Applied Compositional Data Analysis: With Worked Examples in R

288 Pages·2018·7.287 MB·English

by  Peter Filzmoser, Karel Hron, Matthias Templ

Springer Series in Statistics
Peter Filzmoser · Karel Hron 
Matthias Templ
Applied
Compositional
Data Analysis
With Worked Examples in R
Springer Series in Statistics
SeriesEditors:
PeterDiggle,UrsulaGather,ScottZeger
PastEditors:
PeterBickel,NannyWermuth
FoundingEditors:
David Brillinger, Stephen Fienberg, Joseph Gani, John Hartigan, Jack Kiefer,
KlausKrickeberg
Moreinformationaboutthisseriesathttp://www.springer.com/series/692
Peter Filzmoser • Karel Hron (cid:129) Matthias Templ
Applied Compositional Data
Analysis
With Worked Examples in R
123
PeterFilzmoser KarelHron
InstituteofStatisticsandMathematical DepartmentofMathematicalAnalysis
MethodsinEconomics andApplicationsofMathematics
TUWien PalackýUniversityOlomouc
Vienna,Austria Olomouc,CzechRepublic
MatthiasTempl
InstituteofDataAnalysisandProcess
Design
ZHAWZurichUniversityofApplied
Sciences
Winterthur,Switzerland
ISSN0172-7397 ISSN2197-568X (electronic)
SpringerSeriesinStatistics
ISBN978-3-319-96420-1 ISBN978-3-319-96422-5 (eBook)
https://doi.org/10.1007/978-3-319-96422-5
LibraryofCongressControlNumber:2018952636
MathematicsSubjectClassification(2010):62H25,62H30,62H20,62J05,15A03,62P12,62P25
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To ourfamilies
Preface
Compositional data are nowadays widely accepted as multivariate observations
carrying relative information: those following the principle of scale invariance,
typically being representedin proportionsand percentages,but also in other units
like mg/kg and mg/l that reflect their relative nature. In other words, for compo-
sitional data the relevant information is contained in the (log-)ratios between the
components(parts).In2006,20yearsaftertheseminalbookofJohnAitchison,The
statisticalanalysisofcompositionaldata,hasbeenpublished,wemetcompositional
dataandthelogratiomethodologyforthefirsttime—tobehonest,notassomething
highly appealing, but originally for the reason to get a research paper finally
acceptedforpublication,afteratediousreviewingprocess.Wewerenotfullycon-
vincedthatthisapproachwouldbesoimportantforpracticalapplications,because
at that time the methodology was presented more from a theoretical perspective,
andtheapplicationswerepartiallyevenbasedoninventeddata.Ontheotherhand,
it was clear that the logratio methodology formed a consistent approach to deal
withthistypeofdata,andfurtherinterestingdirectionswereproposed:thepaperon
orthonormalcoordinatesforcompositionaldata[Egozcue,J.J., Pawlowsky-Glahn,
V., Mateu-Figueras, G., Barceló-Vidal, C. Isometric logratio transformation for
compositionaldataanalysisinMathematicalGeology]was publishedjust3years
before,andalsotheprincipleofworkingincoordinateswasjustborn.
Whenworkingmoreandmoreinthisarea,wefeltatsomepointthattherecould
beaneedforapracticalguidetocompositionaldataanalysis—notjustforpeople
fromapplications,butalsoforourowncuriosity,tounderstandwhichvalueadded
thelogratiomethodologycouldyieldwhenprocessingcompositionaldata.Howdo
the results differ when simply taking a log-transformation, compared to working
in an appropriate geometry? And are the results (more) reasonable and justified?
In the last ten or more years, we did quite an effortin this direction, by touching
systematically almost all popular multivariate statistical methods and those fields
thatare of primaryimportanceforpracticaldata analysis(robuststatistics, outlier
detection,anddealingwithmissingandzerovalues).
This book provides a summary of our efforts. We wrote it in a great freedom
from what should be followed or mentioned from historical or any other reasons.
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viii Preface
The focus is on a proper orthonormal coordinate representation of compositional
data thatindeedprovidesa usefulway for a reasonableprocessingof multivariate
observations.Thecentralpointareso-calledpivotcoordinatesthataimtoextractall
relativeinformationaboutoneofthepartsinacomposition.Thesecoordinateshave
proventheiradvancesinanumberofapplicationsandprovokedmanydiscussions.
We present the pivot coordinates in a form that shows their flexibility in various
dataprocessingcontextsandtheirstrengthfortheinterpretationoftheresults.Nev-
ertheless, we admit that also other representations,like more generalorthonormal
coordinates,balances,butalsocenteredlogratiocoefficients,orpairwiselogratios,
areusefulinconcretecontexts.
Thebookcanbetakenasaconcise,self-containedmanualonhowtoapplythe
logratio methodology for compositional data analysis in everyday practice, using
thestatisticalsoftwareenvironmentRandthepackagerobCompositions.We
triedtoillustratethetheoreticalpartswithseveralexamplesfromapplicationswith
general understandability, like those from official statistics, economics, geology,
or chemometrics. As a minimum prerequisite for accessing the book, just a basic
courseonprobabilityandstatisticsisrequired,althoughadditionalexperiencewith
multivariate statistics and statistical computing might be advisable. On the other
hand, the book can also be considered as a source of inspiration for those who
are familiar enough with standard knowledge on compositional data analysis, as
presented in the book by V. Pawlowsky-Glahn, J.J. Egozcue, and R. Tolosana-
Delgado, Modeling and analysis of compositional data. According to these aims,
afterprovidingthegeometricalreasoningforarelevant(notexclusivelystatistical)
processingof compositionaldata, manypopularstatistical methods,like principal
component analysis, cluster analysis, classification and regression analysis, are
adaptedfordealingwithdatacarryingrelativeinformation.Moreover,exploratory
andpreprocessingissuesarediscussed:visualization,outlierdetection,anddealing
with missing values and particularly with zeros that form a touchstone of the
logratio analysis. Last but not least, also emerging fields like analyzing high-
dimensional compositional data and compositional tables, with great potential
for future developments, are discussed. This clearly illustrates that not a closed
methodological framework but rather just a state of the art of an intensively
developingresearchfieldispresented.
Finally, the structure of the book can also be used for a one-semester course
on applied compositional data analysis. The interactive form of the book enables
students to practice theoretical knowledge directly with data sets coming from
differentfields of their possible future expertise.Our sincere wish is to contribute
to the education of a new generation of people for which statistical analysis of
compositionaldataisamatterofcreativethinking.
Vienna,Austria PeterFilzmoser
Olomouc,CzechRepublic KarelHron
Winterthur,Switzerland MatthiasTempl
August25,2018
Acknowledgments
We are very gratefulto our colleaguesfrom the Vienna University of Technology
and from the Palacký University Olomouc and to many collaboratorswho helped
us to get familiar with compositionaldata analysis. In particular,we like to thank
Dr. Clemens Reimann from the Geological Survey of Norway, for bringing us in
touch with real data applications from geochemistry, which made it necessary at
somepointtogetacquaintedwithcompositionaldata.WearegratefultoProf.Vera
Pawlowsky-Glahn from the University of Girona and to Prof. Juan José Egozcue
from the Polytechnic University of Catalonia for numerous fruitful discussions—
theyarereally“parents”ofcompositionaldataanalysis.Theirhintsandideasgreatly
helpedtowritethebookinthispresentform.And,finally,ourgreatestgratitudeis
toourfamilies:withouttheirlong-termsupport,anyresearchactivitieswouldbyfar
notbepossible.
ix
Contents
1 CompositionalDataasaMethodologicalConcept...................... 1
1.1 WhatAreCompositionalData? ..................................... 1
1.2 IntroductoryProblems ............................................... 5
1.2.1 PhDStudentsExample..................................... 5
1.2.2 BeerDataExample......................................... 8
1.2.3 GeochemicalDataExample................................ 10
1.3 PrinciplesofCompositionalDataAnalysis......................... 11
1.4 StepstoaConciseMethodology .................................... 14
References.................................................................... 15
2 AnalyzingCompositionalDataUsingR ................................. 17
2.1 BriefOverviewonPackagesRelatedtoCompositionalData
Analysis............................................................... 17
2.1.1 compositions................................................ 18
2.1.2 robCompositions............................................ 18
2.1.3 ggtern........................................................ 21
2.1.4 zCompositions.............................................. 21
2.1.5 mvoutlier,StatDA .......................................... 21
2.1.6 CoDaPack................................................... 21
2.1.7 compositionsGUI........................................... 22
2.2 TheStatisticsEnvironmentR........................................ 22
2.3 BasicsinR............................................................ 22
2.3.1 InstallationofRandUpdates.............................. 24
2.3.2 InstallrobCompositions.................................... 24
2.3.3 Help ......................................................... 25
2.3.4 TheRWorkspaceandtheWorkingDirectory ............ 26
2.3.5 DataTypes.................................................. 27
2.3.6 GenericFunctions,MethodsandClasses.................. 32
References.................................................................... 33
xi