Table Of ContentSpringer Texts in Statistics
SeriesEditors:
G.Casella
S.E.Fienberg
I.Olkin
Forfurthervolumes:
http://www.springer.com/series/417
Andrzej Gałecki (cid:129) Tomasz Burzykowski
Linear Mixed-Effects Models
Using R
A Step-by-Step Approach
123
AndrzejGałecki TomaszBurzykowski
UniversityofMichigan CenterforStatistics
300NorthIngallsBuilding HasseltUniversity
AnnArbor AgoralaanD
Michigan Diepenbeek
USA Belgium
ISSN1431-875X
ISBN978-1-4614-3899-1 ISBN978-1-4614-3900-4(eBook)
DOI10.1007/978-1-4614-3900-4
SpringerNewYorkHeidelbergDordrechtLondon
LibraryofCongressControlNumber:2012941857
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In memoryofTom Ten Have
Preface
Linear mixed-effects models (LMMs) are powerful modeling tools that allow for
the analysis of datasets with complex, hierarchical structures. Intensive research
during the past decade has led to a better understanding of their properties.
The growing body of literature, including recent monographs, has considerably
increased their popularity among applied researchers. There are several statistical
softwarepackagescontainingroutinesforLMMs.Theseinclude,forinstance,SAS,
SPSS,STATA,S+,andR.ThemajoradvantageofRisthatitisafreelyavailable,
dynamically developing, open-source environment for statistical computing and
graphics.
The goal of our book is to provide a description of tools available for fitting
LMMsinR.Thedescriptionisaccompaniedbyapresentationofthemostimportant
theoreticalconceptsofLMMs.Additionally,examplesofapplicationsfromvarious
researchareasillustratethemainfeaturesofboththeoryandsoftware.Thepresented
materialshouldallowreaderstoobtainabasicunderstandingofLMMsandtoapply
them in practice. In particular, we elected to present several theoretical concepts
and their practical implementation in R in the context of simpler, more familiar
classes of models such as e.g., the classical linear regression model. Based on
theseconcepts,moreadvancedclassesofmodels,suchasmodelswithheterogenous
varianceandcorrelatedresidualerrors,alongwithrelatedconceptsareintroduced.
Inthisway,weincrementallysetthestageforLMMs,sothattheexpositionofthe
theory and R tools for these models becomes simpler and clearer. This structure
naturally corresponds to the object-oriented programming concept, according to
which R functions/methods for simpler models are also applicable to the more
complexones.
We assume that readers are familiar with intermediate linear algebra, calculus,
andthebasictheoryofstatisticalinferenceandlinearmodeling.Thus,theintended
audiencefor this book is graduatestudents of statistics and appliedresearchersin
otherfields.
Ourexpositionofthetheoryofvariousclassesofmodelspresentedinthebook
focusesonconcepts,whichareimplementedinthefunctionsavailableinR.Readers
vii
viii Preface
interested in a more detailed description of the theory are referred to appropriate
theoreticalmonographbooks,whichweindicateinthetext.
There are a large number of R packagesthat can be used to fit LMMs. Rather
thanattemptingtodescribeallofthesepackages,wefocusmainlyontwoofthem,
namely,nlme andlme4.0.Inthisway,we canprovidea moredetailedaccountof
thetoolsofferedbythetwopackages,whichincludeawidevarietyoffunctionsfor
modelfitting,diagnostics,inference,etc.
The package nlme includes functions, which allow fitting of a wide range of
linear models and LMMs. Moreover,it has been available for many years and its
codehasbeenstableforsometimenow.Thus,itisawell-establishedRtool.
In turn, lme4.0 is a developmental branch version of the lme4 package. The
latterhasbeenunderdevelopmentforseveralyears.Bothpackagesofferanefficient
computational implementation and an enhanced syntax, though at the cost of a
more restricted choice of LMMs, as compared to the nlme package. At the time
ofwritingofourbook,theimplementationofLMMsinlme4hasundergonemajor
changesintermsofinternalrepresentationoftheobjectsrepresentingfittedmodels.
Consequently,atthebeginningof2012,asnapshotversionoflme4hasbeenmade
availabletotheRusersunderthenameoflme4.0.Asweanticipatethatlme4.0will
notundergoanymajorchanges,wedecidedtopresentitinmoredetailinourbook.
Wewouldliketounderscore,however,thatthemajorpartofthesyntax,presented
inthebook,willbeapplicablebothtolme4andlme4.0.
Allclassesoflinearmodelspresentedinthebookareillustratedusingdatafroma
particulardataset.Inthisway,thedifferencesbetweenthevariousclassesofmodels,
aswellasdifferencesintheRsoftware,canbeclearlydelineated.LMMs,whichare
themainfocusofthebook,arealsoillustratedusingthreeadditionaldatasets,which
extendthepresentationofvariousaspectsofthemodelsandRfunctions.Wehave
decidedtoincludethedirectoutputofRcommandsinthetext.Inthisway,readers
whowouldliketorepeattheanalysesconductedinthebookcandirectlychecktheir
own output. However, in order to avoid the risk of incompatibility with updated
versionsof thesoftware,the resultsofthe analyseshavealso beensummarizedin
theformofeditedtables.
Tofurthersupportthosereaderswhoareinterestedinactivelyusingthematerial
presented in the book, we have developed the package nlmeU. It contains all the
datasets and R code used in the book. The package is downloadable at http://
www-personal.umich.edu/~agalecki/.
We hope that our book, which aims to provide a state-of-the-artdescription of
the details of implementing of LMMs in R, will support a widespread use of the
models by applied researchers in a variety of fields including biostatistics, public
health,psychometrics,educationalmeasurement,andsociology.
When working on the text, we received considerable assistance and valuable
comments from many people. We would like to acknowledgeGeert Molenberghs
(HasseltUniversityandtheCatholicUniversityofLeuven),GeertVerbeke(Catholic
University of Leuven), José Pinheiro (Novartis AG), Paul Murrell (Auckland
University), Przemysław Biecek (Warsaw University), Fabian Scheipl (Ludwig
Maximilian University of Munich), Joshua Wiley (University of California, Los
Preface ix
Angeles), Tim Harrold (NSW Ministry of Health), Jeffrey Halter (University of
Michigan), Shu Chen (University of Michigan), Marta Gałecka (Weill Cornell
MedicalCollege),anonymousreviewersandmembersoftheR-sig-MEdiscussion
group led by Douglas Bates (University of Wisconsin-Madison), and Ben Bolker
(McMasterUniversity)fortheircommentsanddiscussionsatvariousstagesduring
thepreparationofthebook.Wealsoacknowledgeaformidableeffortonthepartof
thedevelopersofthenlmeandlme4packages.Withoutthemthisbookwouldnot
havebeenwritten.Inparticular,BenBolker’scontributionwasinvaluabletoensure
thatthemajorityofthelme4.0syntaxusedinthetextcanalsobeusedwiththelme4
package.WearegratefultoJohnKimmelforencouragingustoconsiderwritingthe
book and to Marc Strauss, Hannah Bracken, and Brian Halm from Springer for
theireditorialassistanceandpatience.Finally,wegratefullyacknowledgefinancial
supportfrom the Claude Pepper Center grantsAG08808and AG024824from the
National Institute of Aging and from the IAP Research Network P7/06 of the
BelgianGovernment(BelgianSciencePolicy).
AnnArbor,MI,USA AndrzejGałecki
Diepenbeek,Belgium,andWarszawa,Poland TomaszBurzykowski
