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LearnNonparam

Overview

This R package implements several non-parametric tests in chapters 1-5 of Higgins (2004), including tests for one sample, two samples, k samples, paired comparisons, blocked designs, trends and association. Built with Rcpp for efficiency and R6 for flexible, object-oriented design, it provides a unified framework for performing or creating custom permutation tests.

Installation

Install the stable version from CRAN:

install.packages("LearnNonparam")

Install the development version from Github:

# install.packages("remotes")
remotes::install_github("qddyy/LearnNonparam")

Usage

library(LearnNonparam)

• Construct a test object

  • from some R6 class directly

  t <- Wilcoxon$new(n_permu = 1e6)

  • using the pmt (permutation test) wrapper

  # recommended for a unified API
  t <- pmt("twosample.wilcoxon", n_permu = 1e6)

• Provide it with samples

  set.seed(-1)
  
  t$test(rnorm(10, 1), rnorm(10, 0))

  

• Check the results

  t$statistic

  

  t$p_value

  

  options(digits = 3)
  
  t$print()

  

  ggplot2::theme_set(ggplot2::theme_minimal())
  
  t$plot(style = "ggplot2", binwidth = 1) # or ggplot2::autoplot(t, binwidth = 1)

  

  

• Modify some settings and observe the change

  t$type <- "asymp"
  t$p_value

  

pmts()

Extending

define_pmt allows users to define new permutation tests. Take the two-sample Wilcoxon test as an example:

t_custom <- define_pmt(
    # this is a two-sample permutation test
    method = "twosample",
    statistic = function(x, y) {
        # (optional) pre-calculate certain constants that remain invariant during permutation
        m <- length(x)
        n <- length(y)
        # return a closure to calculate the test statistic
        function(x, y) sum(x) / m - sum(y) / n
    },
    # reject the null hypothesis when the test statistic is too large or too small
    rejection = "<>", n_permu = 1e5
)

For R >= 4.4.0, the quickr package can be used to accelerate statistic. However, this results in repeated crossings of the R-Fortran boundary and makes pre-calculation of constants impossible.

t_quickr <- define_pmt(
    method = "twosample", rejection = "<>", n_permu = 1e5,
    statistic = function(x, y) {
        sum(x) / length(x) - sum(y) / length(y)
    },
    quickr = TRUE
)

In cases where both pre-calculation and computational efficiency are required, the statistic can be written in C++. Leveraging Rcpp sugars and C++14 features, only minor modifications are needed to make it compatible with C++ syntax.

t_cpp <- define_pmt(
    method = "twosample", rejection = "<>", n_permu = 1e5,
    statistic = "[](const auto& x, const auto& y) {
        auto m = x.length();
        auto n = y.length();
        return [=](const auto& x, const auto& y) {
            return sum(x) / m - sum(y) / n;
        };
    }"
)

It’s easy to check that t_custom, t_quickr and t_cpp are equivalent:

x <- rnorm(10, mean = 0)
y <- rnorm(10, mean = 5)

set.seed(0)
t_custom$test(x, y)$print()

set.seed(0)
t_quickr$test(x, y)$print()

set.seed(0)
t_cpp$test(x, y)$print()

Performance

coin is a commonly used R package for performing permutation tests. Below is a benchmark:

library(coin)

data <- c(x, y)
group <- factor(c(rep("x", length(x)), rep("y", length(y))))

options(LearnNonparam.pmt_progress = FALSE)
benchmark <- microbenchmark::microbenchmark(
    pure_R = t_custom$test(x, y),
    quickr = t_quickr$test(x, y),
    Rcpp = t_cpp$test(x, y),
    coin = wilcox_test(data ~ group, distribution = approximate(nresample = 1e5, parallel = "no"))
)

benchmark

It can be seen that C++ brings significantly better performance than pure R, which enables it to even surpass the coin package in its no-parallelization setting. However, all tests in this package are currently written in pure R with no plans for migration to C++ in the future. This is because the primary goal of this package is not to maximize performance but to offer a flexible framework for permutation tests.

References

These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.
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