Extract, Analyse and Display Permutation Results

The permustats function extracts permutation results of vegan functions. Its support functions can find quantiles and standardized effect sizes, plot densities and Q-Q plots.

Usage

permustats(x, ...)
# S3 method for class 'permustats'
summary(object, interval = 0.95, alternative, ...)
permulattice(x, plot = c("densityplot", "qqmath"), observed = TRUE,
    axislab = "Permutations", ...)
# S3 method for class 'permustats'
densityplot(x, data, observed = TRUE,
    xlab = "Permutations", ...)
# S3 method for class 'permustats'
density(x, observed = TRUE, ...)
# S3 method for class 'permustats'
qqnorm(y, observed = TRUE, ...)
# S3 method for class 'permustats'
qqmath(x, data, observed = TRUE, sd.scale = FALSE,
    ylab = "Permutations", ...)
# S3 method for class 'permustats'
boxplot(x, scale = FALSE, names, ...)
# S3 method for class 'permustats'
pairs(x, ...)

Arguments

object, x, y: The object to be handled.
interval: numeric; the coverage interval reported.
alternative: A character string specifying the limits used for the interval and the direction of the test when evaluating the \(p\)-values. Must be one of "two.sided" (both upper and lower limit), "greater" (upper limit), "less" (lower limit). Usually alternative is given in the result object, but it can be specified with this argument.
plot: Use lattice function densityplot or qqmath.
xlab, ylab, axislab: Label for the axis displaying permutation values.
observed: Add observed statistic among permutations.
sd.scale: Scale permutations to unit standard deviation and observed statistic to standardized effect size.
data: Ignored.
scale: Use standardized effect size (SES).
names: Names of boxes (default: names of statistics).
...: Other arguments passed to the function. In density these are passed to density.default, and in boxplot to boxplot.default.

Details

The permustats function extracts permutation results and observed statistics from several vegan functions that perform permutations or simulations.

The summary method of permustats estimates the standardized effect sizes (SES) as the difference of observed statistic and mean of permutations divided by the standard deviation of permutations (also known as \(z\)-values). It also prints the the mean, median, and limits which contain interval percent of permuted values. With the default (interval = 0.95), for two-sided test these are (2.5%, 97.5%) and for one-sided tests either 5% or 95% quantile and the \(p\)-value depending on the test direction. The mean, quantiles and \(z\) values are evaluated from permuted values without observed statistic, but the \(p\)-value is evaluated with the observed statistic. The intervals and the \(p\)-value are evaluated with the same test direction as in the original test, but this can be changed with argument alternative. Several permustats objects can be combined with c function. The c function checks that statistics are equal, but performs no other sanity tests.

The results can be displayed either as conventional graphics or lattice graphics. Lattice graphics can be used either with function permulattice or directly with lattice functions densityplot or qqmath. Function permulattice can be used directly, but for densityplot and qqmath lattice must be first loaded and attached with library(lattice)

The density and densityplot methods display the kernel density estimates of permuted values. When observed value of the statistic is included in the permuted values, the densityplot method marks the observed statistic as a vertical line. However the density method uses its standard plot method and cannot mark the observed value. Only one statistic can be displayed with density and for several statistics permulattice or densityplot must be used.

The qqnorm and qqmath methods display Q-Q plots of permutations, optionally together with the observed value (default) which is shown as horizontal line in plots. qqnorm plots permutation values against standard Normal variate. qqmath defaults to the standard Normal as well, but can accept other alternatives (see standard qqmath). The qqmath function can also plot observed statistic as standardized effect size (SES) with standandized permutations (argument sd.scale). The permutations are standardized without the observed statistic, similarly as in summary. Only one statistic can be shown with qqnorm and for several statistics permulattice or qqmath must be used.

Function boxplot draws the box-and-whiskers plots of effect size, or the difference of permutations and observed statistic. If scale = TRUE, permutations are standardized to unit standard deviation, and the plot will show the standardized effect sizes.

Function pairs plots permutation values of statistics against each other. The function passes extra arguments to pairs.

The permustats can extract permutation statistics from the results of adonis2, anosim, anova.cca, mantel, mantel.partial, mrpp, oecosimu, ordiareatest, permutest.cca, protest, and permutest.betadisper.

Value

The permustats function returns an object of class "permustats". This is a list of items "statistic" for observed statistics, permutations which contains permuted values, and alternative which contains text defining the character of the test ("two.sided", "less" or "greater"). The qqnorm and density methods return their standard result objects.

Author

Jari Oksanen with contributions from Gavin L. Simpson (permustats.permutest.betadisper method and related modifications to summary.permustats and the print method) and Eduard Szöcs (permustats.anova.cca).

Examples

data(dune, dune.env)
mod <- adonis2(dune ~ Management + A1, data = dune.env)
## use permustats
perm <- permustats(mod)
summary(perm)
#> 
#>       statistic    SES   mean lower median  upper Pr(perm)    
#> Model    2.9966 5.1251 1.0323       0.9659 1.7332    0.001 ***
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#> 
#> (Interval (Upper - Lower) = 0.95)
## lattice graphics
permulattice(perm, "densityplot")

permulattice(perm, "qqmath")

boxplot(perm, scale=TRUE, lty=1, pch=16, cex=0.6, col="hotpink", ylab="SES")
abline(h=0, col="skyblue")

## example of multiple types of statistic
mod <- with(dune.env, betadisper(vegdist(dune), Management))
pmod <- permutest(mod, nperm = 99, pairwise = TRUE)
perm <- permustats(pmod)
summary(perm, interval = 0.90)
#> 
#>             statistic     SES    mean   lower  median   upper Pr(perm)  
#> Overall (F)    1.9506  0.7065  1.1457          0.8238  2.4572    0.151  
#> BF-HF (t)     -0.5634 -0.4211 -0.0327 -2.0185 -0.0244  1.9050    0.589  
#> BF-NM (t)     -2.2387 -1.9005 -0.0008 -1.8177  0.0074  2.0221    0.067 .
#> BF-SF (t)     -1.1675 -0.9474 -0.0166 -1.9013 -0.0394  1.8854    0.285  
#> HF-NM (t)     -2.1017 -1.9381  0.0350 -1.6795  0.0422  1.8083    0.065 .
#> HF-SF (t)     -0.8789 -0.7675  0.0091 -1.9367  0.0263  1.8432    0.405  
#> NM-SF (t)      0.9485  0.8612 -0.0086 -1.8298  0.0276  1.7612    0.359  
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#> 
#> (Interval (Upper - Lower) = 0.9)