shuffle | R Documentation |
Unrestricted and restricted permutation designs for time series, line transects, spatial grids and blocking factors.
shuffle(n, control = how()) permute(i, n, control)
n |
numeric; the length of the returned vector of permuted
values. Usually the number of observations under consideration. May
also be any object that |
control |
a list of control values describing properties of the
permutation design, as returned by a call to |
i |
integer; row of |
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.
permute
is a higher level utility function for use in a loop
within a function implementing a permutation test. The main purpose of
permute
is to return the correct permutation in each iteration
of the loop, either a random permutation from the current design or
the next permutation from control$all.perms
if it is not
NULL
and control$complete
is TRUE
.
For shuffle
a vector of length n
containing a
permutation of the observations 1, ..., n using the permutation
scheme described by argument control
.
For permute
the i
th permutation from the set of all
permutations, or a random permutation from the design.
Gavin Simpson
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).
check
, a utility function for checking
permutation scheme described by how
.
set.seed(1234) ## unrestricted permutations shuffle(20) ## observations represent a time series of line transect CTRL <- how(within = Within(type = "series")) shuffle(20, control = CTRL) ## observations represent a time series of line transect ## but with mirroring allowed CTRL <- how(within = Within(type = "series", mirror = TRUE)) shuffle(20, control = CTRL) ## observations represent a spatial grid, 5rx4c nr <- 5 nc <- 4 CTRL <- how(within = Within(type = "grid", ncol = nc, nrow = nr)) perms <- shuffle(20, control = CTRL) ## view the permutation as a grid matrix(matrix(1:20, nrow = nr, ncol = nc)[perms], ncol = nc, nrow = nr) ## random permutations in presence of strata plots <- Plots(strata = gl(4, 5)) CTRL <- how(plots = plots, within = Within(type = "free")) shuffle(20, CTRL) ## as above but same random permutation within strata CTRL <- how(plots = plots, within = Within(type = "free", constant = TRUE)) shuffle(20, CTRL) ## time series within each level of block CTRL <- how(plots = plots, within = Within(type = "series")) shuffle(20, CTRL) ## as above, but with same permutation for each level CTRL <- how(plots = plots, within = Within(type = "series", constant = TRUE)) shuffle(20, CTRL) ## spatial grids within each level of block, 4 x (5r x 5c) nr <- 5 nc <- 5 nb <- 4 ## number of blocks plots <- Plots(gl(nb, 25)) CTRL <- how(plots = plots, within = Within(type = "grid", ncol = nc, nrow = nr)) shuffle(100, CTRL) ## as above, but with same permutation for each level CTRL <- how(plots = plots, within = Within(type = "grid", ncol = nc, nrow = nr, constant = TRUE)) shuffle(100, CTRL) ## permuting levels of plots instead of observations CTRL <- how(plots = Plots(gl(4, 5), type = "free"), within = Within(type = "none")) shuffle(20, CTRL) ## permuting levels of plots instead of observations ## but plots represent a time series CTRL <- how(plots = Plots(gl(4, 5), type = "series"), within = Within(type = "none")) shuffle(20, CTRL) ## permuting levels of plots but plots represent a time series ## free permutation within plots CTRL <- how(plots = Plots(gl(4, 5), type = "series"), within = Within(type = "free")) shuffle(20, CTRL) ## permuting within blocks grp <- gl(2, 10) # 2 groups of 10 samples each CTRL <- how(blocks = grp) shuffle(length(grp), control = CTRL) ## Simple function using permute() to assess significance ## of a t.test pt.test <- function(x, group, control) { ## function to calculate t t.statistic <- function(x, y) { m <- length(x) n <- length(y) ## means and variances, but for speed xbar <- mean(x) ybar <- mean(y) xvar <- var(x) yvar <- var(y) pooled <- sqrt(((m-1)*xvar + (n-1)*yvar) / (m+n-2)) (xbar - ybar) / (pooled * sqrt(1/m + 1/n)) } ## check the control object #control <- check(x, control)$control ## FIXME ## number of observations Nobs <- nobs(x) ## group names lev <- names(table(group)) ## vector to hold results, +1 because of observed t t.permu <- numeric(length = control$nperm) + 1 ## calculate observed t t.permu[1] <- t.statistic(x[group == lev[1]], x[group == lev[2]]) ## generate randomisation distribution of t for(i in seq_along(t.permu)) { ## return a permutation want <- permute(i, Nobs, control) ## calculate permuted t t.permu[i+1] <- t.statistic(x[want][group == lev[1]], x[want][group == lev[2]]) } ## pval from permutation test pval <- sum(abs(t.permu) >= abs(t.permu[1])) / (control$nperm + 1) ## return value return(list(t.stat = t.permu[1], pval = pval)) } ## generate some data with slightly different means set.seed(1234) gr1 <- rnorm(20, mean = 9) gr2 <- rnorm(20, mean = 10) dat <- c(gr1, gr2) ## grouping variable grp <- gl(2, 20, labels = paste("Group", 1:2)) ## create the permutation design control <- how(nperm = 999, within = Within(type = "free")) ## perform permutation t test perm.val <- pt.test(dat, grp, control) perm.val ## compare perm.val with the p-value from t.test() t.test(dat ~ grp, var.equal = TRUE)
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