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Next issue articles are papers that have been copy-edited and typeset but not yet paginated for inclusion in an issue of the journal. The final version of articles can be downloaded from the "Current issue" and "Downloadable articles" section.

Next issue: volume 48 (1), January-June 2024

  • DOI:10.57645/20.8080.02.13

  • DOI:10.57645/20.8080.02.14

  • DOI:10.57645/20.8080.02.15

  • DOI:10.57645/20.8080.02.16

Current issue: volume 47 (2), July-December 2023. Special issue devoted to 9th International Workshop on Compositional Data Analysis (CODAWORK, 2022). Guest editors: Germà Coenders and Javier Palarea-Albaladejo

  • 40 years after Aitchison’s article “The statistical analysis of compositional data”. Where we are and where we are heading

    Germà Coenders, Juan José Egozcue, Kamila Fačevicová, Carolina Navarro-López, Javier Palarea-Albaladejo, Vera Pawlowsky-Glahn and Raimon Tolosana-Delgado

    Abstract: The year 2022 marked 40 years since Aitchison published the article “The statistical analysis of compositional data”. It is considered to be the foundation of contemporary compositional data analysis. It is time to review what has been accomplished in the feld and what needs to be addressed. Astonishingly enough, many aspects seen as challenging in 1982 continue to lead to fruitful scholarly work. We commence with a bibliometric study and continue with some hot topics such as multi-way compositions, compositional regression models, dealing with zero values, non-logratio transformations, new application felds, and a number of current loose ends. Finally, a tentative future research agenda is outlined.

    Keywords: Compositional data (CoDa), logratios, Aitchison geometry, multi-way compositions, zero replacement, compositional regression

    Pages: 207–228

    DOI:10.57645/20.8080.02.6

  • Subcompositional coherence and and a novel proportionality index of parts

    Juan Jose Egozcue and Vera Pawlowsky-Glahn

    Abstract: Research in compositional data analysis was motivated by spurious (Pearson) correlation. Spurious results are due to semantic incoherence, but the question of ways to relate parts in a statistically consistent way remains open. To solve this problem, we first define a coherent system of functions with respect to a subcomposition and analyze the space of parts. This leads to understanding why measures like covariance and correlation depend on the subcomposition considered, while measures like the distance between parts are independent of the same. It allows the definition of a novel index of proportionality between parts.

    Keywords: Compositional data analysis, Aitchison geometry, simplex, compositional parts, proportionality, dominance, correlation

    Pages: 229–244

    DOI:10.57645/20.8080.02.7

  • Compositional covariance shrinkage and regularised partial correlations

    Suzanne Jin, Cédric Notredame and Ionas Erb

    Abstract: We propose an estimation procedure for covariation in wide compositional data sets. For compositions, widely-used logratio variables are interdependent due to a common reference. Logratio uncorrelated compositions are linearly independent before the unitsum constraint is imposed. We show how they are used to construct bespoke shrinkage targets for logratio covariance matrices and test a simple procedure for partial correlation estimates on both a simulated and a single-cell gene expression data set. For the underlying counts, different zero imputations are evaluated. The partial correlation induced by the closure is derived analytically. Data and code are available from GitHub.

    Keywords: Compositional covariance structure, logratio analysis, partial correlation, James-Stein shrinkage

    DOI:10.57645/20.8080.02.8

  • Simple enough, but not simpler: reconsidering additive logratio coordinates in compositional analysis

    Viktorie Nesrstová, Paulína Jašková, Ivana Pavlů, Karel Hron, Javier Palarea-Albaladejo, Aleš Gába, Jana Pelclová and Kamila Fačevicová

    Abstract: Compositional data, multivariate observations carrying relative information, are popularly expressed in additive logratio coordinates which are easily interpretable as they use one of the components as ratioing part to produce pairwise logratios. These coordinates are however oblique and they lead to issues when applying multivariate methods on them, including widely-used techniques such as principal component analysis and linear regression. In this paper we propose a way to redefine alr coordinates with respect to an orthonormal system and we also extend the idea to the case of compositional tables. The new approach is demonstrated in an application to movement behavior data.

    Keywords: Compositional data, compositional tables, regression, principal component analysis

    Pages: 269–294

    DOI:10.57645/20.8080.02.9

  • Classification of probability density functions in the framework of Bayes spaces: methods and applications

    Ivana Pavlů, Alessandra Menafoglio, Enea Bongiorno and Karel Hron

    Abstract: The process of supervised classification when the data set consists of probability density functions is studied. Due to the relative information contained in densities, it is necessary to convert the functional data analysis methods into an appropriate framework, here represented by the Bayes spaces. This work develops Bayes space counterparts to a set of commonly used functional methods with a focus on classification. Hereby, a clear guideline is provided on how some classification approaches can be adapted for the case of densities. Comparison of the methods is based on simulation studies and real-world applications, reflecting their respective strengths and weaknesses.

    Keywords: Probability density functions, Bayes spaces, classification, functional data analysis

    Pages: 295–322

    DOI:10.57645/20.8080.02.10

  • Fundamentals of convex optimization for compositional data

    Jordi Saperas Riera, Josep Antoni Martín Fernández and Glòria Mateu Figueras

    Abstract: Many of the most popular statistical techniques incorporate optimisation problems in their inner workings. A convex optimisation problem is defined as the problem of minimising a convex function over a convex set. When traditional methods are applied to compositional data, misleading and incoherent results could be obtained. In this paper, we fill a gap in the specialised literature by introducing and rigorously defining novel concepts of convex optimisation for compositional data according to the Aitchison geometry. Convex sets and convex functions on the simplex are defined and illustrated.

    Keywords: Compositional data, logratio, simplex, proportion, function, convexity, optimisation

    Pages: 323–344

    DOI:10.57645/20.8080.02.11

  • Interpretation of coal compositional data on whole-coal versus ash bases through the weighted symmetric pivot coordinates method

    Na Xu, Ru Wang, Mark A. Engle, Wei Zhu, Qiang Li and Zhiwei Wang

    Abstract: In addition to approaches based on a number of physical and chemical analyses, statistical methods have been commonly used for determining the modes of occurrence of elements in coal. The Pearson correlation coefficient of element concentrations vs. ash yields is the simplest method that has been widely used. Concentrations of elements in coal are usually reported on two bases: whole-coal and ash bases. Coal compositional data on whole-coal basis can be converted back to ash basis. However, in many cases, the correlation between corresponding pairs of elements in coal is inconsistent when reported on whole-coal versus ash bases. Therefore, traditional statistical methods, such as correlation analysis, based on whole-coal and ash bases can sometimes lead to misleading or confusing results. Previous investigations have suggested using logratio variance or related parameters (i.e., stability) to examine these data, as they provide consistent results regardless of the sample basis. However, logratio variance based approaches are unable to distinguish the inverse relationships between parts. To provide more clarity on the relationships between parts, weighted symmetric pivot coordinates are used to analyze the correlation between elements in coal on whole-coal basis and ash basis. To illustrate this approach, 106 late Paleozoic coal samples from the Datanhao and Adaohai coal mines, Daqingshan Coalfeld, northern China, are used for performance evaluation. Experimental results show that the weight symmetric pivots method is more effective than the stability method in predicting the modes of occurrence of elements in coal for these samples, providing deeper insight than logratio variance based approaches.

    Keywords: whole-coal basis, ash basis, correlation, WSPC method

    Pages: 345–362

    DOI:10.57645/20.8080.02.12

See also