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, ...)
# S3 method for class 'permustats'
density(x, observed = TRUE, which, ...)
# S3 method for class 'permustats'
qqnorm(y, x, observed = TRUE, which, xlab, ylab, ...)
# 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. Usually this is x, but in qqnorm the permutation values are displayed on \(y\)-axis, and x can be used for user-supplied quantiles.
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.
observed: Add observed statistic among permutations.
which: which (integer) of permutation statistics is displayed.
xlab, ylab: Axis labels to replace defaults.
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 with conventional graphics or as ggplot2 graphics using autoplot function in ggvegan package.

The density prepares kernel density estimates of permuted values; these can be displayed with plot. Only one statistic can be displayed: use which to select the displayed statistic.

The qqnorm method displays 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, but users can supply other reference axis with argument x. The permutations are standardized without the observed statistic, similarly as in summary. Only one statistic can be displayed: use which to select the displayed statistic.

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 5.4237 1.0137       0.9495 1.6706    0.001 ***
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#> 
#> (Interval (Upper - Lower) = 0.95)
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  0.6077  1.2335          0.8982  2.5872    0.183  
#> BF-HF (t)     -0.5634 -0.4466  0.0187 -2.0376 -0.0157  2.1457    0.605  
#> BF-NM (t)     -2.2387 -1.7986  0.0197 -2.0642  0.0297  2.0142    0.073 .
#> BF-SF (t)     -1.1675 -0.9350 -0.0249 -1.9101 -0.0277  1.7764    0.315  
#> HF-NM (t)     -2.1017 -1.8283  0.0365 -1.8312  0.0279  1.9724    0.063 .
#> HF-SF (t)     -0.8789 -0.7373 -0.0144 -1.9970 -0.0642  1.8540    0.405  
#> NM-SF (t)      0.9485  0.8218 -0.0305 -1.9023 -0.0214  1.8619    0.371  
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#> 
#> (Interval (Upper - Lower) = 0.9)