Compositional Data Analysis: Theory and Applications
Abstract
It is difficult to imagine that the statistical analysis of compositional data has been a major issue of concern for more than 100 years. It is even more difficult to realize that so many statisticians and users of statistics are unaware of the particular problems affecting compositional data, as well as their solutions. The issue of spurious correlation'', as the situation was phrased by Karl Pearson back in 1897, affects all data that measures parts of some whole, such as percentages, proportions, ppm and ppb. Such measurements are present in all fields of science, ranging from geology, biology, environmental sciences, forensic sciences, medicine and hydrology. This book presents the history and development of compositional data analysis along with Aitchison's log-ratio approach. Compositional Data Analysis describes the state of the art both in theoretical fields as well as applications in the different fields of science.
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The distribution of time spent in physical behaviors is by nature intrinsically compositional.
“Indeed, the distribution of time spent in physical behaviors is by nature intrinsically compositional[11,12].”
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“…between ratios whose numerators and denominators contain common parts’’ [11], and since that time it has been shown that many other standard analysis techniques are invalid when applied to such compositional data, and that their interpretation is unreliable and often misleading [10], [12], [13].”
BackgroundMethodBayesian stable isotope mixing models
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“Aitchison’s distances were calculated by first imputing zeros from an abundance OTU table, then applying a centered log ratio transform using the robCompositions R package (Pawlowsky-Glahn and Buccianti, 2011).”
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The misuse of ratios in ecological stoichiometry
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“With compositional data like 16S rRNA genes, abundances are relative (that is, sum to 1); these proportions are thus not independent and do not capture the true correlations underlying absolute abundances (Pawlowsky-Glahn and Buccianti, 2011; Friedman and Alm, 2012).”
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“There are many possible isometric log-ratio transformations [41], however for the purpose of the ensuing analysis, the type of isometric log-ratio is inconsequential, i.”
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Self-citationModel-based replacement of rounded zeros in compositional data: Classical and robust approaches
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“In Pawlowsky-Glahn and Buccianti (2011), pp. 47-62.”
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“…2005; Buccianti et al., 2006; Egozcue and Pawlowsky-Glahn, 2011; Filzmoser and Hron, 2008; Filzmoser et al., 2009; Hron et al., 2010; Otero et al., 2005; Pawlowsky-Glahn and Buccianti, 2002, 2011; Pawlowsky-Glahn et al., 2015; Tolosana-Delgado and van den Boogaart, 2011; von Eynatten et al., 2003).”
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Ovarian Antral Follicle Subclasses and Anti-Müllerian Hormone During Normal Reproductive Aging
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PLS‐DA for compositional data with application to metabolomics
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“the relative scale of compositional parts is completely ignored [1,2].”
BackgroundInterpretation of multivariate outliers for compositional data
Filzmoser, P., Hron, K., & Reimann, C. (2011) · Computers & Geosciences · doi:10.1016/j.cageo.2011.06.014 · Cited by 122 · see citing works
Greenacre, M. J., Martínez-Álvaro, M., & Blasco, A. (2021) · Frontiers in Microbiology · doi:10.3389/fmicb.2021.727398 · Cited by 124 · see citing works
“A short, yet comprehensive, review of CoDA is given by (15), with recent books aimed at practitioners by (16) and (8).”
InfluentialEmenike, P. C., Tenebe, I. T., Neris, J. B., Omole, D. O., Afolayan, O. D., Okeke, C. A. U., & Emenike, I. K. (2020) · Environmental Pollution · doi:10.1016/j.envpol.2020.114795 · Cited by 121 · see citing works
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“[51] Pawlowsky-Glahn V, Buccianti A, editors.”
Grunsky, E. C., Mueller, U. A., & Corrigan, D. (2013) · Journal of Geochemical Exploration · doi:10.1016/j.gexplo.2013.07.013 · Cited by 118 · see citing works
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“asymptotically normal [86,96], which allows their application within standard 751 multivariate methods, and within GLMs as presented here.”
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“…into different litter fractions (leaf, twigs, reproductive and undefined debris) differed between the forest types, we used a linear model for compositional data (Pawlowsky-Glahn & Buccianti, 2011) in the R package “compositions” (van den Boogaart, 2008; van den Boogaart, Tolosana, & Bren, 2014).”
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Values below detection limit in compositional chemical data
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Scientist’s guide to developing explanatory statistical models using causal analysis principles
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“Such intuitive features of geochemical data as scale invariance (information conveyed by observations does not depend on the particular units in which the observations are expressed) and relative scale properties are shared by a general concept of compositional data (Aitchison, 1986; Pawlowsky-Glahn and Buccianti, 201…”
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“…patterns in geochemistry (Buccianti, 2011), plant nutrition (Parent, 2011; Parent et al., 2012c), environmental sciences (Filzmoser et al., 2009a), soil physics (Parent et al., 2012b), chemistry and biochemistry (Parent et al., 2012a), and other disciplines (Pawlowsky-Glahn and Buccianti, 2011).”
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What can go wrong at the data normalization step for identification of biomarkers?
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Simplicial principal component analysis for density functions in Bayes spaces
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“This is commonly used for compositional data, i.e., multivariate observations carrying only relative information (e.g., Aitchison, 1986; Pawlowsky-Glahn and Buccianti, 2011, and references therein), which are usually collected in the form of constrained data summing up to a constant, usually set to…”
BackgroundMethodChawchai, S., Kylander, M. E., Chabangborn, A., et al. (2015) · Boreas · doi:10.1111/bor.12145 · Cited by 100 · see citing works
“Principal component analysis (PCA) including the whole data set was not performed because the XRF elemental data are given as peak areas, whereas TOC, LOI and BSi are given as percentages and the sand, silt and clay grain-size fractions are compositional data sets (Pawlowsky-Glahn & Buccianti 2011).”
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Dynamic Pie: A Strategy for Modeling Trade‐Offs in Compositional Variables over Time
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Martin, C., Ménot, G., Thouveny, N., Davtian, N., Andrieu‐Ponel, V., Reille, M., & Bard, É. (2019) · Organic Geochemistry · doi:10.1016/j.orggeochem.2019.06.005 · Cited by 86 · see citing works
“Log-ratio techniques transfer the information from the simplex to a Euclidian space where standard non-constrained multivariate statistics can be used while conserving the relationship between the components (Aitchison, 1986; Filzmoser and Hron, 2011; Pawlowsky-Glahn and Buccianti, 2011; Reimann et al., 2012; van den…”
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The Mathematics of Compositional Analysis
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Coherent forecasts of mortality with compositional data analysis
Bergeron-Boucher, M.-P., Canudas‐Romo, V., Oeppen, J. E., et al. (2017) · Demographic Research · doi:10.4054/demres.2017.37.17 · Cited by 85 · see citing works
“CoDa is a full framework to analyze multivariate data in which the components represent parts of a whole (Aitchison 1986; http://www.demographic-research.org 531 Bergeron-Boucher et al.: Coherent forecasts of mortality with compositional data analysis Pawlowsky-Glahn and Buccianti 2011).”
BackgroundMethodInfluentialSadeghi, M., Billay, A., & Carranza, E. J. M. (2014) · Journal of Geochemical Exploration · doi:10.1016/j.gexplo.2014.11.018 · Cited by 83 · see citing works
The single component geochemical map: Fact or fiction?
McKinley, J. M., Hron, K., Grunsky, E. C., et al. (2015) · Journal of Geochemical Exploration · doi:10.1016/j.gexplo.2015.12.005 · Cited by 81 · see citing works
“The challenge in 411 finding good maps is twofold: there are many more log-contrasts than there are elements in 412 the dataset, and the most appropriate log-contrasts to use will always depend on the aim of 413 the analysis undertaken (Pawlowsky-Glahn and Buccianti, 2011).”
BackgroundInfluentialGonçalves, Í. G., Kumaira, S., & Guadagnin, F. (2017) · Computers & Geosciences · doi:10.1016/j.cageo.2017.03.015 · Cited by 81 · see citing works
“, 2008) consists in interpolating a log-transformed version of the variables of interest, according to compositional data principles (Pawlowsky-Glahn and Buccianti, 2011; Buccianti et al., 2006).”
BackgroundMethodInfluentialForecasting intensifying disturbance effects on coral reefs
Vercelloni, J., Liquet, B., Kennedy, E. V., et al. (2020) · Global Change Biology · doi:10.1111/gcb.15059 · Cited by 80 · see citing works
Chacón, J. E., & Duong, T. (2013) · Electronic Journal of Statistics · doi:10.1214/13-ejs781 · Cited by 87 · see citing works
“…with the effect of rounding zeroes when the chemical measurement was below the instrument sensitivity level and then applying the additive log-ratio transform to place the data in a 7-dimensional Euclidean space (see Pawlowsky-Glahn and Buccianti, 2011, for a recent monograph on compositional data).”
MethodMultiple linear regression modeling for compositional data
Wang, H., Shangguan, L., Wu, J., et al. (2013) · Neurocomputing · doi:10.1016/j.neucom.2013.05.025 · Cited by 78 · see citing works
“…http://d n Corr E-m journal homepage: www.elsevier.com/locate/neucom Multiple linear regression modeling for compositional data Huiwen Wang, Liying Shangguan, Junjie Wu n, Rong Guan School of Economics and Management, Beihang University, Beijing 100191, China a r t i c l e i n f o Article…”
BackgroundMethodAdvances in Principal Balances for Compositional Data
Fernández, J. A. M., Pawlowsky‐Glahn, V., Egozcue, J. J., et al. (2017) · Mathematical Geosciences · doi:10.1007/s11004-017-9712-z · Cited by 78 · see citing works
Self-citationTarabichi, Y., Li, K., Hu, S., Nguyen, C., Wang, X., Elashoff, D., Saira, K., Frank, B., Bihan, M., Ghedin, E., et al. (2015) · Microbiome · doi:10.1186/s40168-015-0133-2 · Cited by 77 · see citing works
“performed by dividing each of the 15 most abundant genera by the sum of the remaining relative abundances of the non-top 15 genera, followed by the natural logarithm transform [34].”
MethodResultKirkwood, C., Everett, P. A., Ferreira, A., et al. (2016) · Journal of Geochemical Exploration · doi:10.1016/j.gexplo.2016.01.010 · Cited by 77 · see citing works
“has been in development in the years since Aitchison's work (e.g. Pawlowsky-Glahn and Egozcue, 2001; Egozcue et al., 2003; Buccianti et al., 2006; Pawlowsky-Glahn and Buccianti, 2011; Van den Boogaart and Tolosana-Delgado, 2013) and a range of mathematical tools now exist for extracting meaningful results from composi…”
BackgroundA survey on pre-processing techniques: Relevant issues in the context of environmental data mining
Gibert, K., Sànchez–Marrè, M., & Izquierdo, J. (2016) · AI Communications · doi:10.3233/aic-160710 · Cited by 77 · see citing works
“Finally, compositional data are sets of s strictly positive real variables with constant sum Z > 0 [181].”
Aitchison’s Compositional Data Analysis 40 Years on: A Reappraisal
Greenacre, M. J., Grunsky, E., Bacon‐Shone, J., Erb, I., & Quinn, T. P. (2023) · Statistical Science · doi:10.1214/22-sts880 · Cited by 81 · see citing works
“Several books have been published that present developments in the theory and practice of CoDA based on logratios [66, 67, 40, 24].”
BackgroundZuzolo, D., Cicchella, D., Lima, A., et al. (2020) · Journal of Geochemical Exploration · doi:10.1016/j.gexplo.2020.106524 · Cited by 74 · see citing works
Some practical aspects of predicting texture data in digital soil mapping
Amirian‐Chakan, A., Minasny, B., Taghizadeh‐Mehrjardi, R., Akbarifazli, R., Darvishpasand, Z., & Khordehbin, S. (2019) · Soil and Tillage Research · doi:10.1016/j.still.2019.06.006 · Cited by 75 · see citing works
Wang, W., Zhao, J., & Cheng, Q. (2013) · Journal of Geochemical Exploration · doi:10.1016/j.gexplo.2013.11.008 · Cited by 73 · see citing works
Scharnweber, T., Hevia, A., Buras, A., van der Maaten, E., & Wilmking, M. (2016) · The Science of The Total Environment · doi:10.1016/j.scitotenv.2016.05.182 · Cited by 72 · see citing works
Menafoglio, A., Guadagnini, A., & Secchi, P. (2014) · Stochastic Environmental Research and Risk Assessment · doi:10.1007/s00477-014-0849-8 · Cited by 72 · see citing works
“We use two viewpoints to interpret these types of data: (a) a Functional Data Analysis [FDA, Ramsay and Silverman (2005)] and (b) a Compositional Data Analysis [CoDa, Aitchison (1982); Aitchison (1986); Pawlowsky-Glahn and Buccianti (2011)] approach.”
MethodSpatial analysis of compositional data: A historical review
Pawlowsky‐Glahn, V., & Egozcue, J. J. (2015) · Journal of Geochemical Exploration · doi:10.1016/j.gexplo.2015.12.010 · Cited by 72 · see citing works
Self-citationGodichon‐Baggioni, A., Maugis-Rabusseau, C., & Rau, A. (2018) · Journal of Applied Statistics · doi:10.1080/02664763.2018.1454894 · Cited by 71 · see citing works
“…the relative proportions of a whole and can be represented in the simplex of d parts: Such data are a common phenomenon in several research domains, including evolutionary ecology [1,6], geochemistry [10,31], economics [15,26], and genomic surveys [20]; see [32] for more examples of applications.”
BackgroundGeometallurgical Modeling at Olympic Dam Mine, South Australia
Boisvert, J. B., Rossi, M. E., Ehrig, K. J., et al. (2013) · Mathematical Geosciences · doi:10.1007/s11004-013-9462-5 · Cited by 71 · see citing works
“A good review of best practice for compositional data modeling techniques is provided by Pawlowsky-Glahn and Buccianti (2011).”
MethodFlem, B., Reimann, C., Fabian, K., et al. (2017) · Applied Geochemistry · doi:10.1016/j.apgeochem.2017.09.006 · Cited by 70 · see citing works
Engle, M. A., & Rowan, E. L. (2012) · Mathematical Geosciences · doi:10.1007/s11004-012-9436-z · Cited by 68 · see citing works
Aurora: A Generalized Retrieval Framework for Exoplanetary Transmission Spectra
Welbanks, L., & Madhusudhan, N. (2021) · The Astrophysical Journal · doi:10.3847/1538-4357/abee94 · Cited by 60 · see citing works
Applications and Comparison of Dimensionality Reduction Methods for Microbiome Data
Armstrong, G., Rahman, G., Martino, C., McDonald, D. T., González, A., Mishne, G., & Knight, R. D. (2022) · Frontiers in Bioinformatics · doi:10.3389/fbinf.2022.821861 · Cited by 68 · see citing works
“…such as the additive log-ratio (ALR), centered log-ratio (CLR), and isometric log-ratio (ILR) can convert abundance data to the space of real numbers such that analysis and interpretation are less skewed by false positives (Aitchison and Greenacre, 2002; Pawlowsky-Glahn and Buccianti, 2011).”
BackgroundWu, C., Peng, N., Ma, X., et al. (2020) · Computers Environment and Urban Systems · doi:10.1016/j.compenvurbsys.2020.101547 · Cited by 65 · see citing works
Contrasting Modes and Tempos of Venom Expression Evolution in Two Snake Species
Margres, M. J., McGivern, J. J., Seavy, M. A., Wray, K. P., Facente, J., & Rokyta, D. R. (2014) · Genetics · doi:10.1534/genetics.114.172437 · Cited by 64 · see citing works
Buccianti, A., Lima, A., Albanese, S., Cannatelli, C., Esposito, R., & Vivo, B. D. (2015) · Journal of Geochemical Exploration · doi:10.1016/j.gexplo.2015.10.006 · Cited by 62 · see citing works
“Consequently, with the objective of investigating thewhole covariance structure of a geochemical dataset and tentatively identifying a baseline composition (1 × D, D number of variables) able to represent frequent and potentially spatially organised processes (following the FOREGS definition), a procedure is proposed…”
MethodSelf-citationOlds, T., Burton, N. W., Sprod, J. A., Maher, C. A., Ferrar, K., Brown, W. J., van Uffelen, J. G. Z., & Dumuid, D. (2018) · PLoS ONE · doi:10.1371/journal.pone.0199605 · Cited by 64 · see citing works
Weighted Pivot Coordinates for Compositional Data and Their Application to Geochemical Mapping
Hron, K., Filzmoser, P., de Caritat, P., et al. (2017) · Mathematical Geosciences · doi:10.1007/s11004-017-9684-z · Cited by 62 · see citing works
Organic carbon stock and composition in 3.5-m core mangrove soils (Trat, Thailand)
Kida, M., Watanabe, I., Kinjo, K., Kondo, M., Yoshitake, S., Tomotsune, M., Iimura, Y., Umnouysin, S., Suchewaboripont, V., Poungparn, S., et al. (2021) · The Science of The Total Environment · doi:10.1016/j.scitotenv.2021.149682 · Cited by 61 · see citing works
Thiombane, M., Albanese, S., Bonito, M. D., et al. (2018) · Environmental Geochemistry and Health · doi:10.1007/s10653-018-0147-3 · Cited by 62 · see citing works
Wekeza, S. V., & Sibanda, M. (2019) · International Journal of Environmental Research and Public Health · doi:10.3390/ijerph16060956 · Cited by 62 · see citing works
“Larger samples are more expressive than smaller samples which decrease the level of accuracy yet moderately accessible and cheap [40].”
BackgroundLinares‐Mustarós, S., Coenders, G., & Vives‐Mestres, M. (2017) · Advances in Accounting · doi:10.1016/j.adiac.2017.10.003 · Cited by 61 · see citing works
Thiombane, M., Petrik, A., Bonito, M. D., et al. (2018) · Environmental Science and Pollution Research · doi:10.1007/s11356-018-2688-5 · Cited by 61 · see citing works
Drone-Borne Hyperspectral and Magnetic Data Integration: Otanmäki Fe-Ti-V Deposit in Finland
Jackisch, R., Madriz, Y., Zimmermann, R., et al. (2019) · Remote Sensing · doi:10.3390/rs11182084 · Cited by 61 · see citing works
Riutta, T., Kho, L. K., Teh, Y. A., Ewers, R. M., Majalap, N., & Malhi, Y. S. (2021) · Global Change Biology · doi:10.1111/gcb.15522 · Cited by 60 · see citing works
“…respiration, and the relative contribution of litter and root inputs to total necromass pool, differed between the forest types, we used linear models for compositional data (Pawlowsky-Glahn & Buccianti, 2011), in the R package ‘compositions’ (van der Boogaart et al., 2014; van der Boogaart, 2008).”
MethodReyes, A., Thiombane, M., Pánico, A., et al. (2019) · Environmental Geochemistry and Health · doi:10.1007/s10653-019-00404-5 · Cited by 59 · see citing works
Phytochemicals in fruits of two Prunus domestica L. plum cultivars during ripening
Usenik, V., Štampar, F., & Kastelec, D. (2012) · Journal of the Science of Food and Agriculture · doi:10.1002/jsfa.5783 · Cited by 57 · see citing works
- Authors
- Glahn, V. P., & Buccianti, A.
- ORCID
- Antonella Buccianti
- Venue
- Wiley eBooks
- Publisher
- Wiley
- Published
- 2011-07-28
- OpenAlex
- W571770348
- Cited by
- 704
- References
- 0
- Citations by year
- 2026: 30 · 2025: 38 · 2024: 34 · 2023: 40 · 2022: 45 · 2021: 71 · 2020: 71 · 2019: 46 · 2018: 61 · 2017: 60 · 2016: 52 · 2015: 42 · 2014: 47 · 2013: 37 · 2012: 22
- FWCI
- 14.85
- Type
- book
- Language
- en
- Open access
- closed
- Locations
- Wiley eBooks (publishedVersion)
- Florence Research (University of Florence) (submittedVersion)
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Geochemistry and Geologic Mapping
- Physical Sciences › Mathematics › Statistics and Probability › Advanced Statistical Methods and Models
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Applications
- Keywords
- compositional data analysis, spurious correlations, parts and wholes
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