RRPP: An <scp>r</scp> package for fitting linear models to high‐dimensional data using residual randomization

TLDR

Residual randomization in permutation procedures (RRPP) generates empirical sampling distributions for ANOVA statistics and linear model coefficients, and is especially useful for high‑dimensional data. The RRPP package offers a comprehensive suite of tools for applying residual randomization to linear models, enabling analysis of univariate and multivariate response data even when variables outnumber observations. It implements OLS or GLS coefficient estimation, supports data or dissimilarity matrix analysis, provides types I–III sums of squares, various effect‑size methods, mixed‑model ANOVA, S3 generic compatibility, pairwise tests for least‑squares means or slopes, and customizable random permutations. Compared to similar packages, RRPP is extremely fast and delivers comprehensive coefficient and ANOVA statistics over many random permutations, facilitating downstream analyses and graphics.

Abstract

Abstract Residual randomization in permutation procedures (RRPP) is an appropriate means of generating empirical sampling distributions for ANOVA statistics and linear model coefficients, using ordinary or generalized least‐squares estimation. This is an especially useful approach for high‐dimensional (multivariate) data. Here, we present an r package that provides a comprehensive suite of tools for applying RRPP to linear models. Important available features include choices for OLS or GLS coefficient estimation, data or dissimilarity matrix analysis capability, choice among types I, II, or III sums of squares and cross‐products, various effect size estimation methods, and an ability to perform mixed‐model ANOVA. The lm.rrpp function is similar to the lm function in many regards, but provides coefficient and ANOVA statistics estimates over many random permutations. The S3 generic functions commonly used with lm also work with lm.rrpp . Additionally, a pairwise function provides statistical tests for comparisons of least‐squares means or slopes, among designated groups. Users have many options for varying random permutations. Compared to similar available packages and functions, RRPP is extremely fast and yields comprehensive results for downstream analyses and graphics, following model fits with lm.rrpp . The RRPP package facilitates analysis of both univariate and multivariate response data, even when the number of variables exceeds the number of observations.