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CRAN Task View: Compositional Data Analysis

In general, compositional data refers to multivariate, positive and scale-invariant data that convey relative information. Although not necessarily, they are often closed or normalized to be expressed in proportions adding up to 1, percentages adding to 100, or the like; but the scale-invariance property implies that the normalization constant used is actually irrelevant. That is, compositional methods are applicable whenever the researcher recognizes that the relevant information in the data is relative and, thus, there is an intrinsic interdependence between the parts that make up the composition. These particularities are not considered by ordinary statistical methods, which are generally designed for unconstrained real-valued data.

This task view provides a curated collection of R packages to support compositional data analysis within the log-ratio coordinate framework. The main goal is serving as a guide to practitioners interested in applying such methods. The packages can be broadly categorized into the following topics, although many provide functionalities spanning multiple categories, as detailed below.

Table of Contents

• General purpose packages
• Irregular data: Zeros, censoring, missing and outliers
• Visualization
• Compositional tables
• Density data analysis
• Regression modeling
• High-dimensional compositional data with applications to omics data
• Special applications in geostatistics and geochemistry
• Other packages
• Background

General purpose packages

This section refers to packages that provide a general platform for compositional data analysis in R, implementing functions to conduct basic operations and calculations, log-ratio representations, data visualization and some common statistical analyses. They typically accompany a published monograph and provide an environment for analysis that is compatible with the basic properties of compositional data for those approaching the methodology from diverse domains.

• compositions: once a class for the data is set, which corresponds to the assumed underlying geometry (either compositional, acomp class, or multivariate positive data, aplus class), the package operates through functions for their consistent analysis and modeling; including descriptive statistics, visualization, statistical testing, and multivariate analysis (e.g. principal component analysis, clustering, MANOVA and regression). It also implements some geostatistical tools such a variogram for compositions and compositional ordinary kriging. This package is linked to the monograph Van den Boogaart and Tolosana-Delgado (2013) and supports the analyses and examples therein.
  
• robCompositions: with a main focus on robust statistical methods (see Robust for an overview of other robust statistical methods available in R). The package includes a wide range of tools for the manipulation and analysis of compositional data within the log-ratio framework. This includes ordinary transformations, dealings with irregular data, and robust versions of methods such as principal component analysis, factor analysis and discriminant analysis and regression with compositional predictors. Additionally, it implements specialized methods for two-factorial compositions (a.k.a compositional tables) and functional-compositional analysis of density data. The main reference monograph is Filzmoser, Hron and Templ (2018).
  
• easyCODA: provides methods and graphics for univariate and multivariate analysis of compositional data in the spirit of Greenacre (2018), emphasizing the use of basic pairwise log-ratios. Particular features include procedures for stepwise selecting log-ratios, correspondence analysis and redundance analysis.

Irregular data: Zeros, censoring, missing and outliers

Compositional data, like ordinary datasets, often face challenges that complicate statistical analysis. A key issue in the log-ratio approach is handling zeros without distorting data properties. Three types are distinguished: rounded zeros (small values rounded or below detection limits), count zeros (from discrete counting processes), and essential zeros (true absences in the composition). Rounded zeros, akin to left-censored data, have received the most attention in the literature.

Moreover, analogously to non-compositional statistical methods, the presence of either missing values or outliers poses practical challenges. Again, coherent handling is required for consistent data analysis within the compositional framework.

The following are specialized packages focused on addressing these issues while respecting the compositional nature of the data.

• zCompositions: a suite of data imputation methods applicable to zeros, nondetects, missing data, and combinations of them, following the principles of the log-ratio approach (Palarea-Albaladejo and Martín-Fernández (2015)). This includes a consistent treatment of closed and non-closed compositions, unique or varying detection limits, parametric and nonparametric imputation, single and multiple imputation, maximum likelihood and robust estimation, as well as some tools for the exploration of zero patterns and statistical testing of grouping structures.
  
• mvoutlier: specific tools for visualizing and identifying multivariate outliers in compositional data.

Visualization

Visualization is a critical component of compositional data analysis, allowing researchers to explore patterns, relationships, and distributions within the constrained simplicial geometry.

On top of the functionality provided with the general purpose packages cited above, this section compiles specialized tools for producing ternary plots, compositional biplots, or pairwise log-ratio plots, among others.

• ggtern: enables plotting and managing ternary diagrams following the style and syntax of the graphical package ggplot2; supporting both standard and additional geometries with a high level of customization.
  
• Ternary: produces ternary diagrams and Holdridge life zone plots using base graphics. Particular features include custom annotation, interpolation, contouring, scaling, and a Shiny interface for interactive plotting.
  
• isopleuros: visualisation of data in ternary space, customising graphical elements, and displaying statistical summaries. Includes specialized diagrams in archaeology, e.g. soil texture charts and ceramic phase diagrams.
  
• provenance: representation of compositional and count data on ternary diagrams and point-counting data on radial plots. Allows to compute sample size required for specified levels of statistical precision, and to assess the effects of hydraulic sorting on detrital compositions. Provides an intuitive query-based user interface for users who are not proficient in R.

Compositional tables

Compositional tables (i.e., ordinary contingency tables in their discrete version) represent frequencies or proportions structured across multiple categories. The compositional nature of these tables, often constrained by row or column sums, requires specialized methods to analyze relationships, dependencies, and patterns while respecting their relative nature. This section refers to tools for their analysis, including log-ratio representation and selected multivariate methods.

• robCompositions: log-ratio coordinate representation of compositional tables and methods for their statistical processing using principal component analysis and regression analysis with a real response and the compositional table as predictor. See Filzmoser, Hron and Templ (2018) (Chapter 12) and Nesrstová et al. (2023) for more details.

Density data analysis

Probability density functions are essentially scale invariant data objects, usually subject to a unit integral constraint. Therefore, they can be considered as infinite dimensional compositional data and embedded in a Hilbert space, so-called a Bayes space (see Van den Boogaart, Egozcue and Pawlowsky-Glahn (2014) for details).

The packages listed below implement methods for density data analysis from this perspective. Unlike the methods in the FunctionalData task view, here it is assumed that the sample space for density functions is the Bayes space.

• robCompositions: methods for representation of probability density functions using compositional smoothing splines, grounded on the theory of Bayes spaces. Additionally, a functional version of the centered log-ratio transformation is included.

Regression modeling

Regression modeling with compositional data allows researchers to explore associations between compositions and other variables, either as predictors/covariates or response; and also between compositions on both sides of the regression model. Packages specifically devoted to compositional regression analysis are listed below. It should be noted that complmrob and robregcc do not offer anything essential beyond, for example, robCompositions.

• complmrob: robust linear regression models for compositional data, where the response variable is a real-valued vector and the covariates are compositional data. See also Hron, Filzmoser and Thompson (2012).
  
• robregcc: algorithm estimating the parameters of the robust regression model with compositional covariates. The model simultaneously treats outliers and parameter estimates as described in Mishra and Mueller (2019).
  
• codaredistlm: linear regression models with compositional predictors, providing predictions and confidence intervals for outcome changes based on reallocations of compositional values, see Dumuid et al. (2017a) and Dumuid et al. (2017b).
  
• DirichletReg: functions to analyze compositional data using Dirichlet regression models.
  
• multilevelcoda: Bayesian multilevel modeling with compositional data, both as predictors and outcomes, and post hoc isotemporal substitution analysis.

High-dimensional compositional data with applications to the omics sciences

Compositional data analysis has gained importance in omics sciences and bioinformatics, where microbiome compositions, gene expression, and metabolomic profiles are inherently compositional. These applications require methods to handle high dimensionality, zero inflation, overdispersion, and phylogenetic integration.

This section highlights packages that provide compositional tools designed for omics data, but certainly most of them could also be considered for the statistical processing of high-dimensional compositional data in general.

• FLORAL: log-ratio lasso regression for continuous, binary, and survival outcomes with compositional features as described in Fei et al. (2023).
  
• coda4microbiome: tools for microbiome data analysis while accounting for its compositional nature. Includes penalized regression methods for variable selection in cross-sectional and longitudinal studies with binary or continuous outcomes.
  
• codacore: identification of sparse log-ratios of a composition acting as predictor in regression problems. Scale invariant log-ratios are derived which are optimized to account for association with the response variable.
  
• lnmCluster: logistic normal-multinomial clustering for microbiome compositional data, including extensions for factor analysis, bi-clustering, and sparse covariance estimation.
  
• MicrobiomeStat: robust methods for analysing microbiome compositional data, addressing zero inflation, phylogenetic structure, and compositional effects. Applicable to other high-dimensional compositional data sets from sequencing experiments.
  
• QFASA: quantitative fatty acid signature analysis to estimate predator diets, leveraging fatty acid diversity, biosynthesis limitations, and digestion properties in monogastric animals. Both methods for compositional and constrained data are used.

Special applications in geostatistics and geochemistry

Compositional data analysis is essential in geostatistics and geochemistry, where it applies to element, mineral, or isotope proportions with spatial dependencies. These applications require methods that respect relative data structures while accounting for spatial relationships (see SpatioTemporal for a task view focused on spatiotemporal methods).

Thus, this section refers to packages for geostatistical modeling, spatial interpolation, variogram analysis, and compositional kriging; as well as techniques for analyzing spatial geochemical compositions. Note that some methods would be equally applicable to any data set with analogous structures in any other application area.

• provenance: statistical tools for sedimentary provenance analysis, including kernel density estimation, principal component analysis, correspondence analysis, and multidimensional scaling. Comparison of univariate proxies (e.g., single-grain ages, isotopic compositions) and categorical data are supported using distances like Kolmogorov-Smirnov, Wasserstein, Aitchison, and Bray-Curtis. Tools for visualizing data on ternary and radial plots, calculating sample sizes, and assessing hydraulic sorting effects are included. Additionally, a user-friendly interface is provided for R beginners.
  
• ArArRedux: data reduction and error propagation for $Ar^/Ar^$ geochronology, processing isotopic compositions from noble gas mass spectrometer data. Methods for regression, blank and decay corrections, detector intercalibration, interference corrections, and age calculation. Argon isotope ratios are treated as compositional data for accurate statistical handling.
  
• gmGeostats: tools for multivariate data with restrictions, including compositions and positive amounts. Descriptive analysis and modeling using two-point Gaussian and multipoint perspectives. Compositional variograms and compositional kriging.

Other packages

This collection is meant to include other useful small packages, typically having a fairly specific purpose. In accordance with the log-ratio framework considered here, the condition for inclusion is that the scale invariance property of compositional data is, at least partially, respected.

• coda.base: provides optimized and user-friendly implementations of functions to compute log-ratio coordinate representations of various types, including principal component and principal balance coordinates, as well as log-ratio coordinates from tailored orthonormal basis. It also allows to compute some basic compositional statistics.
  
• aIc: statistical tests to identify compositional pathologies in data. Namely, coherence of correlations, dominance of distances, perturbation invariance, and singularity of the covariation matrix. Supports multiple data transformations such as proportional, centred log-ratio (clr), and others from common R packages.
  
• SARP.compo: tools for network-based interpretation of changes in compositional data, including computation of pairwise ratios, statistical testing between conditions, and network representation of results.
  
• ToolsForCoDa: selected multivariate analysis tools for compositional data, including compositional canonical correlation analysis, log-ratio principal component analysis with condition number computations, and log-ratio discriminant analysis.

Background

The following should explain which direction in compositional data analysis this task view follows.

Awareness of the problems with compositional data dates back to the end of the 19th century, when the renowned statistician Karl Pearson recognized the problem of spurious correlations between variables scaled with respect to a common denominator. When closed to add up to constant value, compositional data are formally projected on a simplex sample space, and this is often a convenient representation in a practical setting. The simplex is a constrained space with its own internal operations and geometry. However, any coherent approach to analyzing compositional data should not depend on the chosen representation, nor require any preliminary normalization.

The mainstream approach to compositional data analysis, as originally formulated by Aitchison (1982), involves the use of log-ratio transformations (or log-ratio coordinates to use a more more modern terminology) which project the data into real space. Nowadays, the compositional literature offers a wide range of methods within this methodological framework, many of which are implemented in R packages.

Compositional data are common in diverse scientific fields, including the chemical, biological, and environmental sciences; where they typically represent portions of a total sample weight or volume and are expressed in units such as percent, parts per million, mg/l, mmol/mol, or similar. Some examples include chemical compositions of soil, water, or air, food compositions, behavioral or time-use profiles, and relative abundances of species. They are also common in socio-economical sciences; for example when dealing with market shares, investment portfolios, or household budgets.

In recent years, the popularity of compositional methods has grown significantly. Simultaneously, new methodological challenges have arisen requiring novel ways to transfer and formulate compositional knowledge to meet the needs of different scientific fields.

CRAN packages

Other resources

• CRAN Task View: FunctionalData
• CRAN Task View: Robust
• CRAN Task View: SpatioTemporal

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.