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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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Advances in Compositional Data Analysis
Hron, K. (2018) · Wiley StatsRef: Statistics Reference Online · doi:10.1002/9781118445112.stat08130 · Cited by 4
Hinton, A. L., & Mucha, P. J. (2021) · Research Square · doi:10.21203/rs.3.rs-703177/v1 · Cited by 4
Alqurashi, Y. (2026) · Sustainability · doi:10.3390/su18021087 · Cited by 3
Determining Provenance from Compositional Data
López‐García, P. A., & Argote, D. L. (2026) · Cambridge University Press eBooks · doi:10.1017/9781009634205 · Cited by 3
Гололобова, А. Г., & Legostaeva, Y. (2024) · Plants · doi:10.3390/plants13172440 · Cited by 4
“…of the dataset was assessed using the Kolmogorov–Smirnov ( p < 0.2) and Shapiro–Wilk ( p < 0.05) methods; if the distribution value was not normal, the data were transformed according to the principles of compositional data analysis (CoDa) [38–40] using centered logarithmic ratio (clr) conversion.”
MethodInfluentialChappell, M. A., Rojas, H., Andros, C. S., et al. (2025) · PLoS ONE · doi:10.1371/journal.pone.0315147 · Cited by 3
“Most visualizations were created using ggplot [50] while ternary diagrams were created using the ggtern package [51] in R. Compositional data analysis (CoDa) was used for the bulk and pXRF datasets to correct for geometric distortions in proportional data [52–55].”
Multivariate Statistical Methods in Researching Biocultural Diversity
Sindik, J., & Šarac, J. (2016) · Environment and Ecology Research · doi:10.13189/eer.2016.040104 · Cited by 3
“This issue (spurious correlation) is especially important for the field of compositional data analysis, which deals with the analysis of variables that carry only relative information, such as proportions, percentages and parts-per-million [21].”
BackgroundAmjad, M. (2019) · Applied Ecology and Environmental Research · doi:10.15666/aeer/1706_1390913929 · Cited by 3
Three-Dimensional Modeling of Mineral/Elemental Compositions for Shale Reservoirs
Ma, Y. Z. (2020) · SPE Journal · doi:10.2118/201118-pa · Cited by 3
Covariates impacts in spatial autoregressive models for compositional data
Laurent, T., Thomas‐Agnan, C., & Ruiz‐Gazen, A. (2023) · Journal of Spatial Econometrics · doi:10.1007/s43071-023-00035-0 · Cited by 3
Outlier Detection for Pandemic-Related Data Using Compositional Functional Data Analysis
Rieser, C., & Filzmoser, P. (2021) · Springer Actuarial · doi:10.1007/978-3-030-78334-1_12 · Cited by 3
Orbital Forcing and Evolution of the Southern African Monsoon From Late Miocene to Early Pliocene
de Azevedo, A. Q., Jiménez-Espejo, F. J., Bulian, F., et al. (2023) · Paleoceanography and Paleoclimatology · doi:10.1029/2022pa004588 · Cited by 3
“We exhibited the XRF data in the natural log (ln) of relevant elemental ratios, as it provides a more accurate and precise value of sediment composition (Pawlowsky-Glahn & Buccianti, 2011; Weltje & Tjallingii, 2008).”
MethodOptimal designs for a linear-model compositional response
Rodríguez‐Díaz, J. M., López, M. J. R., Santos-Martín, M. T., et al. (2019) · Stochastic Environmental Research and Risk Assessment · doi:10.1007/s00477-019-01755-2 · Cited by 3
Zaaboubi, S., Khiari, L., Abdesselam, S., et al. (2020) · Agriculture · doi:10.3390/agriculture10070296 · Cited by 3
Analyis of Compositional Data using Robust Methods. The R-package robCompositons
Templ, M., Filzmoser, P., & Hron, K. (2011) · Universitat de Girona Digital Repository (Universitat de Girona) · Cited by 3
Covariance functions for bivariate Gaussian random fields
Moreva, O., & Schlather, M. (2016) · Cited by 3
Survey Data on Perceptions of Contraceptive Methods as Compositional Tables
Pawlowsky‐Glahn, V., Egozcue, J. J., & Planes, M. (2018) · Revista Latinoamericana de Psicología · doi:10.14349/rlp.2018.v50.n3.5 · Cited by 3
Self-citationRimlinger, M., Frosio, T., Menaa, N., et al. (2020) · Applied Radiation and Isotopes · doi:10.1016/j.apradiso.2020.109419 · Cited by 3
Speranza, A., Caggiano, R., & Summa, V. (2022) · Pollutants · doi:10.3390/pollutants2010001 · Cited by 3
Robust multivariate analysis of compositional data of treated wastewaters
Praus, P. (2019) · Environmental Earth Sciences · doi:10.1007/s12665-019-8248-6 · Cited by 3
Independent Component Analysis for Compositional Data
Muehlmann, C., Fačevicová, K., Gardlo, A., et al. (2021) · Springer eBooks · doi:10.1007/978-3-030-73249-3_27 · Cited by 3
“For further details and examples of compositional data see for example [1, 2, 3, 4, 5, 6, 7].”
BackgroundA Compositional Data Analysis of Market Share DynamicsPreprint
Arata, Y., & Onozaki, T. (2017) · RePEc: Research Papers in Economics · Cited by 3
Multimodal data analysis reveals asynchronous aging dynamics across female reproductive organs
Soldatkina, O., Pedro, L. V.-S., Pujol‐Gualdo, N., Hommad, A. E., Ramírez, J. M., Ripoll-Cladellas, A., Sopena-Rios, M., Tabares, D., Pérez-Elena, M. Á., Torrents, D., et al. (2026) · Nature Aging · doi:10.1038/s43587-026-01098-y · Cited by 2
“To select the optimal model, we compared the metrics (accuracy/MAE) and loss using the following metrics: The final model was chosen based on the highest ratio between diff(loss) and diff(metric).”
Statistical Learning Improves Classification of Limestone Provenance
Brajkovič, R., & Koselj, K. (2025) · Heritage · doi:10.3390/heritage8110464 · Cited by 2
Anvari, K., & Benndorf, J. (2025) · Minerals · doi:10.3390/min15121249 · Cited by 2
Biagetti, S., Ruiz-Giralt, A., Rix, K. S., Koutroumpas, A., Ibàñez-Insa, J., Lancelotti, C., Tuset, N. G., Kerfant, C. E., Grillo, K. M., Hildebrand, E., et al. (2026) · Journal of Archaeological Method and Theory · doi:10.1007/s10816-025-09759-9 · Cited by 3
Log-ratio approach in curve fitting for concentration-response experiments
Monti, G. S., Migliorati, S., Hron, K., et al. (2014) · Environmental and Ecological Statistics · doi:10.1007/s10651-014-0298-z · Cited by 2
“…above requirements simultaneously is to consider a regression model, based on logratio methodology for compositional data (Aitchison 1986; Egozcue et al. 2003; Pawlowsky-Glahn and Buccianti 2011), that is able to handle the limitations of compositions as observations carrying relative information.”
BackgroundDissecting Motivation: Translational Approaches and Clinical Implications
Avlar, B. (2016) · doi:10.7916/d8df6r7r · Cited by 2
Heteroskedastic linear regression model with compositional response and covariates
Chen, J., Zhang, X., & Li, S. (2017) · Journal of Applied Statistics · doi:10.1080/02664763.2017.1413075 · Cited by 2
“Preliminaries In the simplex SD, the perturbation operation, powering operation and Aitchison inner product [18,20] are defined.”
MethodSpatially Explicit Land-Use Modelling for Assessing Climate-Resilient Sustainable Urban Forms
Yamagata, Y., & Murakami, D. (2018) · Lecture notes in energy · doi:10.1007/978-3-319-75798-8_12 · Cited by 2
Menafoglio, A. (2021) · Springer eBooks · doi:10.1007/978-3-030-71175-7_11 · Cited by 2
Young, A., Buren, S. V., & Rashid, N. U. (2023) · Biostatistics · doi:10.1093/biostatistics/kxad008 · Cited by 2
Brudzińska-Kosior, A., Kosior, G., Sporek, M., et al. (2023) · PLoS ONE · doi:10.1371/journal.pone.0285306 · Cited by 2
“Variance in a component concentration may not be strictly related to variance in the abundance of the component, because this variability is also affected by variabilities in the abundances of other components [23, 24].”
BackgroundRSim: A reference-based normalization method via rank similarity
Yuan, B., & Wang, S. (2023) · PLoS Computational Biology · doi:10.1371/journal.pcbi.1011447 · Cited by 4
Ordinal compositional data and time series
Weiß, C. H. (2023) · Statistical Modelling · doi:10.1177/1471082x231190971 · Cited by 2
Kouřil, Š., de Sousa, J., Fačevicová, K., et al. (2023) · International Journal of Neonatal Screening · doi:10.3390/ijns9040060 · Cited by 2
“Similar to the approach used in [17], we treat the metabolomic data as relative-valued and the final algorithm thus combines ICA with the principles of compositional data analysis [19].”
MethodMolecular and associated approaches for studying soil biota and their functioning
Karaöz, U., Emerson, J., & Brodie, E. (2024) · Elsevier eBooks · doi:10.1016/b978-0-12-822941-5.00006-5 · Cited by 4
Pairwise share ratio interpretations of compositional regression models
Dargel, L., & Thomas‐Agnan, C. (2024) · Computational Statistics & Data Analysis · doi:10.1016/j.csda.2024.107945 · Cited by 2
Generalized Decomposition Priors on R2
Aguilar, J. E., & Bürkner, P. (2025) · Bayesian Analysis · doi:10.1214/25-ba1524 · Cited by 6
“Nonetheless when analyzing quantities contained in the simplex, it is customary to study ratios or loga-rithms of ratios of simplex components instead of raw proportions (Aitchison, 1986; Boogaart and Tolosana-Delgado, 2013; Pawlowsky-Glahn and Buccianti, 2011).”
InfluentialModeling and Forecasting Healthy Life Expectancy With Compositional Data Analysis
Bergeron-Boucher, M.-P., Strozza, C., Simonacci, V., & Oeppen, J. (2025) · Demography · doi:10.1215/00703370-11974712 · Cited by 5
Interpretable seasonal multisite hidden Markov model for stochastic rain generation in France
Emmanuel Gobet, A., Métivier, D., & Parey, S. (2025) · Advances in statistical climatology, meteorology and oceanography · doi:10.5194/ascmo-11-159-2025 · Cited by 2
“, set for some degree Deg For all k K the transition matrices transformation well-known in compositional data analysis (Pawlowsky-Glahn and Buccianti, 2011).”
Statistical Evaluation of the Solid-Solution State in Ternary Nanoalloys
Tran, X. Q., Kono, Y., Yamamoto, T., et al. (2020) · The Journal of Physical Chemistry C · doi:10.1021/acs.jpcc.0c06813 · Cited by 2
Rockwell, B. G., Girty, G. H., & Rockwell, T. (2014) · Pure and Applied Geophysics · doi:10.1007/s00024-014-0851-6 · Cited by 2
“In the context of compositional data (e.g., AITCHISON 1986; BUCCIANTI et al. 2006; PAWLOWSKY-GLAHN and BUCCIANTI 2011), our evaluation of these changes utilizes multivariate and small-sample statistical procedures including non-central principal component analysis, one-way analysis of variance, and the Student’s t dif…”
MethodSome Comments on Compositional Analysis in Management and Production Engineering
Vives‐Mestres, M., & Fernández, J. A. M. (2015) · Management and Production Engineering Review · doi:10.1515/mper-2015-0018 · Cited by 2
“The role played by both operations in most common statistical models and its usefulness in many applications from different fields are illustrated in [3].”
BackgroundMethodInfluentialComputational Statistics in the Earth Sciences: With Applications in MATLAB
Chave, A. D. (2017) · Cited by 2
Projections with Logarithmic Divergences
Tao, Z., & Wong, T. L. (2021) · Lecture notes in computer science · doi:10.1007/978-3-030-80209-7_52 · Cited by 2
“In Figure 2 we also show the outputs of the popular Aitchison-PCA based on the ilr-transformation [7,16].”
MethodCompositional Linear Regression on Interval-valued Data
Pekaslan, D., & Wagner, C. (2021) · IEEE Symposium Series on Computational Intelligence (SSCI) · doi:10.1109/ssci50451.2021.9660018 · Cited by 2
Hypothesis-driven mediation analysis for compositional data: an application to gut microbiome
Kartiosuo, N., Nevalainen, J., Raitakari, O. T., Pahkala, K., & Auranen, K. J. (2024) · Biostatistics & Epidemiology · doi:10.1080/24709360.2024.2360375 · Cited by 3
“In this framework, the compositionality of observations is accounted for by scaling taxon-specific read counts by their total into proportions of the whole [3, 4].”
BackgroundMethodInfluentialAmiri, L., Khazaei, M., & Ganjali, M. (2019) · Journal of Applied Statistics · doi:10.1080/02664763.2019.1579307 · Cited by 2
Reducing Traffic Congestion by LSTM-LOF Framework
Mansouri, D. E. K., Benkabou, S.-E., Kaddar, B., Larriba-Pey, J.-L., & Benabdeslem, K. (2019) · IEEE/ACS International Conference on Computer Systems and Applications (AICCSA) · doi:10.1109/aiccsa47632.2019.9035324 · Cited by 2
“It indicates how well data differ with each other [53].”
BackgroundMorais, J., & Trinh, T.-H. (2017) · RePEc: Research Papers in Economics · Cited by 2
Garrido-Fernández, A., Cortés‐Delgado, A., & López‐López, A. (2017) · Data in Brief · doi:10.1016/j.dib.2017.11.038 · Cited by 2
“2] and the ilr transformed values (or coordinates) (Table 3) [10,11].”
BackgroundBayesian Stable Isotope Mixing ModelsPreprint
Parnell, A. C., Phillips, D. L., Bearhop, S., et al. (2012) · arXiv (Cornell University) · doi:10.48550/arxiv.1209.6457 · Cited by 2
“It is209 also not sub-compositionally coherent (see Pawlowsky-Glahn and Buccianti, 2011, for further discussion of210 these terms).”
BackgroundBuren, S. V., & Rashid, N. (2020) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/2020.05.22.111450 · Cited by 1
“However, the alr transformation is not an isometric transformation, where distances between different elements of pi pre-transformation are not preserved post-transformation, potentially leading to inaccurate significance testing results (Pawlowsky-Glahn and Buccianti, 2011).”
BackgroundMethodInfluentialGrunsky, E., Greenacre, M. J., & KJARSGAARD, B. A. (2023) · SSRN Electronic Journal · doi:10.2139/ssrn.4530906 · Cited by 2
Ziembik, Z. (2013) · Journal of Radioanalytical and Nuclear Chemistry · doi:10.1007/s10967-013-2828-9 · Cited by 1
Graphical model for mixed data types
Wu, Q., Wang, H., Lu, S., et al. (2024) · Neurocomputing · doi:10.1016/j.neucom.2024.128706 · Cited by 1
Indoor moss biomonitoring proving construction-related pollution load from outdoors
Štrbová, K., Motyka, O., Mikesková, G., et al. (2024) · Building and Environment · doi:10.1016/j.buildenv.2024.112198 · Cited by 1
Buttafuocò, G. (2024) · Land · doi:10.3390/land13111835 · Cited by 1
Franchi, G., & Truquet, L. (2025) · Journal of Time Series Analysis · doi:10.1111/jtsa.12836 · Cited by 1
Measure of shape for object data
Virta, J. (2025) · Journal of nonparametric statistics · doi:10.1080/10485252.2025.2517775 · Cited by 1
Seyedrahimi-Niaraq, M., & Mahdiyanfar, H. (2025) · Scientific Reports · doi:10.1038/s41598-025-05955-5 · Cited by 1
Lemos, N. B. A. G., Clark, C. C. T., Pesce, C., Soares, Í. A. A., Lemos, F. D. A., & Martins, C. (2025) · Psychology of sport and exercise · doi:10.1016/j.psychsport.2025.103002 · Cited by 1
Customized Nutrient Standards to Diagnose Nutrient Imbalance in Fertigated ‘Nanica’ Banana Groves
Neto, A. J. D. L., de Deus, J. A. L., Rozane, D. E., et al. (2025) · Horticulturae · doi:10.3390/horticulturae11111327 · Cited by 1
On Spatial Point Processes With Composition‐Valued Marks
Eckardt, M., Myllymäki, M., & Greven, S. (2025) · International Statistical Review · doi:10.1111/insr.70019 · Cited by 1
Krishnamoorthi, T., LakshmiNarasimhan, C., Venkatmuthukumar, J., et al. (2026) · Soil and Sediment Contamination An International Journal · doi:10.1080/15320383.2026.2623423 · Cited by 1
Fačevicová, K., Vymazal, J., & Popelka, S. (2026) · Behavior Research Methods · doi:10.3758/s13428-026-03054-5 · Cited by 1
Palombi, F., Toti, S., & Filippini, R. (2017) · Journal of Probability and Statistics · doi:10.1155/2017/6579537 · Cited by 1
“rms can be always projected onto S vvia the closure operator Cxfx 1=jxj 1;:::;x v=jxj 1g. There are countless types of compositional data, whose analysis raises problems of interest for Statistics [4], e.g. geochemical data, balance sheet data, election data, etc. In order to measure distances on S v, Aitchison introd…”
BackgroundPark, N.-W., & Yoo, H. Y. (2013) · IEEE International Geoscience and Remote Sensing Symposium (IGARSS) · doi:10.1109/igarss.2013.6723678 · Cited by 1
“Several log-ratio transformations such as additive log-ratio (alr), centered log-ratio (clr), and isometric log-ratio (ilr) have been proposed [4], [5], [6].”
BackgroundMethodEngle, M. A., Fernández, J. A. M., Geboy, N. J., et al. (2011) · Universitat de Girona Digital Repository (Universitat de Girona) · Cited by 1
Moeini, H., & Aryafar, A. (2017) · Journal of mining and environment · doi:10.22044/jme.2016.656 · Cited by 1
“This problem has recently been considered in detail in the literature, and many solutions have been presented [34-36].”
BackgroundThe Analysis of Human Serum Albumin Proteoforms Using Compositional Framework
Sinari, S. A., Nedelkov, D., Reaven, P. D., & Billheimer, D. D. (2016) · Springer eBooks · doi:10.1007/978-3-319-45809-0_8 · Cited by 1
Using compositional geochemical ground survey data as predictors for geogenic radon potential
McKinley, J. (2015) · Research Portal (Queen's University Belfast) · Cited by 1
Fifty Years’ Experience with Hidden Errors in Applying Classical Mathematical Geology
Thiergärtner, H. (2018) · Springer eBooks · doi:10.1007/978-3-319-78999-6_40 · Cited by 1
“The modern approach to processing data that form a closed system was developed only later and therefore could not be applied (e.g., Pawlowsky-Glahn 2005; Pawlowsky-Glahn and Buccianti 2011).”
MethodEstimating transition coefficients for reconstructing coherent series of mortality by cause of Death
Camarda, C. G. (2019) · Statistical Modelling · doi:10.1177/1471082x19832398 · Cited by 1
Buccianti, A., & Gozzi, C. (2021) · Springer eBooks · doi:10.1007/978-3-030-71175-7_13 · Cited by 1
Self-citationLog-contrast and Orthonormal Log-ratio Coordinates for Compositional Data with a Total
Fernández, J. A. M., & Barceló‐Vidal, C. (2021) · Springer eBooks · doi:10.1007/978-3-030-73249-3_26 · Cited by 1
Data-Driven Intelligent Decision Support Systems
Sànchez–Marrè, M. (2022) · Springer eBooks · doi:10.1007/978-3-030-87790-3_6 · Cited by 2
Garrido-Fernández, A., Cortés‐Delgado, A., & López‐López, A. (2022) · Foods · doi:10.3390/foods11244024 · Cited by 1
“Central tendency and dispersion The standard means and standard deviation (developed for the Euclidean space) have no meaning in CoDa and are substituted by the following concepts [23].”
BackgroundMethodInfluentialCompositional Analysis of Microbiome Data
Xia, Y., & Sun, J. (2023) · Springer eBooks · doi:10.1007/978-3-031-21391-5_14 · Cited by 1
Small area estimation ‒ model-based approach in economic research
Krzciuk, M. (2023) · doi:10.22367/uekat.9788378758860 · Cited by 1
Qi, Y., Chen, H., Wu, S., Kuritani, T., Du, Z., Xia, Q., & Liu, R. (2024) · Chemical Geology · doi:10.1016/j.chemgeo.2024.122282 · Cited by 1
Fiori, A. M., & Coenders, G. (2025) · Risks · doi:10.3390/risks13020021 · Cited by 1
Гололобова, А. Г., & Legostaeva, Y. (2025) · Soil Systems · doi:10.3390/soilsystems9020048 · Cited by 1
Chollett, I., Gardner, C., Perruso, L., et al. (2025) · Geoscience Data Journal · doi:10.1002/gdj3.70014 · Cited by 1
“Compositional kriging (Pawlowsky-Glahn and Buccianti 2011) is a method that has been used to analyse soil and sediment fraction data over the last 20 years.”
Stanley, C. R. (2025) · Geochemistry Exploration Environment Analysis · doi:10.1144/geochem2024-064 · Cited by 1
The Use Of Pb-210 Isotope As An Indicator Of Pollutants’ Migration In The Environment
Dołhańczuk-Śródka, A. (2015) · Ecological Chemistry and Engineering S · doi:10.1515/eces-2015-0020 · Cited by 1
Representation of Species Composition
Pawlowsky‐Glahn, V., Monreal-Pawlowsky, T., & Egozcue, J. J. (2016) · Springer proceedings in mathematics & statistics · doi:10.1007/978-3-319-44811-4_11 · Cited by 1
Self-citationQuality and Yield of Triticum durum Under Temperate Continental Climate of the Czech Republic
Políšenská, I., Jirsa, O., Spitzer, T., et al. (2018) · Acta Universitatis Agriculturae et Silviculturae Mendelianae Brunensis · doi:10.11118/actaun201866020371 · Cited by 1
Data Assimilation for Resource Model Updating
Benndorf, J. (2020) · SpringerBriefs in applied sciences and technology · doi:10.1007/978-3-030-40900-5_3 · Cited by 1
ORGANIC COMPOUNDS IN ROAD DUST AND THEIR ASSOCIATION WITH TRAFFIC
Čabanová, K., Motyka, O., Plachá, D., & Mališ, J. (2020) · NANOCON 2019 Conference Proeedings · doi:10.37904/nanocon.2019.8571
Heng, P., Ariffin, K. S., Zabidi, H. B., et al. (2020) · AIP conference proceedings · doi:10.1063/5.0023794 · Cited by 1
UNDERSTANDING ADOPTION FACTORS OF SUBSCRIPTION BASED ENTERTAINMENT SERVICES AMONG CONSUMERS IN INDIA
Khatri, T. (2021) · INFORMATION TECHNOLOGY IN INDUSTRY · doi:10.17762/itii.v9i1.200 · Cited by 1
“It is evident that larger sample size is more reliable than smaller samples which may lead to decrease in the level of accuracy but is moderately accessible and cheap [2].”
BackgroundAdditive regression for predictors of various natures and possibly incomplete Hilbertian responses
Jeon, J. M., Park, B. U., & Keilegom, I. V. (2021) · Electronic Journal of Statistics · doi:10.1214/21-ejs1823 · Cited by 1
“Examples are the proportions of votes earned by candidates in an election, the proportions of races/religions in cities/countries and the proportions of chemical materials constituting bodies/air/sea-water/soil [32, 9].”
BackgroundGeographically Weighted Regression Analysis for Two-Factorial Compositional Data
Fačevicová, K., Kynčlová, P., & Macků, K. (2021) · Springer eBooks · doi:10.1007/978-3-030-71175-7_6 · Cited by 1
Mentesana, R., Hein, A., Fernández, M. M. I., Kilikoglou, V., & Garrigós, J. B. I. (2022) · Minerals · doi:10.3390/min12040423 · Cited by 2
Govindaraj, M., Kaliappan, S., & Swaminathan, G. (2023) · Ingénierie des systèmes d information · doi:10.18280/isi.280328 · Cited by 1
Covariance Structure of Principal Components for Three-Part Compositional Data
Hrůzová, K., Hron, K., Rypka, M., et al. (2013) · Czech digital mathematics library · Cited by 1
Multidimensional Scaling and Relatedness ResearchPreprint
Graffelman, J., Galván‐Femenía, I., de Cid, R., et al. (2018) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/297879 · Cited by 1
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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Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
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