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January26,

2013

ChihPingChou

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Whatis

SEM

StructuralEquationModeling(SEM)isastatisticaltechniqueinvolvingthehypothesesonassociationsamonglatent

variablesand

observable

variables.

SEM

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Whatis

SEM?

TheSEM

allows

for

more

explicit

and

precisetheoreticalinferencestobemadethanthosebasedonordinarymultiple

regression

or

simple

comparisons

of

meansandproportions.

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Advantagesof

SEM

Explicitspecification

and

test

of

hypothesesonassociationsandcausations.

SEM

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Advantagesof

SEM

Appropriateness

of

the

model

can

be

testedbyexaminingthedifferencebetweenthecovariancematricesbased

on

the

model

and

empirical

data.

Controlfor

measurement

errors.

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KeyAdvances

in

SEM

Thedevelopment

of

SEM

can

be

consideredfromtwoseparatelinesofstatisticalapproach:

PathAnalysis

and

FactorAnalysis

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7

FamilyTree

of

SEM

BivariateCorrelation

(ttest)

ConfirmatoryFactor

Analysis(GCM)

PathModel

(MANOVA)

Factor

Analysis

MultipleRegression

(ANOVA)

StructuralEquation

Model

ExploratoryFactor

Analysis

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PathAnalysis

PathAnalysis

SewallWright(1918,1921,1934).

HermanWold (1954)treatedpathmodelasa

formof

simultaneous

equation

modeling

in

econometrics.

HubertMBlalock(1961)andOtisDudley

Duncan(1966)

launched

the

application

of

path

analysisinsociology,andthen,inpoliticalscience.

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Ching

Chun

Li,, (1956)appliedpathmodelonpopulationgeneticsandpublishedPathAnalysis:APrimer(1975).

Inthe80s,pathanalysishasevolvedinto

a

structural

equation

modeling

approach.

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FactorAnalysis

Charles

Spearman

(1904,

1927)

was

the

firsttointroducethetermfactoranalysistopresenttheconceptoffactorbasedoncorrelations(Pearson,1896)amongasetofitems.

MajorcontributorstoFAduring1900to1920includeCyrilBurt,KarlPearson,G.H.Thomson,J.C.MaxwellGarnett,KarlHolzinger.

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Application

of

FA

was

primarily

in

the

fieldofpsychologyandbecamepopularinotherfieldssince1950.

FA

was

also

known

as

Exploratory

Factor

Analysis(EFA)untilJreskogpublishedthefirstpaperonCFAin1969.

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Jreskog

published

his

paper

on

a

general

methodanalyzingcovariancestructures.

Inearlierstageofthedevelopmentof

SEM,

we

call

this

technique:

Covariance

StructureAnalysis(CSA).

1st LISREL.Joreskog,K.G.;VanThillo,M.

(1972)

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Starting

1970,

the

applications

of

SEM

techniquebegantospreadoutduetothedevelopmentsinmethodology,statisticaltechniques,softwareprograms,andempiricalapplicationsinsocialsciencesandotherresearchareas.

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Methodologicalissuessuchasdatawithclusterstructureddata,longitudinaldata.

Technicalissuessuchasanalysisofnonnormallydistributeddata,dichotomizeddata,orderedcategoricaldataandmissingdata.

Computationalissuessuchasthecalculationofgoodnessoffitindices,ofstandarderrorsfordirectandindirecteffectsincausalmodels.

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SomeQuotes

Analysis

of

covariance

structures

is

explicitlyaimedatcomplextestingoftheory,andsuperblycombinesmethodshithertoconsideredandusedseparately. Italsomakespossibletherigoroustestingoftheoriesthathaveuntilnowbeenverydifficulttotestadequately. (Kerlinger,1977)

Allmodelsarewrong,butsomeareuseful.(Box,1979)

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Modelsusing

Latent

Variables

16

ObservableVariables

LatentVariables Continuous Categorical

Continuous SEM,

FactorAnalysisLatent

Trait Analysis

(ItemResponseTheory,IRT)

Categorical LatentProfile

AnalysisLatent

Class Analysis

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StructuralEquation

Model

V4V9

V10

V11

V12

F1

F3

E1

E9

E10

E11

E12

D3

V3V2V1

E2 E3 E4

F2

V8V7V6V5

E5 E6 E7 E8

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InterestingQuotes

Allmodels

are

wrong,

butsomeareuseful.(Box,1979)

Somemodelsareright,

butmostareuseless.

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ExamineMediation

and

Moderation

EffectsusingSEM

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TheoreticalModelofSmokingamongYouth

DistalFactors Mediators Outcome

Friends

Smoking

ParentsSmoking

SiblingsSmoking

MediaExposure

Attitude

SelfEfficacy

Social

NormativeBelief

ParentsReaction

FriendsReaction

SmokingBehavior

SmokingIntention

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MediationEffect

A

given

variable

may

be

said

to

function

asamediatorifitaccountsfortherelationbetweenapredictorandanoutcome.

Mediatorsprovideexplanationtohowor

why

certain

effects

occurred.

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ApplicationofSEM

in

RandomizedClinicalTrials

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WellElderly2ConceptualModel

Activitybasedinterventionsforelders

CognitiveFunctioning

HealthyActivity

ActiveCoping

SocialSupport

PerceivedControl

PositiveReinterpretationBasedCoping

StressRelated

BiomarkersLifestyleRedesign

InterventionProgram

Perceived

Physical

Health

PsychosocialWellBeing

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Program

Activity

Frequency

ActivityPurpose

ActiveCoping

SocialSupport

PerceivedControl

SF36v2Mental

SF36v2Physical

CESD

LSIZ

PathAnalysis

CovariatesAge EducationGender Ethnicity

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ActivityFrequency

Activity

Purpose

ActiveCoping

SocialSupport

Perceived

Control

SF36v2

Mental

SF36v2

Physical

CESD

LSIZ

SignificantRelationships

NonsignificantRelationshipsCovariates

Age Education

Gender

Ethnicity

PathAnalysis:RegressionWeights

Program

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Results

Significantdirectpathsdemonstratedwithsolidlineswerepresented.

Intervention

program

didnt

show

any

significant

directeffectonoutcomemeasures.

TheEffects

of

the

intervention

program

on

outcomesareprimarilythroughthemediators.

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Results cont.

TheprogramhadsignificantimpactsonMAPA

(Health

Activity)

related

mediatorsandperceivedcontrol.

BothMAPA

measures,

especially

the

MAPASurvey,socialsupportandperceivedcontrolalsodemonstrated

significant

influence

on

most

of

the

outcomes.

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Conclusions

Interventiondemonstratedsignificant

indirecteffects

on

all

four

outcome

measuresthroughMAPAmeasures.

Inotherwords,theUSCWellElderlyII

interventionalprogram

has

been

found

to

haveimpactsprimarilyonengaginginactivities,whichinturnimprovesthe

outcomes.

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ModerationEffect

A

variable

is

considered

a

moderator

if

it

affectsthedirectionand/orstrengthoftherelationbetweenapredictorandanoutcomeorcriterionvariable.

Moderatorvariablesspecifywhencertaineffectswillhold

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TheoreticalModelofSmokingamongYouth

DistalFactors Mediators Outcome

Friends

Smoking

ParentsSmoking

SiblingsSmoking

MediaExposure

Attitude

SelfEfficacy

Social

NormativeBelief

ParentsReaction

FriendsReaction

SmokingBehavior

SmokingIntention

Moderators:

Gender,Race,Age,SES,etc.

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1990:Second

Generation

of

SEM

IcalledthisyearasthesecondgenerationofSEMprimarilybecauseoftheworkofMeredithandTisak (1990)onLatentCurveAnalysis,ormorecommonlyknown

as

latent

growth

curve

model

or

growthcurvemodel(GCM).

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Applicationof

SEM

in

Longitudinal

Studies32

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LongitudinalStudy

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X11

Y2Y1

X2

X3

X4

2

Y4Y3 Y6Y5 Y8Y7

3

4

1 2 3 4 5 6 7 8

32

1

2

1 2 3 4

1 2 3 4

21 43

11

12

21

X11

X21

X32

X42

Y11 Y21 Y32 Y42 Y53 Y63 Y74 Y84

LongitudinalStudy

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GrowthCurveModel

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AdvancedApplications(Handbookod

SEM,

Hoyle,

2012)

GrowthMixtureModeling

MultilevelSEM(multilevelstructure,multilevelpathmodels)

Spatial

SEM

(incorporates

neighbor

adjacencymatrixintolatentfactors)

SpatialRegressionModel:

y=Wy +

0 +

1X

+e

whereWisaNNcontiguitymatrix

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SEMinGenetics,orGeneticCovarianceStructural

Model

(GCSM)

GeneticModelfortwindataisSEM

37

A D C E

P

A:AdditiveGeneticFactor;D:DominantGeneticFactor;C:CommonEnvironmentalFactor;E:SpecificFactor(Neale,1995)

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GCSM

Withphenotypesmeasuredfromtwindesignsinvolvingbothmonozygoticanddizygotictwinslivingtogetherorseparately,SEMcanbedevelopedwith

certainparameters

fixed

per

genotyping

information.

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GCSM

Modelscanbedevelopedforcommonpathway

(treating

phenotype

as

mediating

latentfactor)orindependentpathway(treatingphenotypesasseparateobservable

variables).

GCSMcanbedevelopedtostudyGE(GenotypebyEnvironmental)Interaction.

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FutureApplications

SEMofNeuroimagingData

TemporalinformationofneuroimagingdatacanbeadequatelyhandledusingtheSEMapproach.

ThemainfocusofSEMistounderstandiftherearetaskdependentchangesofeffective connectionsbetweenbrainregions.

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FutureApplications

BayesianSEM(Bayesianapproachtoalltypes

of

SEM

application)

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