Latent Variable Models: An Introduction to Factor, Path, and Structural Equation Analysis

391 Pages·2017·1.63 MB·English

by  John C. Loehlin

Latent Variable Models
An Introduction to Factor, Path,
and Structural Equation Analysis
FifthEdition
LatentVariableModels: AnIntroductiontoFactor,Path,andStructuralEquation
Analysisintroduceslatentvariablemodelsbyutilizingpathdiagramstoexplainthe
relationshipsinthemodels. Thisapproachhelpslessmathematically-inclinedreaders
tograsptheunderlyingrelationsamongpathanalysis,factoranalysis,andstructural
equationmodeling,andtosetupandcarryoutsuchanalyses.
Thisrevisedandexpandedfiftheditionagaincontainskeychaptersonpathanalysis,
structuralequationmodels,andexploratoryfactoranalysis. Inaddition,itcontainsnew
materialoncompositereliability,modelswithcategoricaldata,theminimumaverage
partialprocedure,bi-factormodels,andcommunicatingaboutlatentvariablemodels.
Theinformalwritingstyleandthenumerousillustrativeexamplesmakethebook
accessibletoreadersofvaryingbackgrounds. Notesattheendofeachchapter
expandthediscussionandprovideadditionaltechnicaldetailandreferences.
Moreover,mostchapterscontainanextendedexampleinwhichtheauthorswork
throughoneofthechapter’sexamplesindetailtoaidreadersinconductingsimilar
analyseswiththeirowndata. Thebookandaccompanyingwebsiteprovideallofthe
dataforthebook’sexamplesaswellassyntaxfromlatentvariableprogramsso
readerscanreplicatetheanalyses. Thebookcanbeusedwithanyofavarietyof
computerprograms,butspecialattentionispaidtoLISRELandR.
Animportantresourceforadvancedstudentsandresearchersinnumerousdisciplines
inthebehavioralsciences,education,business,andhealthsciences,LatentVariable
Modelsisapracticalandreadablereferenceforthoseseekingtounderstandor
conductananalysisusinglatentvariables.
JohnC.LoehlinisProfessorEmeritusofPsychologyandComputerScienceatthe
UniversityofTexasatAustin. HereceivedhisPhDinPsychologyfromtheUniversity
ofCalifornia(Berkeley).
A.AlexanderBeaujeanisanAssociateProfessorofEducationalPsychologyat
BaylorUniversity. HereceivedPhDsinEducationalPsychologyandSchool
PsychologyfromtheUniversityofMissouri.
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Latent Variable Models
An Introduction to Factor, Path,
and Structural Equation Analysis
FifthEdition
JohnC.Loehlin
A.AlexanderBeaujean
RO Routledge
U
TLED Taylor & Francis Group
G
E
LONDON AND NEW YORK
Firstpublished2017
byRoutledge
711ThirdAvenue,NewYork,NY10017
andbyRoutledge
2ParkSquare,MiltonPark,Abingdon,Oxon,OX144RN
RoutledgeisanimprintoftheTaylor&FrancisGroup,aninformabusiness
©2017Taylor&Francis
TherightofJohnC.LoehlinandA.AlexanderBeaujeantobeidentifiedasauthorofthisworkhasbeen
assertedbytheminaccordancewithsections77and78oftheCopyright,DesignsandPatentsAct1988.
Allrightsreserved.Nopartofthisbookmaybereprintedorreproduced
orutilisedinanyformorbyanyelectronic,mechanical,orothermeans,
nowknownorhereafterinvented,includingphotocopyingandrecording,
orinanyinformationstorageorretrievalsystem,withoutpermissioninwritingfromthepublishers.
Publisher’sNote
Thisbookhasbeenpreparedfromcamera-readycopyprovidedbytheauthors.
Trademarknotice:Productorcorporatenamesmaybetrademarksorregisteredtrademarks,andareused
onlyforidentificationandexplanationwithoutintenttoinfringe.
LibraryofCongressCataloginginPublicationData
Names:Loehlin,JohnC.|Beaujean,A.Alexander.
Title:Latentvariablemodels:anintroductiontofactor,path,andstructuralequationanalysis.
Description:Fifthedition/JohnC.Loehlin,A.AlexanderBeaujean.|NewYork,NY:Routledge,2017.|
Includesbibliographicalreferencesandindex.
Identifiers:LCCN2016038052|ISBN9781138916067(hb:alk.paper)|
ISBN9781138916074(pb:alk.paper)|ISBN9781315643199(epub)
Subjects:LCSH:Latentvariables.|Latentstructureanalysis.|Factoranalysis.|
Pathanalysis(Statistics)|Structuralequationmodeling.
Classification:LCCQA278.6.L642017|DDC519.5/35–dc23
LCrecordavailableathttps://lccn.loc.gov/2016038052
ISBN:978-1-138-91606-7(hbk)
ISBN:978-1-138-91607-4(pbk)
ISBN:978-1-315-64319-9(ebk)
TypesetinHelvetica
byJohnC.LoehlinandA.AlexanderBeaujean
Visitthecompanionwebsite:routledge.com/cw/loehlin
Contents
Preface ix
Chapter1: PathModelsinFactor,Path,andStructuralEquation
Analysis 1
PathDiagrams 2
PathAnalysis 7
FactorModels 16
StructuralEquations 23
OriginalandStandardizedVariables 24
ManifestVersusLatentVariableModels 28
ExtendedExample 28
Notes 31
Exercises 33
Chapter2: FittingPathModels 37
IterativeSolutionofPathEquations 37
MatrixFormulationofPathModels 42
Full-FledgedModel-FittingPrograms 46
FitFunctions 54
2
Hierarchicalffl Tests 63
DescriptiveCriteriaofModelFit 69
ThePowertoRejectanIncorrectModel 72
Identification 76
MissingData 78
CorrelationsVersusCovariancesinModelFitting 82
ExtendedExample 84
Notes 86
Exercises 91
Chapter3: FittingPathandStructuralModelstoDatafromaSingle
GrouponaSingleOccasion 95
StructuralandMeasurementModels 95
ConfirmatoryFactorAnalysis 100
SomePsychometricApplicationsofPathandStructuralModels 103
StructuralModels—ControllingExtraneousVariables 111
ModelswithReciprocalInfluencesandCorrelatedErrors 115
NonlinearEffectsAmongLatentVariables 120
ExtendedExample 124
v
Notes 126
Exercises 129
Chapter4: FittingModelsInvolvingRepeatedMeasures,Multiple
Groups,orMeans 133
ModelsofEventsOverTime 133
ModelsComparingDifferentGroups 142
FittingModelstoMeansaswellasCovariances 151
TheVersatilityofMultiple-GroupDesigns 159
ModelswithCategoricalIndicators 160
AConcludingComment 163
ExtendedExample 163
Notes 166
Exercises 169
Chapter5: ExploratoryFactorAnalysis—Basics 171
FactorExtraction 174
EstimatingCommunalities 179
DeterminingtheNumberofFactors 183
Rotation 189
AnExample: Thurstone’sBoxProblem 197
FactorAnalysisUsingPackagedPrograms 201
ExtendedExample 204
Notes 205
Exercises 208
Chapter6: ExploratoryFactorAnalysis—Elaborations 211
Rescalings—AlphaandCanonicalFactors 211
AlternativeStoppingCriteria 214
AlternativeRotationMethods 217
EstimatingFactorScores 220
HierarchicalFactors 225
NonlinearFactorAnalysis 232
ExtendedExample 235
Notes 240
Exercises 241
Chapter7: IssuesintheApplicationofLatentVariableModels 243
ExploratoryModificationofaModel 243
AlternativeModels 248
CanPathDiagramsbeConstructedAutomatically? 252
ModesofLatentVariableAnalysis 255
AdvancedTopicsinLatentVariableModels 260
CriticismsofLatentVariableModeling 263
vi
Notes 268
Exercises 271
Appendices 273
A. SimpleMatrixOperations 273
B. DerivationofMatrixVersionofPathEquations 281
C. LISRELMatricesandExamples 284
D. ModelFitIndices 289
E. TableofChi-squareValues 299
F. NoncentralChi-squareValuesforEstimatingPower 301
G. PowerofaTestofPoorFitandSampleSizesNeededforPower 303
H. CommunicatingAboutLatentVariableModels 305
AnswerstoExercises 309
References 321
Index 367
vii
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Preface to the First Edition
Thisbookisintendedasanintroductiontoanexcitinggrowthareainsocialscience
methodology—theuseofmultiple-latent-variablemodels. Psychologistsandother
socialscientistshavelongbeenfamiliarwithonesubvarietyofsuchmodeling,factor
analysis—moreproperly,exploratoryfactoranalysis. Inrecentdecades,confirmatory
factoranalysis,pathanalysis,andstructuralequationmodelinghavecomeoutof
specializednichesandaremakingtheirbidtobecomebasictoolsintheresearch
repertoireofthesocialscientist,particularlytheonewhoisforcedtodealwithcomplex
real-lifephenomenaintheround: thesociologist,thepoliticalscientist,thesocial,
educational,clinical,industrial,personalityordevelopmentalpsychologist,the
marketingresearcher,andthelike.
Allthesemethodsareatheartone,asIhavetriedtoemphasizeinthechaptersto
follow. Ihaveusedearlierversionsofthisbookinteachinggraduatestudentsfrom
psychologyandrelateddisciplines,andhavefoundtheparticularapproachused—via
pathdiagrams—tobeeffectiveinhelpingnot-too-mathematicalstudentsgrasp
underlyingrelationships,asopposedtomerelygoingthroughthemotionsofrunning
computerprograms. Insomesectionsofthebookacertainamountofelementary
matrixalgebraisemployed;anappendixonthetopicisprovidedforthosewhomay
needhelphere.
Intheinterestsofaccessibility,Ihavetriedtomaintainarelativelyinformalstyle,
andtokeepthemaintextfairlyunclutteredwithreferences. Thenotesattheendof
eachchapterareintendedloprovidetheseriousstudentwithapathintothetechnical
literature,aswellastodrawhisorherattentiontosomeissuesbeyondthescopeof
thebasictreatment.
Thebookisnotcloselytiedtoaparticularcomputerprogramorpackage,although
thereissomespecialattentionpaidtoLISREL.Iassumethatmostuserswillhave
accesstoalatent-variablemodel-fittingprogramontheorderofLISREL,COSAN,
EQS,orMILS,andanexploratoryfactoranalysispackagesuchasthoseinSPSS,
BMDP,orSAS.Insomeplaces,amatrixmanipulationfacilitysuchasthatinMINITAB
orSASwouldbehelpful. Ihaveprovidedsomeintroductorymaterialbuthavenottried
totellstudentsalltheyneedtoknowtorunactualprograms—suchinformationisoften
local,ephemeral,orboth. Theinstructorshouldexpecttoprovidesomehandoutsand
perhapsabitofhands-onassistanceingettingstudentsstarted. Thereadergoingit
onhisorherownwillrequireaccesstocurrentmanualsforthecomputerprogramsto
beused.
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