Categorical swap randomization (swapcat)

Categorical generalization of the binary 2x2 swap algorithm to matrices of categorical data. This function is a convenience wrapper around nullcat() with method = "swapcat".

Usage

swapcat(
  x,
  n_iter = 1000L,
  output = c("category", "index"),
  swaps = "auto",
  wt_row = NULL,
  wt_col = NULL,
  seed = NULL
)

Arguments

x

A matrix of categorical data, encoded as integers. Values should represent category or stratum membership for each cell.

n_iter

Number of iterations. Default is 1000. Larger values yield more thorough mixing. Ignored for non-sequential methods. Minimum burn-in times can be estimated with suggest_n_iter().

output

Character indicating type of result to return:

• "category" (default) returns randomized matrix

• "index" returns an index matrix describing where original entries (a.k.a. "tokens") moved. Useful mainly for testing, and for applications like quantize() that care about token tracking in addition to generic integer categories.

swaps

Character string controlling the direction of token movement. Only used when method is "curvecat", "swapcat", or "tswapcat". Affects the result only when output = "index", otherwise it only affects computation speed. Options include:

• "vertical": Tokens move between rows (stay within columns).

• "horizontal": Tokens move between columns (stay within rows).

• "alternating": Tokens move in both dimensions, alternating between vertical and horizontal swaps. Provides full 2D mixing without preserving either row or column token sets.

• "auto" (default): For output = "category", automatically selects the fastest option based on matrix dimensions. For output = "index", defaults to "alternating" for full mixing. When wt_row or wt_col is supplied, defaults to the appropriate direction, or "alternating" if both are supplied.

wt_row

An optional square numeric matrix of non-negative weights controlling which pairs of rows are likely to exchange tokens during randomization. Must be nrow(x) by nrow(x). This enables spatially or trait-constrained null models where nearby or similar sites exchange tokens more frequently.

Values are treated as relative weights (not probabilities) and are normalized internally. The diagonal is ignored. The matrix should be symmetric. Only supported for sequential methods (curvecat, swapcat, tswapcat).

When both wt_row and wt_col are supplied, swaps is forced to "alternating", producing a Gibbs-like sweep that applies each weight matrix on its respective margin in alternation.

wt_col

An optional square numeric matrix of non-negative weights controlling which pairs of columns are likely to exchange tokens during randomization. Must be ncol(x) by ncol(x). See wt_row for details on weight interpretation.

seed

Integer used to seed random number generator, for reproducibility.

Value

A matrix of the same dimensions as x, either randomized categorical values (when output = "category") or an integer index matrix describing the permutation of entries (when output = "index").

Details

The swapcat algorithm attempts random 2x2 swaps of the form:

a b        b a
b a   <->  a b

where \(a\) and \(b\) are distinct categories. These swaps preserve the multiset of categories in each row and column. With only two categories present, swapcat() reduces to the behavior of the standard binary swap algorithm.

References

Gotelli, N. J. (2000). Null model analysis of species co-occurrence patterns. Ecology, 81(9), 2606–2621.

See also

curvecat() for an algorithm that produces equivalent results with better computational efficiency.

Examples

set.seed(123)
x <- matrix(sample(1:4, 100, replace = TRUE), nrow = 10)
x_rand <- swapcat(x, n_iter = 1000)