CRAN Task View proposal: CompositionalData

[matthias-da]

There was a little hiccup at the start with a task view on compositional data analysis. It seemed that the initial authors were having trouble getting on board with the new authors, didn't agree with comments or simple did not have time to proceed, which is totally understandable. After about a year, it was decided to write this view with new authors.

Following a review of the initial proposal, we have removed a significant number of packages that were not aligned with the requirements of compositional data analysis. We have also created a new task view from scratch, incorporating new packages, sections and did not use text from the old proposal (because mostly copy and paste from package descriptions), as well as restructuring the task view itself.

This is the new proposal:

---

name: CompositionalData
topic: Compositional Data Analysis
maintainer: Karel Hron, Javier Palarea-Albaladejo, Matthias Templ, Alessandra Menafoglio
email: [email protected]
version: 2024-11-18
source: https://github.com/cran-task-views/CoDa/

In general terms, compositional data refers to multivariate, positive and scale
invariant data that convey relative information. Although not necessarily,
they are often closed or normalised to be expressed in proportions adding up to
1, percentages adding up to 100, or the like; but the scale invariance property
implies that the value of any normalisation
constant is in fact irrelevant. That is, compositional methods are applicable
whenever the researcher recognises that the relevant information in the data is
relative and there is an intrinsic
interdependence between the parts configuring the composition. These particular
characteristics are missed by ordinary statistical methods generally designed
for unconstrained real-valued data.

Awareness of the issues with compositional data dates back to the end of the
19th century, when the renowned statistician Karl Pearson already identified
the problem of spurious correlation between variables
representing ratios with respect to a common denominator caused by the scaling
of the data. When closed, compositional data formally live on a simplex sample
space, and this can be 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 analyse compositional data should not depend
on any particular representation chosen nor require any preliminary
normalisation.

The mainstream approach to analysing compositional data, as originally
formulated by
[Aitchison (1982)] (https://doi.org/10.1111/j.2517-6161.1982.tb01195.x),
involves the use of log-ratio transformations, or log-ratio coordinates using a
more modern terminology, that project the data onto the real space. Nowadays,
the literature offers a wide
range of methods and tools to tackle the analysis of compositional data within
this methodological framework, many of which are implemented in R packages.

Compositional data are common in diverse scientific areas, including the
chemical, biological and environmental sciences; typically representing portions
of a total sample weight or volume and
expressed in units such as percentages, parts per million, mg/l, mmol/mol or
similar. Some examples include chemical compositions of soil, water or air,
food compositions, behavioural time-use profiles,
and species relative abundances. They are also common in social sciences like
economics. For example, market shares, investment portfolios, or household
budgets.

In recent years, the popularity of compositional methods has increased notably,
with this meaning new methodological challenges and requiring new ways to
transfer and formulate compositional knowledge
to meet the needs of diverse scientific fields.

Thus, this task view provides a curated collection of R packages aimed at
supporting compositional data analysis, with the purpose of serving as guide
for practitioners
interested in applying such methods. The packages can be broadly categorised
into the following topics, although in fact many offer functionalities that
span multiple categories:

General purpose packages

This 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 visualisation and some common statistical analyses. They, typically
accompanying a published monograph, offer a platform compatible with the basic
properties of compositional data to those approaching
the methodology from diverse domains.

• r pkg("compositions", priority = "core"): once the adequate 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 provides functions for
  their consistent analysis and modelling; including descriptive statistics,
  visualisation, statistical testing, and multivariate analysis (e.g. principal
  component analysis, clustering, MANOVA and regression). It supports the
  monograph
  van den Boogaart and Tolosana-Delgado (2013)
  and allows to reproduce the analyses therein.

• r pkg("robCompositions", priority = "core"): with a main focus on robust
  statistical methods, this package includes a wide range of tools for the
  manipulation and analysis of
  compositional data within the log-ratio framework: transformations, dealings
  with irregular data, robust implementations of multivariate methods such as
  principal component analysis,
  factor analysis and discriminant analysis, robust regression with compositional
  predictors, two-factorial compositions (compositional tables) and
  functional-compositional analysis of density data.
  The main reference monograph is
  Filzmoser, Hron and Templ (2018) .

• r pkg("easyCODA", priority = "core"): univariate and multivariate
  methods for compositional data analysis following the approach in
  Greenacre (2018), emphasising
  the use simple pairwise log-ratios.
  Particular features include procedures for selecting log-ratios that explain
  maximum log-ratio variance and conducting various multivariate analyses.

• r pkg("Compositional"): regression, classification, contour plots, hypothesis
  testing and fitting of distributions for compositional data are some of the
  functions included in this package. Further some functions for percentages
  (or proportions) are included. The package deals, however, with compositional
  data mostly as with constrained data, thus avoiding the scale invariance
  property and, more generally, the principles of compositional data analysis
  characterizing the log-ratio approach
  (despite referring to the classical reference
  Aitchison (1986)). This admits
  direct incorporation of zero components for the analysis, but leads to some
  conceptual inconsistencies with respect to the log-ratio approach. For these
  reasons, analyses run using this package may be incoherent with those run with
  the packages r pkg("composition", priority = "core") or
  r pkg("robCompositions", priority = "core").

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 specialised methods to analyse relationships, dependencies, and patterns while respecting their
relative nature. This section refers to packages implementing tools for their analysis, including log-ratio representation and selected multivariate methods.

• r pkg("robCompositions", priority = "core"): 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.

Density data analysis

Probability density functions are essentially scale invariant data objects which are commonly subject to a unit integral constraint. They can, therefore, be considered as
infinite dimensional compositional data and embedded into a Hilbert space, so-called a Bayes space. This section refers to packages implementing methods and tools for density data analysis
from this perspective.

Note that these methods differs from those included in the CRAN Task View on CRAN Task View: Functional Data Analysis,
in that they assume the Bayes space as sample space for density functions.

• r pkg("robCompositions", priority = "core"): some methods for
  representation of probability density functions using compositional smoothing splines, grounded on the theory of Bayes spaces.
  Additionally, the package includes a functional version of the centered log-ratio transformation.

Irregular data: zeros, censoring, missing and outliers

As with ordinary data sets, compositional data sets can be often affected by different issues in real-world applications, which might prevent for the immediate use of statistical methods and should be treated
in a data preprocessing stage. Of particular relevance for the application of the log-ratio methodology is the presence of zeros, which require careful handling to preserve the basic properties of the data and the
integrity of the subsequent analyses.

Traditionally, three types of zeros have been distinguished in the compositional data literature: rounded zeros, count zeros and essential zeros. Briefly,
rounded zeros appear in continuous-valued compositions, and are commonly associated with small values that have been rounded off or have fallen below the detection limit of the
measuring device; count zeros refer to zeros that occurring in discrete compositions derived from a counting process, and are generally associated to limited sampling; and, finally,
essential zeros refer to genuine zero values, i.e. the case of parts of the composition that are truly absent. Rounded zeros is the case that has received the most attention in the literature
and represent a class of left-censored data.

Moreover, the presence of both missing values and outliers poses practical challenges, and a proper handling of them is required to
ensure consistency, validity and robustness of a compositional data analysis.

This section focuses on specialised packages including methods to address the above issues while respecting the compositional nature of the data.

• r pkg("zCompositions", priority = "core"): integrated suite of data imputation methods applicable to zeros, nondetects, missing data, and combinations of them, following the
  principles of the log-ratio approach as described in 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 structure.

• r pkg("mvoutlier"): specific tools for visualising and identifying multivariate outliers in compositional data.

• r pkg("robCompositions", priority = "core"): routines included to impute rounded zeros and missing data, as well as tools to detect outlying samples.

• r pkg("compositions", priority = "core"): routines included to detect, represent, and provide some analysis of irregular data, either missing values, zeros or outliers.

Visualisation

Visualisation is a crucial component of compositional data analysis, allowing researchers to explore patterns, relationships, and distributions within the constrained simplex geometry. This section includes
tools for creating ternary diagrams, biplots or pairwise log-ratio plots, among others. On top of overall visualisation functionality included in the general purpose packages above, some others particularly
devoted to such purpose are listed in the following.

• r pkg("ggtern"): extends ggplot2 to create ternary diagrams, supporting standard and
  additional custom geometries, including specialised ternary visualisations.

• r pkg("Ternary"): ternary diagrams and Holdridge life zone plots using base graphics. Features include custom annotation, interpolation, contouring, scaling, and a
  Shiny interface for interactive plotting.

• r pkg("isopleuros"): tools for visualising data in ternary space, customising graphical elements,
  and displaying statistical summaries. Includes specialised diagrams for fields like archaeology (e.g., soil texture charts, ceramic phase diagrams).

• r pkg("provenance"): tools for plotting compositional and count data on ternary diagrams and point-counting data on radial plots. Calculations of sample size required for specified levels of statistical precision,
  and to assess the effects of hydraulic sorting on detrital compositions. Intuitive query-based user interface for users who are not proficient in R.

Regression modelling

Specialised regression modelling with compositional data allows researchers to explore associations between compositions and other variables,
either acting as predictors/covariates or as response, and also between compositions on both sides of the regression model. Packages
specifically devoted to compositional regression analysis are listed in the following. It might be mentioned that r pkg("complmrob") and r pkg("robregcc")
offering nothing essential beyond, e.g., r pkg("robCompositional").

• r pkg("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).

• r pkg("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).

• r pkg("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).

• r pkg("DirichletReg"): functions to analyse compositional data using Dirichlet regression models.

• r pkg("multilevelcoda"): Bayesian multilevel modelling with compositional data, both as predictors and outcomes, and post hoc isotemporal substitution analysis.

High-dimensional compositional data: with applications to omics data

In recent years, compositional data analysis is having a notable impact on the omics sciences and bioinformatics, where types of data such as microbiome compositions, gene expression or metabolomic profiles
have been recognised as inherently compositional. Applications in this area require methods that address unique challenges, including high dimensionality, zero inflation, overdispersion or the integration of
phylogenetic information. This section highlights packages providing tools specifically designed for omics data, but certainly most of them could be equally considered for the statistical processing of
high-dimensional compositional data in general.

• r pkg("FLORAL"): log-ratio lasso regression for continuous, binary, and survival outcomes with compositional features as described in Fei et al. (2023).

• r pkg("BRACoD.R"): Implements Bayesian regression to identify associations between
  microbiome compositional data and environmental variables.
  Corrects for compositional distortions by treating total abundance as an unknown variable.
  Integrates with Python via reticulate.

• r pkg("coda4microbiome"): Provides tools for microbiome data analysis while accounting for its compositional nature. Includes penalised regression methods for variable selection in cross-sectional
  and longitudinal studies with binary or continuous outcomes.

• r pkg("codacore"): identification of sparse log-ratios of a composition acting as predictor in regression problems. Scale-invariant log-ratios are derived optimised to account for
  association with the response variable.

• r pkg("lnmCluster"): logistic normal-multinomial clustering for microbiome compositional data, including extensions for factor analysis, bi-clustering, and sparse covariance estimation.

• r pkg("MicrobiomeStat"): robust methods for analysing microbiome compositional data, addressing zero-inflation, phylogenetic structure, and compositional effects.
  Applicable to other high-dimensional compositional datasets from sequencing experiments.

• r pkg("QFASA"): Implements 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 integral to geostatistics and geochemistry, areas where the methodology found its early successful applications. Data sets here often represent proportions of elements,
minerals, or isotopes, and are subject to spatial dependencies. These applications require methods that respect the relative nature of compositions while addressing spatial structures and relationships.
This section features packages which implement methods for specialised areas such as geostatistical modelling, spatial interpolation, variogram analysis, and compositional kriging; as well as techniques
for analysing geochemical compositions in the context of spatial data. In any case, some methods would be equally applicable to any data sets sharing analogous structures in any other application fields.

• r pkg("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 visualising data on ternary and radial plots, calculating sample sizes, and
  assessing hydraulic sorting effects are included. Additionally, a user-friendly interface for non-R users is provided.

• r pkg("ArArRedux"): data reduction and error propagation for
  Ar(^\text{40})/Ar(^\text{39}) geochronology, processing isotopic compositions from noble
  gas mass spectrometer data. Methods for regression to $t=0$, blank and decay corrections,
  detector intercalibration, interference corrections, and age calculation.
  Argon isotope ratios are treated as compositional data for accurate statistical handling.

• r pkg("gmGeostats"): geostatistical tools for multivariate data with restrictions,
  including compositions and positive amounts. Descriptive analysis and
  modelling using two-point Gaussian and multipoint perspectives. Compositional
  variograms and compositional kriging.

• r pkg("compositions"): includes a compositional variogram and kriging methods.

Other packages

• r pkg("aIc"): statistical tests for identifying compositional pathologies in datasets,
  including coherence of correlations, dominance of distance, 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.

• r pkg("CMMs"): compositional mediation models for continuous and binary outcomes, handling mediators represented as compositional data.

• r pkg("ccmm"): compositional mediation models to estimate direct and indirect effects of a treatment on an outcome, designed for the case in which mediators are high-dimensional microbiome data.

• r pkg("coda.base"): optimal implementation of friendly functions to compute log-ratio coordinate representations of various types,
  including principal component and principal balance coordinates and coordinates from tailored orthonormal basis; as well as some basic compositional statistics.

• r pkg("countprop"): model-based metrics of proportionality using the logit-normal multinomial model. It can also provide empirical and plugin estimates of these metrics.

• r pkg("FlexDir"): tools for using the flexible Dirichlet distribution,
  including maximum likelihood estimation via EM algorithm, variance-covariance matrix estimation,
  random data generation, and visualisation. Supports applications to compositional data.

• r pkg("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.

Links

• CRAN Task View: Functional Data Analysis
• CRAN Task View: Bayesian
• CRAN Task View: Cluster
• CRAN Task View: MachineLearning
• CRAN Task View: Robust
• CRAN Task View: SpatioTemporal

References

[zeileis]

Matthias @matthias-da, thanks for following up on this, very much appreciated. I've had a quick look and think that this is in good-enough shape to endorse you to move ahead. If the others agree, then you could set up a GitHub project (or I can do that for you) and start polishing the proposal a bit more.

Some first quick feedback:

• The intro is useful but rather long. Maybe have a shorter intro first and then a "Background" section later?
• The inclusion/exclusion criteria could be sharpened a bit more.
• Including a table of contents at the beginning might be useful to know what the "multiple categories" are.
• Please use AE (rather than BE) spelling.
• Include the task view cross references with r view("...") in the text and not as hyperlinks (and not just mostly at the end).

[jpiaskowski]

This looks very useful! Agreed with comments from @zeileis. Additionally, shorter descriptions of each package will make this task view easier to maintain over time.

[tuxette]

Thank you for the proposal! In addition to previous comments, I am under the impression that line breaks are sometimes a bit weird and non homogeneous within the task view. Manual line breaks should probably be removed except for the end of paragraphs maybe.

[matthias-da]

Dear Achim, Julia and Nathalie

Thanks a lot for your valuable feedback.

We hopefully incorporated all suggested changes.

We put the text to a gitHub site:
https://github.com/matthias-da/coda-ctv-draft/blob/main/CompositionalData.md

Achim: Please give us feedback about the further actions. We are happy to further fine-tune the text if needed.

Kind regards
Matthias