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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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“Indeed, the distribution of time spent in physical behaviors is by nature intrinsically compositional[11,12].”
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Shelton, J. L., Andrews, R. S., Akob, D. M., et al. (2020) · Scientific investigations report · doi:10.3133/sir20205037 · Cited by 1
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Tao, Z., & Wong, T. L. (2021) · arXiv (Cornell University) · doi:10.48550/arxiv.2105.07767 · Cited by 1
“In Figure 2 we also show the outputs of the popular Aitchison-PCA based on the ilr-transformation [7,16].”
MethodOrtego, M. I. (2022) · Wiley StatsRef: Statistics Reference Online · doi:10.1002/9781118445112.stat08348 · Cited by 1
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Morais, J. (2017) · doi:10.70675/9b4e06d6z39fez481bzabcbz37ea1f4e2127 · Cited by 1
“The compositional regression models have been recently investigated from a theoretical perspective, in the following books: Pawlowsky-Glahn and Buccianti [54] in 2011, Van Den Boogaart and Tolosana-Delgado [68] in 2013, and Pawlowsky-Glahn, Egozcue and Tolosana-Delgado [56] in 2015.”
BackgroundMethodInfluentialInterval Compositional Data: Problems and Possibilities
Pavlačka, O., & Hron, K. (2014) · Advances in intelligent systems and computing · doi:10.1007/978-3-319-10765-3_4
“The concept of compositional data frequently occurs in many applications, covering such situations, where not the absolute values of variables, but rather relative information they contain is of primary interest [1,8].”
BackgroundHigh-Throughput Data Analysis: Application to Micronuclei Frequency and T-cell Receptor Sequencing
Makowski, M. (2015) · VCU Scholars Compass (Virginia Commonwealth University) · doi:10.25772/4cy7-ph72
“The observations can be moved to a new sample space or represented using an orthonormal basis [Pawlowsky-Glahn and Buccianti, 2011].”
BackgroundMethodInfluentialSelected Topics for Further Research
Agterberg, F. P. (2014) · Quantitative geology and geostatistics · doi:10.1007/978-3-319-06874-9_12
Analysis of Total Abundances of Phytoplankton Compositions in a River
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Self-citationMeasuring Unemployment: A Composition Model
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Vidal, C. B. I. (2011) · LA Referencia (Red Federada de Repositorios Institucionales de Publicaciones Científicas) · doi:10.2436/20.2002.01.32
“0. b) Centre: c 2=6;1=6;3=6 0.”
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Park, N.-W. (2014) · Journal of the Korean earth science society · doi:10.5467/jkess.2014.35.1.69
“일반적으로 다변량 통계 기법은 특정 공간에 제한되지 않는 자료에 적용이 가능하기 때문에, 제한된 공간 안에서 값을 가지는 구성 자료 에 직접적으로 적용할 수 없는 것으로 알려져 있다 (Pawlowsky-Glahn and Buccianti, 2011).”
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Steeves, H. N. (2013) · Library and Archives Canada (Government of Canada)
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“…ect of soil management on its radioisotopic composition Studies of relationships between concentrations require utilization of appropriate methods to avoid false or delusive statistical inferences (Aitchison 2003, Aitchison & Egozcue 2005, Aitchison 2010, Pawlowsky-Glahn & Buccianti 2011).”
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Willich, F. (2015) · INFM-OAR (INFN Catania) · doi:10.5281/zenodo.31700
Chemical Equilibria in Compositional Data
van den Boogaart, K. G., Tolosana‐Delgado, R., & Konsulke, S. (2013) · Lecture notes in earth system sciences · doi:10.1007/978-3-642-32408-6_26
“[2] or [3] for details), clr(z) = ln z − (1D, ln z) D 1D = ln y − (1D, ln y) D 1D = clr(y),”
EFEITO DA ADUBAÇÃO NITROGENADA E POTÁSSICA EM
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“…25 compounds listed in Table 1 were used to calculate standardised peak areas using a centred log ratio transformation on proportional peak areas (Pawlowsky-Glahn and Buccianti 2011), as follows: where the divisor is the geometric mean of the proportional area of all k traits and the numerator…”
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Yamagata, Y., Seya, H., & Murakami, D. (2016) · Advanced sciences and technologies for security applications · doi:10.1007/978-3-319-39812-9_2 · Cited by 1
“To examine it, we first modeled the composition of land uses using land attributes by employing a compositional data model (see, Pawlowsky-Glahn and Buccianti 2011).”
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Lonardo, A. J., Parekh, B. S., & Srivastava, R. (2017) · Biotechnology and Bioengineering · doi:10.1002/bit.26318
“A history (Pawlowsky-Glahn and Egozcue, 2016) and extensive treatment of CoDa are found in Aitchison et al. (2002), Egozcue et al. (2003), and Pawlowsky-Glahn and Buccianti (2011).”
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Jarauta‐Bragulat, E., Sala, C., & Egozcue, J. J. (2013) · Lecture notes in earth system sciences · doi:10.1007/978-3-642-32408-6_23
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“One way to do this is by means of Compositional Data Analysis (CDA) (Aitchinson, 1986; Egozcue and Pawlowsky-Glahn, 2011), which is the study of compositions, i.”
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“Compositional Data Analysis (CODA) is a wellestablished set of statistical methods for the analyses of compositional data, defined in general as a data vector with positive elements summing to a constant value and thereby containing only relative information (Pawlowsky-Glahn and Buccianti, 2011).”
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“In addition, shape analysis (Dryden & Mardia, 2016) and compositional data analysis (Pawlowsky-Glahn & Buccianti, 2011) also deal with complex data defined on Riemannian manifolds.”
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Briscoe, L., Balliu, B., Sankararaman, S., Halperin, E., & Garud, N. R. (2021) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/2021.03.19.436199
Didkovskyi, O., Menafoglio, A., Secchi, P., et al. (2019) · Virtual Community of Pathological Anatomy (University of Castilla La Mancha)
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Caffo, B. S., Wang, Z., Faria, A. V., et al. (2021) · Wiley StatsRef: Statistics Reference Online · doi:10.1002/9781118445112.stat08226
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Barceló‐Vidal, C., & Fernández, J. A. M. (2021) · Springer eBooks · doi:10.1007/978-3-030-71175-7_7
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Huang, T., Saporta, G., & Wang, H. (2021) · Springer eBooks · doi:10.1007/978-3-030-73249-3_24
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Background
Metadata
- 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 › Earth and Planetary Sciences › Geochemistry and Petrology › 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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