The Statistical Analysis Of Compositional Data
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The Statistical Analysis Of Compositional Data
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Author : J. Aitchison
language : en
Publisher: Springer
Release Date : 1986-08-21
The Statistical Analysis Of Compositional Data written by J. Aitchison and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986-08-21 with Science categories.
As long ago as 1897 Karl Pearson, in a now classic paper on spurious correlation, first pointed out dangers that may befall the analyst who attempts to interpret correlations between ratios whose numerators and denominators contain common parts. He thus implied that the analysis of compositional data, with its concentration on relation ships between proportions of some whole, is likely to be fraught with difficulty. History has proved him correct: over the succeeding years and indeed right up to the present day, there has been no other form of data analysis where more confusion has reigned and where more improper and inadequate statistical methods have been applied. The special and intrinsic feature of compositional data is that the proportions of a composition are naturally subject to a unit-sum constraint. For other forms of constrained data, in particular for directional data where there is a unit-length constraint on each direction vector, scientist and statistician alike have readily appre ciated that new statistical methods, appropriate to the special nature of the data, are required; and there now exists an extensive literature on the successful statistical analysis of directional data. It is paradox ical that for compositional data, subject to an apparently simpler constraint, such an appreciation and development have been slower to emerge. In applications the unit-sum constraint has been widely ignored or wished away and inappropriate 'standard' statistical methods, devised for and successfully applied to unconstrained data, have been used with disastrous consequences.
Modeling And Analysis Of Compositional Data
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Author : Vera Pawlowsky-Glahn
language : en
Publisher: John Wiley & Sons
Release Date : 2015-03-30
Modeling And Analysis Of Compositional Data written by Vera Pawlowsky-Glahn and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-03-30 with Mathematics categories.
Modeling and Analysis of Compositional Data presents a practical and comprehensive introduction to the analysis of compositional data along with numerous examples to illustrate both theory and application of each method. Based upon short courses delivered by the authors, it provides a complete and current compendium of fundamental to advanced methodologies along with exercises at the end of each chapter to improve understanding, as well as data and a solutions manual which is available on an accompanying website. Complementing Pawlowsky-Glahn’s earlier collective text that provides an overview of the state-of-the-art in this field, Modeling and Analysis of Compositional Data fills a gap in the literature for a much-needed manual for teaching, self learning or consulting.
Applied Compositional Data Analysis
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Author : Peter Filzmoser
language : en
Publisher: Springer
Release Date : 2018-11-03
Applied Compositional Data Analysis written by Peter Filzmoser and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-11-03 with Mathematics categories.
This book presents the statistical analysis of compositional data using the log-ratio approach. It includes a wide range of classical and robust statistical methods adapted for compositional data analysis, such as supervised and unsupervised methods like PCA, correlation analysis, classification and regression. In addition, it considers special data structures like high-dimensional compositions and compositional tables. The methodology introduced is also frequently compared to methods which ignore the specific nature of compositional data. It focuses on practical aspects of compositional data analysis rather than on detailed theoretical derivations, thus issues like graphical visualization and preprocessing (treatment of missing values, zeros, outliers and similar artifacts) form an important part of the book. Since it is primarily intended for researchers and students from applied fields like geochemistry, chemometrics, biology and natural sciences, economics, and social sciences, all the proposed methods are accompanied by worked-out examples in R using the package robCompositions.
Compositional Data Analysis
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Author : Vera Pawlowsky-Glahn
language : en
Publisher: John Wiley & Sons
Release Date : 2011-09-19
Compositional Data Analysis written by Vera Pawlowsky-Glahn and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-09-19 with Mathematics categories.
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. Key Features: Reflects the state-of-the-art in compositional data analysis. Gives an overview of the historical development of compositional data analysis, as well as basic concepts and procedures. Looks at advances in algebra and calculus on the simplex. Presents applications in different fields of science, including, genomics, ecology, biology, geochemistry, planetology, chemistry and economics. Explores connections to correspondence analysis and the Dirichlet distribution. Presents a summary of three available software packages for compositional data analysis. Supported by an accompanying website featuring R code. Applied scientists working on compositional data analysis in any field of science, both in academia and professionals will benefit from this book, along with graduate students in any field of science working with compositional data.
Analyzing Compositional Data With R
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Author : K. Gerald van den Boogaart
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29
Analyzing Compositional Data With R written by K. Gerald van den Boogaart and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-29 with Mathematics categories.
This book presents the statistical analysis of compositional data sets, i.e., data in percentages, proportions, concentrations, etc. The subject is covered from its grounding principles to the practical use in descriptive exploratory analysis, robust linear models and advanced multivariate statistical methods, including zeros and missing values, and paying special attention to data visualization and model display issues. Many illustrated examples and code chunks guide the reader into their modeling and interpretation. And, though the book primarily serves as a reference guide for the R package “compositions,” it is also a general introductory text on Compositional Data Analysis. Awareness of their special characteristics spread in the Geosciences in the early sixties, but a strategy for properly dealing with them was not available until the works of Aitchison in the eighties. Since then, research has expanded our understanding of their theoretical principles and the potentials and limitations of their interpretation. This is the first comprehensive textbook addressing these issues, as well as their practical implications with regard to software. The book is intended for scientists interested in statistically analyzing their compositional data. The subject enjoys relatively broad awareness in the geosciences and environmental sciences, but the spectrum of recent applications also covers areas like medicine, official statistics, and economics. Readers should be familiar with basic univariate and multivariate statistics. Knowledge of R is recommended but not required, as the book is self-contained.
Coda
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Author : John Aitchison
language : en
Publisher:
Release Date : 1986
Coda written by John Aitchison and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986 with Correlation (Statistics) categories.
Microcomputer Package for the Statistical Analysis of Compositional Data
Geostatistical Analysis Of Compositional Data
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Author : Vera Pawlowsky-Glahn
language : en
Publisher: Oxford University Press
Release Date : 2004-06-03
Geostatistical Analysis Of Compositional Data written by Vera Pawlowsky-Glahn and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-06-03 with Science categories.
Geostatistical Analysis of Compositional Data provides a comprehensive coverage of the theory and practice of analysis of data that have both spatial and compositional dependence, characteristics of most earth science and environmental measurements.
Compositional Data Analysis In The Geosciences
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Author : Antonella Buccianti
language : en
Publisher: Geological Society of London
Release Date : 2006
Compositional Data Analysis In The Geosciences written by Antonella Buccianti and has been published by Geological Society of London this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Mathematics categories.
Since Karl Pearson wrote his paper on spurious correlation in 1897, a lot has been said about the statistical analysis of compositional data, mainly by geologists such as Felix Chayes. The solution appeared in the 1980s, when John Aitchison proposed to use Iogratios. Since then, the approach has seen a great expansion, mainly building on the idea of the `natural geometry' of the sample space. Statistics is expected to give sense to our perception of the natural scale of the data, and this is made possible for compositional data using Iogratios. This publication will be a milestone in this process.
Compositional Data Analysis In Practice
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Author : Michael Greenacre
language : en
Publisher: CRC Press
Release Date : 2018-07-17
Compositional Data Analysis In Practice written by Michael Greenacre and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-07-17 with Business & Economics categories.
Compositional Data Analysis in Practice is a user-oriented practical guide to the analysis of data with the property of a constant sum, for example percentages adding up to 100%. Compositional data can give misleading results if regular statistical methods are applied, and are best analysed by first transforming them to logarithms of ratios. This book explains how this transformation affects the analysis, results and interpretation of this very special type of data. All aspects of compositional data analysis are considered: visualization, modelling, dimension-reduction, clustering and variable selection, with many examples in the fields of food science, archaeology, sociology and biochemistry, and a final chapter containing a complete case study using fatty acid compositions in ecology. The applicability of these methods extends to other fields such as linguistics, geochemistry, marketing, economics and finance. R Software The following repository contains data files and R scripts from the book https://github.com/michaelgreenacre/CODAinPractice. The R package easyCODA, which accompanies this book, is available on CRAN -- note that you should have version 0.25 or higher. The latest version of the package will always be available on R-Forge and can be installed from R with this instruction: install.packages("easyCODA", repos="http://R-Forge.R-project.org").
Compositional Data Analysis
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Author : Josep Antoni Martín-Fernández
language : en
Publisher: Springer
Release Date : 2016-11-19
Compositional Data Analysis written by Josep Antoni Martín-Fernández and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-11-19 with Mathematics categories.
The authoritative contributions gathered in this volume reflect the state of the art in compositional data analysis (CoDa). The respective chapters cover all aspects of CoDa, ranging from mathematical theory, statistical methods and techniques to its broad range of applications in geochemistry, the life sciences and other disciplines. The selected and peer-reviewed papers were originally presented at the 6th International Workshop on Compositional Data Analysis, CoDaWork 2015, held in L’Escala (Girona), Spain. Compositional data is defined as vectors of positive components and constant sum, and, more generally, all those vectors representing parts of a whole which only carry relative information. Examples of compositional data can be found in many different fields such as geology, chemistry, economics, medicine, ecology and sociology. As most of the classical statistical techniques are incoherent on compositions, in the 1980s John Aitchison proposed the log-ratio approach to CoDa. This became the foundation of modern CoDa, which is now based on a specific geometric structure for the simplex, an appropriate representation of the sample space of compositional data. The International Workshops on Compositional Data Analysis offer a vital discussion forum for researchers and practitioners concerned with the statistical treatment and modelling of compositional data or other constrained data sets and the interpretation of models and their applications. The goal of the workshops is to summarize and share recent developments, and to identify important lines of future research.