  1  2  3  4  5
#> p9  11 12 13 14 15 16 17 18 19 20  1  2  3  4  5  6  7  8  9 10
#> p10 16 17 18 19 20  1  2  3  4  5  6  7  8  9 10 11 12 13 14 15

## 10 random permutations in presence of Plot-level strata
plotStrata <- Plots(strata = gl(4,5))
CTRL <- how(plots = plotStrata,
            within = Within(type = "free"))
numPerms(20, control = CTRL)
#> [1] 207360000
shuffleSet(20, 10, control = CTRL)
#> No. of Permutations: 10
#> No. of Samples: 20 (Nested in: plots; Randomised)
#> Restricted by Plots: gl(4, 5) (4 plots)
#> 
#>     1 2 3 4 5  6  7  8  9 10 11 12 13 14 15 16 17 18 19 20
#> p1  5 4 2 3 1  8 10  7  6  9 12 13 11 14 15 17 16 20 18 19
#> p2  4 2 5 3 1  9  7  6 10  8 12 11 15 13 14 20 18 17 16 19
#> p3  1 3 5 4 2 10  7  9  6  8 13 15 11 14 12 18 16 19 17 20
#> p4  3 5 2 4 1  9  8  6 10  7 13 11 15 14 12 19 18 16 20 17
#> p5  1 3 5 4 2  7  9 10  8  6 13 11 12 15 14 19 20 18 16 17
#> p6  5 3 4 2 1  7  6  8 10  9 11 14 13 12 15 19 17 16 20 18
#> p7  3 1 5 4 2  7  6 10  9  8 13 15 11 14 12 20 16 18 17 19
#> p8  2 3 4 5 1  7  6  9 10  8 13 12 11 15 14 17 16 20 18 19
#> p9  4 3 2 1 5  7  8  9  6 10 12 15 11 13 14 19 20 17 18 16
#> p10 1 5 2 4 3  8  7  6  9 10 11 15 13 12 14 16 20 17 19 18
## as above but same random permutation within Plot-level strata
CTRL <- how(plots = plotStrata,
            within = Within(type = "free", constant = TRUE))
numPerms(20, control = CTRL)
#> [1] 120
shuffleSet(20, 10, CTRL) ## check this.
#> Set of permutations < 'minperm'. Generating entire set.
#> No. of Permutations: 10
#> No. of Samples: 20 (Nested in: plots; Randomised; same permutation in
#> each plot)
#> Restricted by Plots: gl(4, 5) (4 plots)
#> 
#>     1 2 3 4 5  6  7  8  9 10 11 12 13 14 15 16 17 18 19 20
#> p1  1 5 4 3 2  6 10  9  8  7 11 15 14 13 12 16 20 19 18 17
#> p2  2 3 1 5 4  7  8  6 10  9 12 13 11 15 14 17 18 16 20 19
#> p3  1 5 4 2 3  6 10  9  7  8 11 15 14 12 13 16 20 19 17 18
#> p4  3 2 4 1 5  8  7  9  6 10 13 12 14 11 15 18 17 19 16 20
#> p5  4 3 5 2 1  9  8 10  7  6 14 13 15 12 11 19 18 20 17 16
#> p6  1 2 5 3 4  6  7 10  8  9 11 12 15 13 14 16 17 20 18 19
#> p7  3 4 1 2 5  8  9  6  7 10 13 14 11 12 15 18 19 16 17 20
#> p8  5 1 3 4 2 10  6  8  9  7 15 11 13 14 12 20 16 18 19 17
#> p9  2 5 1 3 4  7 10  6  8  9 12 15 11 13 14 17 20 16 18 19
#> p10 1 3 2 4 5  6  8  7  9 10 11 13 12 14 15 16 18 17 19 20

## time series within each level of Plot strata
CTRL <- how(plots = plotStrata,
            within = Within(type = "series"))
shuffleSet(20, 10, CTRL)
#> Set of permutations < 'minperm'. Generating entire set.
#> No. of Permutations: 10
#> No. of Samples: 20 (Nested in: plots; Sequence)
#> Restricted by Plots: gl(4, 5) (4 plots)
#> 
#>     1 2 3 4 5  6  7 8  9 10 11 12 13 14 15 16 17 18 19 20
#> p1  2 3 4 5 1 10  6 7  8  9 14 15 11 12 13 18 19 20 16 17
#> p2  3 4 5 1 2 10  6 7  8  9 12 13 14 15 11 17 18 19 20 16
#> p3  2 3 4 5 1 10  6 7  8  9 11 12 13 14 15 18 19 20 16 17
#> p4  2 3 4 5 1 10  6 7  8  9 13 14 15 11 12 19 20 16 17 18
#> p5  3 4 5 1 2  7  8 9 10  6 14 15 11 12 13 19 20 16 17 18
#> p6  3 4 5 1 2  7  8 9 10  6 15 11 12 13 14 17 18 19 20 16
#> p7  2 3 4 5 1 10  6 7  8  9 13 14 15 11 12 18 19 20 16 17
#> p8  1 2 3 4 5  6  7 8  9 10 13 14 15 11 12 17 18 19 20 16
#> p9  3 4 5 1 2 10  6 7  8  9 12 13 14 15 11 18 19 20 16 17
#> p10 4 5 1 2 3  9 10 6  7  8 14 15 11 12 13 18 19 20 16 17
## as above, but  with same permutation for each Plot-level stratum
CTRL <- how(plots = plotStrata,
            within = Within(type = "series", constant = TRUE))
shuffleSet(20, 10, CTRL)
#> 'nperm' >= set of all permutations: complete enumeration.
#> Set of permutations < 'minperm'. Generating entire set.
#> No. of Permutations: 4
#> No. of Samples: 20 (Nested in: plots; Sequence; same permutation in
#> each plot)
#> Restricted by Plots: gl(4, 5) (4 plots)
#> 
#>    1 2 3 4 5  6  7  8  9 10 11 12 13 14 15 16 17 18 19 20
#> p1 2 3 4 5 1  7  8  9 10  6 12 13 14 15 11 17 18 19 20 16
#> p2 3 4 5 1 2  8  9 10  6  7 13 14 15 11 12 18 19 20 16 17
#> p3 4 5 1 2 3  9 10  6  7  8 14 15 11 12 13 19 20 16 17 18
#> p4 5 1 2 3 4 10  6  7  8  9 15 11 12 13 14 20 16 17 18 19