{"product_id":"compositional-data-analysis-isbn-9780470711354","title":"Compositional Data Analysis","description":"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.  \u003cp\u003eThis book presents the history and development of compositional data analysis along with Aitchison's log-ratio approach. \u003ci\u003eCompositional Data Analysis\u003c\/i\u003e describes the state of the art both in theoretical fields as well as applications in the different fields of science.\u003c\/p\u003e \u003cp\u003e\u003cbr\u003e Key Features:\u003c\/p\u003e \u003cul\u003e \u003cli\u003eReflects the state-of-the-art in compositional data analysis.\u003c\/li\u003e \u003cli\u003eGives an overview of the historical development of compositional data analysis, as well as basic concepts and procedures.\u003c\/li\u003e \u003cli\u003eLooks at advances in algebra and calculus on the simplex.\u003c\/li\u003e \u003cli\u003ePresents applications in different fields of science, including, genomics, ecology, biology, geochemistry, planetology, chemistry and economics.\u003c\/li\u003e \u003cli\u003eExplores connections to correspondence analysis and the Dirichlet distribution.\u003c\/li\u003e \u003cli\u003ePresents a summary of three available software packages for compositional data analysis.\u003c\/li\u003e \u003cli\u003eSupported by an accompanying website featuring R code.\u003c\/li\u003e \u003c\/ul\u003e \u003cp\u003eApplied 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.\u003c\/p\u003e \u003cp\u003ePreface xvii\u003c\/p\u003e \u003cp\u003eList of Contributors xix\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart I Introduction 1\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1 A Short History of Compositional Data Analysis 3\u003cbr\u003e \u003c\/b\u003e\u003ci\u003eJohn Bacon-Shone\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e1.1 Introduction 3\u003c\/p\u003e \u003cp\u003e1.2 Spurious Correlation 3\u003c\/p\u003e \u003cp\u003e1.3 Log and Log-Ratio Transforms 4\u003c\/p\u003e \u003cp\u003e1.4 Subcompositional Dependence 5\u003c\/p\u003e \u003cp\u003e1.5 alr, clr, ilr: Which Transformation to Choose? 5\u003c\/p\u003e \u003cp\u003e1.6 Principles, Perturbations and Back to the Simplex 6\u003c\/p\u003e \u003cp\u003e1.7 Biplots and Singular Value Decompositions 7\u003c\/p\u003e \u003cp\u003e1.8 Mixtures 7\u003c\/p\u003e \u003cp\u003e1.9 Discrete Compositions 8\u003c\/p\u003e \u003cp\u003e1.10 Compositional Processes 8\u003c\/p\u003e \u003cp\u003e1.11 Structural, Counting and Rounded Zeros 8\u003c\/p\u003e \u003cp\u003e1.12 Conclusion 9\u003c\/p\u003e \u003cp\u003eAcknowledgement 9\u003c\/p\u003e \u003cp\u003eReferences 9\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 Basic Concepts and Procedures 12\u003cbr\u003e \u003c\/b\u003e\u003ci\u003eJuan José Egozcue and Vera Pawlowsky-Glahn\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e2.1 Introduction 12\u003c\/p\u003e \u003cp\u003e2.2 Election Data and Raw Analysis 13\u003c\/p\u003e \u003cp\u003e2.3 The Compositional Alternative 15\u003c\/p\u003e \u003cp\u003e2.4 Geometric Settings 17\u003c\/p\u003e \u003cp\u003e2.5 Centre and Variability 22\u003c\/p\u003e \u003cp\u003e2.6 Conclusion 27\u003c\/p\u003e \u003cp\u003eAcknowledgements 27\u003c\/p\u003e \u003cp\u003eReferences 27\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart II Theory – Statistical Modelling 29\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3 The Principle of Working on Coordinates 31\u003cbr\u003e \u003c\/b\u003e\u003ci\u003eGlòria Mateu-Figueras, Vera Pawlowsky-Glahn and Juan José Egozcue\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e3.1 Introduction 31\u003c\/p\u003e \u003cp\u003e3.2 The Role of Coordinates in Statistics 32\u003c\/p\u003e \u003cp\u003e3.3 The Simplex 33\u003c\/p\u003e \u003cp\u003e3.4 Move or Stay in the Simplex 38\u003c\/p\u003e \u003cp\u003e3.5 Conclusions 40\u003c\/p\u003e \u003cp\u003eAcknowledgements 41\u003c\/p\u003e \u003cp\u003eReferences 41\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4 Dealing with Zeros 43\u003cbr\u003e \u003c\/b\u003e\u003ci\u003eJosep Antoni Martín-Fernández, Javier Palarea-Albaladejo and Ricardo Antonio Olea\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e4.1 Introduction 43\u003c\/p\u003e \u003cp\u003e4.2 Rounded Zeros 44\u003c\/p\u003e \u003cp\u003e4.3 Count Zeros 50\u003c\/p\u003e \u003cp\u003e4.4 Essential Zeros 53\u003c\/p\u003e \u003cp\u003e4.5 Difficulties, Troubles and Challenges 55\u003c\/p\u003e \u003cp\u003eAcknowledgements 57\u003c\/p\u003e \u003cp\u003eReferences 57\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5 Robust Statistical Analysis 59\u003cbr\u003e \u003c\/b\u003e\u003ci\u003ePeter Filzmoser and Karel Hron\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e5.1 Introduction 59\u003c\/p\u003e \u003cp\u003e5.2 Elements of Robust Statistics from a Compositional Point of View 60\u003c\/p\u003e \u003cp\u003e5.3 Robust Methods for Compositional Data 63\u003c\/p\u003e \u003cp\u003e5.4 Case Studies 66\u003c\/p\u003e \u003cp\u003e5.5 Summary 70\u003c\/p\u003e \u003cp\u003eAcknowledgement 71\u003c\/p\u003e \u003cp\u003eReferences 71\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6 Geostatistics for Compositions 73\u003cbr\u003e \u003c\/b\u003e\u003ci\u003eRaimon Tolosana-Delgado, Karl Gerald van den Boogaart and Vera Pawlowsky-Glahn\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e6.1 Introduction 73\u003c\/p\u003e \u003cp\u003e6.2 A Brief Summary of Geostatistics 74\u003c\/p\u003e \u003cp\u003e6.3 Cokriging of Regionalised Compositions 76\u003c\/p\u003e \u003cp\u003e6.4 Structural Analysis of Regionalised Composition 76\u003c\/p\u003e \u003cp\u003e6.5 Dealing with Zeros: Replacement Strategies and Simplicial Indicator Cokriging 78\u003c\/p\u003e \u003cp\u003e6.6 Application 79\u003c\/p\u003e \u003cp\u003e6.7 Conclusions 84\u003c\/p\u003e \u003cp\u003eAcknowledgements 84\u003c\/p\u003e \u003cp\u003eReferences 84\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7 Compositional VARIMA Time Series 87\u003cbr\u003e \u003c\/b\u003e\u003ci\u003eCarles Barceló-Vidal, Lucía Aguilar and Josep Antoni Martín-Fernández\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e7.1 Introduction 87\u003c\/p\u003e \u003cp\u003e7.2 The Simplex S D as a Compositional Space 89\u003c\/p\u003e \u003cp\u003e7.3 Compositional Time Series Models 91\u003c\/p\u003e \u003cp\u003e7.4 CTS Modelling: An Example 94\u003c\/p\u003e \u003cp\u003e7.5 Discussion 99\u003c\/p\u003e \u003cp\u003eAcknowledgements 99\u003c\/p\u003e \u003cp\u003eReferences 100\u003c\/p\u003e \u003cp\u003eAppendix 102\u003c\/p\u003e \u003cp\u003e\u003cb\u003e8 Compositional Data and Correspondence Analysis 104\u003cbr\u003e \u003c\/b\u003e\u003ci\u003eMichael Greenacre\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e8.1 Introduction 104\u003c\/p\u003e \u003cp\u003e8.2 Comparative Technical Definitions 105\u003c\/p\u003e \u003cp\u003e8.3 Properties and Interpretation of LRA and CA 107\u003c\/p\u003e \u003cp\u003e8.4 Application to Fatty Acid Compositional Data 107\u003c\/p\u003e \u003cp\u003e8.5 Discussion and Conclusions 111\u003c\/p\u003e \u003cp\u003eAcknowledgements 112\u003c\/p\u003e \u003cp\u003eReferences 112\u003c\/p\u003e \u003cp\u003e\u003cb\u003e9 Use of Survey Weights for the Analysis of Compositional Data 114\u003cbr\u003e \u003c\/b\u003e\u003ci\u003eMonique Graf\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e9.1 Introduction 114\u003c\/p\u003e \u003cp\u003e9.2 Elements of Survey Design 115\u003c\/p\u003e \u003cp\u003e9.3 Application to Compositional Data 122\u003c\/p\u003e \u003cp\u003e9.4 Discussion 126\u003c\/p\u003e \u003cp\u003eReferences 126\u003c\/p\u003e \u003cp\u003e\u003cb\u003e10 Notes on the Scaled Dirichlet Distribution 128\u003cbr\u003e \u003c\/b\u003e\u003ci\u003eGianna Serafina Monti, Glòria Mateu-Figueras and Vera Pawlowsky-Glahn\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e10.1 Introduction 128\u003c\/p\u003e \u003cp\u003e10.2 Genesis of the Scaled Dirichlet Distribution 129\u003c\/p\u003e \u003cp\u003e10.3 Properties of the Scaled Dirichlet Distribution 131\u003c\/p\u003e \u003cp\u003e10.4 Conclusions 136\u003c\/p\u003e \u003cp\u003eAcknowledgements 137\u003c\/p\u003e \u003cp\u003eReferences 137\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart III Theory – Algebra and Calculus 139\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e11 Elements of Simplicial Linear Algebra and Geometry 141\u003cbr\u003e \u003c\/b\u003e\u003ci\u003eJuan José Egozcue, Carles Barceló-Vidal, Josep Antoni Martín-Fernández, Eusebi Jarauta-Bragulat, José LuisDíaz-Barrero and Glòria Mateu-Figueras\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e11.1 Introduction 141\u003c\/p\u003e \u003cp\u003e11.2 Elements of Simplicial Geometry 142\u003c\/p\u003e \u003cp\u003e11.3 Linear Functions 151\u003c\/p\u003e \u003cp\u003e11.4 Conclusions 156\u003c\/p\u003e \u003cp\u003eAcknowledgements 156\u003c\/p\u003e \u003cp\u003eReferences 156\u003c\/p\u003e \u003cp\u003e\u003cb\u003e12 Calculus of Simplex-Valued Functions 158\u003cbr\u003e \u003c\/b\u003e\u003ci\u003eJuan José Egozcue, Eusebi Jarauta-Bragulat and José LuisDíaz-Barrero\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e12.1 Introduction 158\u003c\/p\u003e \u003cp\u003e12.3 Integration 171\u003c\/p\u003e \u003cp\u003e12.4 Conclusions 174\u003c\/p\u003e \u003cp\u003eAcknowledgements 175\u003c\/p\u003e \u003cp\u003eReferences 175\u003c\/p\u003e \u003cp\u003e\u003cb\u003e13 Compositional Differential Calculus on the Simplex 176\u003cbr\u003e \u003c\/b\u003e\u003ci\u003eCarles Barceló-Vidal, Josep Antoni Martín-Fernández and Glòria Mateu-Figueras\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e13.1 Introduction 176\u003c\/p\u003e \u003cp\u003e13.2 Vector-Valued Functions on the Simplex 177\u003c\/p\u003e \u003cp\u003e13.3 C-Derivatives on the Simplex 178\u003c\/p\u003e \u003cp\u003e13.4 Example: Experiments with Mixtures 185\u003c\/p\u003e \u003cp\u003e13.5 Discussion 189\u003c\/p\u003e \u003cp\u003eAcknowledgements 190\u003c\/p\u003e \u003cp\u003eReferences 190\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart IV Applications 191\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e14 Proportions, Percentages, PPM: Do the Molecular Biosciences Treat Compositional Data Right? 193\u003cbr\u003e \u003c\/b\u003e\u003ci\u003eDavid Lovell, Warren Müller, Jen Taylor, Alec Zwart and Chris Helliwell\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e14.1 Introduction 193\u003c\/p\u003e \u003cp\u003e14.2 The Omics Imp and Two Bioscience Experiment Paradigms 194\u003c\/p\u003e \u003cp\u003e14.3 The Impact of Compositional Constraints in the Omics 197\u003c\/p\u003e \u003cp\u003e14.4 Impact of Compositional Constraints on Correlation and Covariance 201\u003c\/p\u003e \u003cp\u003e14.5 Implications 204\u003c\/p\u003e \u003cp\u003eAcknowledgements 206\u003c\/p\u003e \u003cp\u003eReferences 206\u003c\/p\u003e \u003cp\u003e\u003cb\u003e15 Hardy–Weinberg Equilibrium: A Nonparametric Compositional Approach 208\u003cbr\u003e \u003c\/b\u003e\u003ci\u003eJan Graffelman and Juan José Egozcue\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e15.1 Introduction 208\u003c\/p\u003e \u003cp\u003e15.2 Genetic Data Sets 209\u003c\/p\u003e \u003cp\u003e15.3 Classical Tests for HWE 210\u003c\/p\u003e \u003cp\u003e15.4 A Compositional Approach 210\u003c\/p\u003e \u003cp\u003e15.5 Example 214\u003c\/p\u003e \u003cp\u003e15.6 Conclusion and Discussion 215\u003c\/p\u003e \u003cp\u003eAcknowledgements 215\u003c\/p\u003e \u003cp\u003eReferences 215\u003c\/p\u003e \u003cp\u003e\u003cb\u003e16 Compositional Analysis in Behavioural and Evolutionary Ecology 218\u003cbr\u003e \u003c\/b\u003e\u003ci\u003eMichele Edoardo Raffaele Pierotti and Josep Antoni Martín-Fernández\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e16.1 Introduction 218\u003c\/p\u003e \u003cp\u003e16.2 CODA in Population Genetics 219\u003c\/p\u003e \u003cp\u003e16.3 CODA in Habitat Choice 222\u003c\/p\u003e \u003cp\u003e16.4 Multiple Choice and Individual Variation in Preferences 224\u003c\/p\u003e \u003cp\u003e16.5 Ecological Specialization 228\u003c\/p\u003e \u003cp\u003e16.6 Time Budgets: More on Specialization 229\u003c\/p\u003e \u003cp\u003e16.7 Conclusions 231\u003c\/p\u003e \u003cp\u003eAcknowledgements 231\u003c\/p\u003e \u003cp\u003eReferences 231\u003c\/p\u003e \u003cp\u003e\u003cb\u003e17 Flying in Compositional Morphospaces: Evolution of Limb Proportions in Flying Vertebrates 235\u003cbr\u003e \u003c\/b\u003e\u003ci\u003eLuis Azevedo Rodrigues, Josep Daunis-i-Estadella, Glòria Mateu-Figueras and Santiago Thió-Henestrosa\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e17.1 Introduction 235\u003c\/p\u003e \u003cp\u003e17.2 Flying Vertebrates – General Anatomical and Functional Characteristics 236\u003c\/p\u003e \u003cp\u003e17.3 Materials 236\u003c\/p\u003e \u003cp\u003e17.4 Methods 238\u003c\/p\u003e \u003cp\u003e17.5 Aitchison Distance Disparity Metrics 239\u003c\/p\u003e \u003cp\u003e17.6 Statistical Tests 243\u003c\/p\u003e \u003cp\u003e17.7 Biplots 244\u003c\/p\u003e \u003cp\u003e17.8 Balances 246\u003c\/p\u003e \u003cp\u003e17.9 Size Effect 249\u003c\/p\u003e \u003cp\u003e17.10 Final Remarks 249\u003c\/p\u003e \u003cp\u003eAcknowledgements 252\u003c\/p\u003e \u003cp\u003eReferences 252\u003c\/p\u003e \u003cp\u003e\u003cb\u003e18 Natural Laws Governing the Distribution of the Elements in Geochemistry: The Role of the Log-Ratio Approach 255\u003cbr\u003e \u003c\/b\u003e\u003ci\u003eAntonella Buccianti\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e18.1 Introduction 255\u003c\/p\u003e \u003cp\u003e18.2 Geochemical Processes and Log-Ratio Approach 256\u003c\/p\u003e \u003cp\u003e18.3 Log-Ratio Approach and Water Chemistry 258\u003c\/p\u003e \u003cp\u003e18.4 Log-Ratio Approach and Volcanic Gas Chemistry 261\u003c\/p\u003e \u003cp\u003e18.5 Log-Ratio Approach and Subducting Sediment Composition 263\u003c\/p\u003e \u003cp\u003e18.6 Conclusions 265\u003c\/p\u003e \u003cp\u003eAcknowledgements 265\u003c\/p\u003e \u003cp\u003eReferences 265\u003c\/p\u003e \u003cp\u003e\u003cb\u003e19 Compositional Data Analysis in Planetology: The Surfaces of Mars and Mercury 267\u003cbr\u003e \u003c\/b\u003e\u003ci\u003eHelmut Lammer, Peter Wurz, Josep Antoni Martín-Fernández and Herbert Iwo Maria Lichtenegger\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e19.1 Introduction 267\u003c\/p\u003e \u003cp\u003e19.2 Compositional Analysis of Mars’ Surface 270\u003c\/p\u003e \u003cp\u003e19.3 Compositional Analysis of Mercury’s Surface 274\u003c\/p\u003e \u003cp\u003e19.4 Conclusion 278\u003c\/p\u003e \u003cp\u003eAcknowledgement 278\u003c\/p\u003e \u003cp\u003eReferences 278\u003c\/p\u003e \u003cp\u003e\u003cb\u003e20 Spectral Analysis of Compositional Data in Cyclostratigraphy 282\u003cbr\u003e \u003c\/b\u003e\u003ci\u003eEulogio Pardo-Igúzquiza and Javier Heredia\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e20.1 Introduction 282\u003c\/p\u003e \u003cp\u003e20.2 The Method 283\u003c\/p\u003e \u003cp\u003e20.3 Case Study 285\u003c\/p\u003e \u003cp\u003e20.4 Discussion 287\u003c\/p\u003e \u003cp\u003e20.5 Conclusions 288\u003c\/p\u003e \u003cp\u003eAcknowledgement 288\u003c\/p\u003e \u003cp\u003eReferences 288\u003c\/p\u003e \u003cp\u003e\u003cb\u003e21 Multivariate Geochemical Data Analysis in Physical Geography 290\u003cbr\u003e \u003c\/b\u003e\u003ci\u003eJennifer McKinley and Christopher David Lloyd\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e21.1 Introduction 290\u003c\/p\u003e \u003cp\u003e21.2 Context 291\u003c\/p\u003e \u003cp\u003e21.3 Data 293\u003c\/p\u003e \u003cp\u003e21.4 Analysis 295\u003c\/p\u003e \u003cp\u003e21.5 Discussion 299\u003c\/p\u003e \u003cp\u003e21.6 Conclusion 300\u003c\/p\u003e \u003cp\u003eAcknowledgement 300\u003c\/p\u003e \u003cp\u003eReferences 300\u003c\/p\u003e \u003cp\u003e\u003cb\u003e22 Combining Isotopic and Compositional Data: A Discrimination of Regions Prone to Nitrate Pollution 302\u003cbr\u003e \u003c\/b\u003e\u003ci\u003eRoger Puig, Raimon Tolosana-Delgado, Neus Otero and Albert Folch\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e22.1 Introduction 302\u003c\/p\u003e \u003cp\u003e22.2 Study Area 303\u003c\/p\u003e \u003cp\u003e22.3 Analytical Methods 306\u003c\/p\u003e \u003cp\u003e22.4 Statistical Treatment 307\u003c\/p\u003e \u003cp\u003e22.5 Results and Discussion 311\u003c\/p\u003e \u003cp\u003e22.6 Conclusions 314\u003c\/p\u003e \u003cp\u003eAcknowledgements 315\u003c\/p\u003e \u003cp\u003eReferences 315\u003c\/p\u003e \u003cp\u003e\u003cb\u003e23 Applications in Economics 318\u003cbr\u003e \u003c\/b\u003e\u003ci\u003eTim Fry\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e23.1 Introduction 318\u003c\/p\u003e \u003cp\u003e23.2 Consumer Demand Systems 319\u003c\/p\u003e \u003cp\u003e23.3 Miscellaneous Applications 322\u003c\/p\u003e \u003cp\u003e23.4 Compositional Time Series 323\u003c\/p\u003e \u003cp\u003e23.5 New Directions 323\u003c\/p\u003e \u003cp\u003e23.6 Conclusion 325\u003c\/p\u003e \u003cp\u003eReferences 325\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart V Software 327\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e24 Exploratory Analysis Using CoDaPack 3D 329\u003cbr\u003e \u003c\/b\u003e\u003ci\u003eSantiago Thió-Henestrosa and Josep Daunis-i-Estadella\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e24.1 CoDaPack 3D Description 329\u003c\/p\u003e \u003cp\u003e24.2 Data Set Description 331\u003c\/p\u003e \u003cp\u003e24.3 Exploratory Analysis 333\u003c\/p\u003e \u003cp\u003e24.4 Summary and Conclusions 339\u003c\/p\u003e \u003cp\u003eAcknowledgements 340\u003c\/p\u003e \u003cp\u003eReferences 340\u003c\/p\u003e \u003cp\u003e\u003cb\u003e25 robCompositions: An R-package for Robust Statistical Analysis of Compositional Data 341\u003cbr\u003e \u003c\/b\u003e\u003ci\u003eMatthias Templ, Karel Hron and Peter Filzmoser\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e25.1 General Information on the R-package robCompositions 341\u003c\/p\u003e \u003cp\u003e25.2 Expressing Compositional Data in Coordinates 343\u003c\/p\u003e \u003cp\u003e25.3 Multivariate Statistical Methods for Compositional Data Containing Outliers 345\u003c\/p\u003e \u003cp\u003e25.4 Robust Imputation of Missing Values 351\u003c\/p\u003e \u003cp\u003e25.5 Summary 354\u003c\/p\u003e \u003cp\u003eReferences 354\u003c\/p\u003e \u003cp\u003e\u003cb\u003e26 Linear Models with Compositions in R 356\u003cbr\u003e \u003c\/b\u003e\u003ci\u003eRaimon Tolosana-Delgado and Karl Gerald van den Boogaart\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e26.1 Introduction 356\u003c\/p\u003e \u003cp\u003e26.2 The Illustration Data Set 357\u003c\/p\u003e \u003cp\u003e26.3 Explanatory Binary Variable 360\u003c\/p\u003e \u003cp\u003e26.4 Explanatory Categorical Variable 363\u003c\/p\u003e \u003cp\u003e26.5 Explanatory Continuous Variable 365\u003c\/p\u003e \u003cp\u003e26.6 Explanatory Composition 367\u003c\/p\u003e \u003cp\u003e26.7 Conclusions 370\u003c\/p\u003e \u003cp\u003eAcknowledgement 371\u003c\/p\u003e \u003cp\u003eReferences 371\u003c\/p\u003e \u003cp\u003eIndex 373\u003c\/p\u003e  \u003cp\u003e\u003cstrong\u003eVera Pawlowsky-Glahn\u003c\/strong\u003e, Department of Computer Science and Applied Mathematics, University of Girona, Spain. \u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eAntonella Buccianti\u003c\/strong\u003e, Department of Earth Sciences, University of Florence, Italy.   \u003cb\u003eCompositional Data Analysis: Theory and Applications\u003c\/b\u003e  \u003c\/p\u003e\u003cp\u003e\u003cb\u003eEdited by\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003eVera Pawlowsky-Glahn,\u003c\/b\u003e Department of Computer Science and Applied Mathematics, University of Girona, Spain.\u003c\/p\u003e \u003cp\u003e\u003cb\u003eAntonella Buccianti\u003c\/b\u003e, Department of Earth Sciences, University of Florence, Italy\u003c\/p\u003e \u003cp\u003eIt 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.\u003c\/p\u003e \u003cp\u003eThis book presents the history and development of compositional data analysis along with Aitchison's log-ratio approach. \u003ci\u003eCompositional Data Analysis\u003c\/i\u003e describes the state of the art both in theoretical fields as well as applications in the different fields of science.\u003c\/p\u003e \u003cp\u003e\u003cbr\u003e Key Features:\u003c\/p\u003e \u003cp\u003e• Reflects the state-of-the-art in compositional data analysis.\u003cbr\u003e • Gives an overview of the historical development of compositional data analysis, as well as basic concepts and procedures.\u003cbr\u003e • Looks at advances in algebra and calculus on the simplex.\u003cbr\u003e • Presents applications in different fields of science, including, genomics, ecology, biology, geochemistry, planetology, chemistry and economics.\u003cbr\u003e • Explores connections to correspondence analysis and the Dirichlet distribution.\u003cbr\u003e • Presents a summary of three available software packages for compositional data analysis.\u003cbr\u003e • Supported by an accompanying website featuring R code.\u003c\/p\u003e \u003cp\u003eApplied 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.\u003c\/p\u003e","brand":"Wiley","offers":[{"title":"Default Title","offer_id":47988961018085,"sku":"NP9780470711354","price":133.95,"currency_code":"USD","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/1842\/7735\/files\/9780470711354.jpg?v=1761782219","url":"https:\/\/k12savings.com\/products\/compositional-data-analysis-isbn-9780470711354","provider":"K12savings","version":"1.0","type":"link"}