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)

  

• Modify some settings and observe the change

  t$type <- "asymp"
  t$p_value

  

See pmts() for tests implemented in this package.

key	class	test
onesample.quantile	Quantile	Quantile Test
onesample.cdf	CDF	Inference on Cumulative Distribution Function
twosample.difference	Difference	Two-Sample Test Based on Mean or Median
twosample.wilcoxon	Wilcoxon	Two-Sample Wilcoxon Test
twosample.scoresum	ScoreSum	Two-Sample Test Based on Sum of Scores
twosample.ansari	AnsariBradley	Ansari-Bradley Test
twosample.siegel	SiegelTukey	Siegel-Tukey Test
twosample.rmd	RatioMeanDeviance	Ratio Mean Deviance Test
twosample.ks	KolmogorovSmirnov	Two-Sample Kolmogorov-Smirnov Test
ksample.oneway	OneWay	One-Way Test for Equal Means
ksample.kw	KruskalWallis	Kruskal-Wallis Test
ksample.jt	JonckheereTerpstra	Jonckheere-Terpstra Test
multcomp.studentized	Studentized	Multiple Comparison Based on Studentized Statistic
paired.sign	Sign	Two-Sample Sign Test
paired.difference	PairedDifference	Paired Comparison Based on Differences
rcbd.oneway	RCBDOneWay	One-Way Test for Equal Means in RCBD
rcbd.friedman	Friedman	Friedman Test
rcbd.page	Page	Page Test
association.corr	Correlation	Test for Association Between Paired Samples
table.chisq	ChiSquare	Chi-Square Test on Contingency Table

Extending

The define_pmt function 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
    inherit = "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 = "lr", n_permu = 1e5
)

Also, 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(
    inherit = "twosample", rejection = "lr", 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;
        };
    }"
)

The following demonstrates that t_custom 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_cpp$test(x, y)$print()

Performance

The coin package is a commonly used R package for performing permutation tests. Below is a benchmark comparing the computational efficiency of coin and LearnNonparam:

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(
    R = t_custom$test(x, y),
    Rcpp = t_cpp$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, even surpassing the coin package. However, all tests in this package are currently written in 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

Higgins, J. J. 2004. An Introduction to Modern Nonparametric Statistics. Duxbury Advanced Series. Brooks/Cole.