Introduction to PLS-SEM.ppt

8/9/2019 Introduction to PLS-SEM.ppt

1/30

Joe F. Hair, Jr.Joe F. Hair, Jr.

Founder & Senior ScholarFounder & Senior Scholar

PLS-SEM: Introduction and OverviewPLS-SEM: Introduction and Overview


2/30

The greatest interest in any factor solution centers on the correlations between the original

variables and the factors. The matrix of such test-factor correlations is called the factor structure,

and it is the primary interpretative device in principal components analysis. In the factor

structure the element rjkgives the correlation of the j thtest with the kthfactor. Assuming that the

content of the observation variables is well known, the correlations in the kthcolumn of the

structure help in interpreting, and perhaps naming, the kthfactor. Also, the coefficients in the jthrow give the best view of the factor composition of the jthtest.

Another set of coefficients of interest in factor analysis is the weights that compound predicted

observations from factor scores f. These regression coefficients for the multiple regression of

each element of the observation vector on the factor fare called factor loadings and the matrix

A that contains them as its rows is . . . . .

!ource" #ooley, $illiam $., and %aul &. 'ohnes,Multivariate Data Analysis, (ohn $iley ) !ons,

Inc., *ew +ork, , page /0.

2/12/1

2/1

2/1

2/1

1

sinceand

)(1

)(1

1

))((1

:followsasisstructurefactortheofderivationThe

1'1''

1'&1

&1'

1'

1'

f

mfm

==

=

=

=

=

=

=

=

S

S

S

ii

ii

ii

N

i

fizi

N

N

N

N


3/30

Sewall Wright, Correlation and Causation,Sewall Wright, Correlation and Causation, JournalJournal

of Agricultural Researchof Agricultural Research, Vol. XX, No. 7, 1921., Vol. XX, No. 7, 1921.

SEM Model:SEM Model:

Predicting the Birth WeightPredicting the Birth Weight

of Guinea Pigsof Guinea Pigs

X & Y = different outcomesX & Y = different outcomes

B, C & = common causesB, C & = common causes

! & E = inde"endent causes! & E = inde"endent causes


4/30

Structural EquationStructural Equation

Modelin!Modelin!

"hat co#e to #ind$"hat co#e to #ind$

CB-SEMCB-SEM

!S"E #M$S%!S"E #M$S%

&S-SEM&S-SEM


5/30

BrandBrand!ttitudes!ttitudes

!d#ertising!d#ertising

BudgetBudget

$nformation$nformation

SearchSearch

PurchasePurchase

%ielihood%ielihood

'is'is

E("erienceE("erience

Structural EquationsStructural EquationsModelingModeling

"irele Phone Service"irele Phone Service


6/30

Structural Equations Modeling (SEMStructural Equations Modeling (SEM))

)*o Ste"s:)*o Ste"s:

++ Confirm measurement model -C.!/Confirm measurement model -C.!/ == C.! assessesC.! assesses

relia0ilit1 and #alidit1 of the modelrelia0ilit1 and #alidit1 of the model22s constructss constructs

CB3SEM 4 must achie#e fit to mo#e to 5CB3SEM 4 must achie#e fit to mo#e to 5ndndste" P%S3ste" P%S3

SEM 4 confirm measurement 0efore e(aminingSEM 4 confirm measurement 0efore e(amining

structural model -5structural model -5ndndste"/ste"/

55 E#aluate structuralE#aluate structuralmodel -SEM/model -SEM/ == SEM determinesSEM determines

*hether h1"othesi6ed relationshi"s e(ist 0et*een*hether h1"othesi6ed relationshi"s e(ist 0et*een

the constructsthe constructs

$n de#elo"ing models to test using C.!7SEM,$n de#elo"ing models to test using C.!7SEM,

researchers dra* u"on theor1, "rior e("erience,researchers dra* u"on theor1, "rior e("erience,

e("ert 8udgment, and research o08ecti#es to identif1e("ert 8udgment, and research o08ecti#es to identif1

and de#elo" h1"otheses a0out relationshi"s 0et*eenand de#elo" h1"otheses a0out relationshi"s 0et*een

multi"le inde"endent and de"endent #aria0lesmulti"le inde"endent and de"endent #aria0les


7/30

%-SEM '%ovariance-(aed SEM)%-SEM '%ovariance-(aed SEM)

* tatitical o(+ective to reroduce* tatitical o(+ective to reroduce

the theoretical covariance #atri,the theoretical covariance #atri,

without /ocuin! on elained variance.without /ocuin! on elained variance.

PLS-SEM 'Partial Leat Square SEM)PLS-SEM 'Partial Leat Square SEM)* tatitical o(+ective to #ai#i0e* tatitical o(+ective to #ai#i0ethe elained variance o/ thethe elained variance o/ the

endo!enou latent contructendo!enou latent contruct

'deendent varia(le).'deendent varia(le).


8/30

%-SEM%-SEM * tatitical o(+ective '!oodne o/* tatitical o(+ective '!oodne o/

1t) #ini#i0e the di2erence (etween the1t) #ini#i0e the di2erence (etween theo(erved covariance #atri and theo(erved covariance #atri and the

eti#ated covariance #atri.eti#ated covariance #atri.

3eearch o(+ective: tetin! and con1r#ation where3eearch o(+ective: tetin! and con1r#ation whererior theor4 i tron!.rior theor4 i tron!.

' 5u#e nor#alit4 o/ data ditri(ution,5u#e nor#alit4 o/ data ditri(ution,

ho#ocedaticit4, lar!e a#le i0e, etc.ho#ocedaticit4, lar!e a#le i0e, etc.

' 55 6/ull in/or#ation aroach7 which #ean #all6/ull in/or#ation aroach7 which #ean #allchan!e in #odel eci1cation can reult inchan!e in #odel eci1cation can reult in

u(tantial chan!e in #odel 1t.u(tantial chan!e in #odel 1t.


9/30

PLS-PLS-SEMSEM ** tatitical o(+ective #ai#i0etatitical o(+ective #ai#i0ethe elained 'redicted) variance o/ thethe elained 'redicted) variance o/ the

deendent varia(le.deendent varia(le.3eearch3eearcho(+ective: theor4 develo#ent ando(+ective: theor4 develo#ent and

rediction.rediction.

'8or#alit4 o/ data ditri(ution8or#alit4 o/ data ditri(ution

notnot

au#ed.au#ed.

' 9ood olution with #aller a#le i0e.9ood olution with #aller a#le i0e.

' Meaure#ent #odel:Meaure#ent #odel:

%an (e ued with /ewer indicator varia(le ' or%an (e ued with /ewer indicator varia(le ' or

;) er contruct.;) er contruct. O< to have ordinal caled quetion.O< to have ordinal caled quetion.

%an include a lar!er nu#(er o/ indicator varia(le%an include a lar!er nu#(er o/ indicator varia(le'%-SEM olution unli=el4 with >?@ ite#).'%-SEM olution unli=el4 with >?@ ite#).

' Pre/erred alternative with /or#ative contruct.Pre/erred alternative with /or#ative contruct.


10/30

PLS Path ModelPLS Path Model

Ste & ; are co#(ined,Ste & ; are co#(ined,

(ut till loo= at(ut till loo= at#eaure#ent theor4 1rt#eaure#ent theor4 1rt

(e/ore #ovin! to(e/ore #ovin! to

tructural #odeltructural #odel

ae#ent.ae#ent.


11/30

(se CB-SEM when)(se CB-SEM when)

'*he goal is theor+ testing, theor+ oniration, or*he goal is theor+ testing, theor+ oniration, or

the o/arison o alternati0e theories.the o/arison o alternati0e theories.'Strutural odel has non-reursi0e relationshi/s.Strutural odel has non-reursi0e relationshi/s.

'"esearh reuires a gloal goodness o it riterion."esearh reuires a gloal goodness o it riterion.

"ules o *hu) &S-SEM or CB-SEM"ules o *hu) &S-SEM or CB-SEM

"hich SEM 5roach Should e Aed$"hich SEM 5roach Should e Aed$


12/30

"ules o *hu) &S-SEM or CB-SEM%"ules o *hu) &S-SEM or CB-SEM%

(se &S-SEM when)(se &S-SEM when)

'*he goal is /rediting 3e+ target onstruts.*he goal is /rediting 3e+ target onstruts.'4orati0e onstruts are inluded in the strutural odel.4orati0e onstruts are inluded in the strutural odel.

Note that orati0e easures an also e used with CB-SEM,Note that orati0e easures an also e used with CB-SEM,

ut doing so reuires onstrut s/eiiation odiiationsut doing so reuires onstrut s/eiiation odiiations

5e.g., the onstrut ust inlude oth orati0e and releti0e5e.g., the onstrut ust inlude oth orati0e and releti0eindiators to eet identiiation reuireents 6 M!M!Cindiators to eet identiiation reuireents 6 M!M!C

easureent odel.easureent odel.'*he strutural odel is o/le8 5an+ onstruts and an+*he strutural odel is o/le8 5an+ onstruts and an+

indiators.indiators.

'*he sa/le sie is sall and:or the data is not-norall+*he sa/le sie is sall and:or the data is not-norall+

distriuted.distriuted.'*he /lan is to use latent 0ariale sores in suseuent*he /lan is to use latent 0ariale sores in suseuent

anal+ses.anal+ses.


13/30

Should Bou Ae SEM In Bour 3eearch$Should Bou Ae SEM In Bour 3eearch$Journal reviewer rate SEM aer #ore /avora(l4Journal reviewer rate SEM aer #ore /avora(l4

on =e4 #anucrit attri(ute . .on =e4 #anucrit attri(ute . . ..

Mean SoreMean Sore

#ttriutes#ttriutes SEMSEM No SEMNo SEM /-0alue/-0alue

*o/i "ele0ane*o/i "ele0ane ;.2;.2

Cone/tualiationCone/tualiation .?1=.?1=

Writing ualit+Writing ualit+


14/30

Mareting -9air et al 5+5a/

M$S; -'ingle et al 5+5/

Strategic Mgmt-'ingle et al 5+50/

Mgmt !ccounting- 5++ 5

Year

Cumulati#enum0erofarticles

9air, ? ., M Sarstedt, C M 'ingle, and ? ! Mena -5+5a/ !n !ssessment of the @se of Partial %east SAuares Structural EAuation

Modeling in Mareting 'esearch, ?ournal of the !cadem1 of Mareting Science, -/, +3

9air, ? ., M Sarstedt, ) Pie"er, and C M 'ingle -5+50/ )he @se of Partial %east SAuares Structural EAuation Modeling in Strategic

Management 'esearch: ! 'e#ie* of Past Practices and 'ecommendations for .uture !""lications, Long Range Planning, D-D7/, 53


15/30

+D!ll rights reser#ed F Cannot 0e re"roduced ordistri0uted *ithout e("ress *ritten "ermission from


16/30

..

..

..

#ll rights reser0ed F. Cannot e re/rodued or distriuted without e8/ress written /erission ro

&rentie-all, MGraw-ill, Sage, Sart&S, and session /resenters.


17/30

..

!nnerModelH$uterModel%%!nnerModelH$uterModel%%


18/30

5 PLS ath #odel conit o/ two ele#ent:5 PLS ath #odel conit o/ two ele#ent:

FirtFirt, there i a, there i a tructural #odeltructural #odel 'alo re/erred to a'alo re/erred to a

the inner #odel in the contet o/ PLS-SEM) thatthe inner #odel in the contet o/ PLS-SEM) thatrereent the contruct 'circle or oval). Cherereent the contruct 'circle or oval). Che

tructural #odel alo dila4 the relationhitructural #odel alo dila4 the relationhi

'ath) (etween the contruct.'ath) (etween the contruct.

SecondSecond, there are the, there are the #eaure#ent #odel#eaure#ent #odel 'alo'alore/erred to a the outer #odel in PLS-SEM) o/ there/erred to a the outer #odel in PLS-SEM) o/ the

contruct that dila4 the relationhi (etween thecontruct that dila4 the relationhi (etween the

contruct and the indicator varia(le 'rectan!le).contruct and the indicator varia(le 'rectan!le).

Chere are two t4e o/ contruct in a SEM: theChere are two t4e o/ contruct in a SEM: theeo!enou latent varia(le 'i.e., thoe contructeo!enou latent varia(le 'i.e., thoe contruct

that elain other contruct in the #odel) and thethat elain other contruct in the #odel) and the

endo!enou latent varia(le 'i.e., thoe contructendo!enou latent varia(le 'i.e., thoe contruct

that are (ein! elained in the #odel).that are (ein! elained in the #odel).#ll rights reser0ed F. Cannot e re/rodued or distriuted without e8/ress written /erission ro&rentie-all, MGraw-ill, Sage, Sart&S, and session /resenters.


19/30

Path #odelPath #odel dia!ra# ued to viuall4 dila4 the dia!ra# ued to viuall4 dila4 theh4othee and varia(le relationhi that are ea#inedh4othee and varia(le relationhi that are ea#ined

when SEM i alied.when SEM i alied.

%ontruct%ontruct varia(le that are not directl4 #eaured) varia(le that are not directl4 #eaured)are rereented in ath #odel a circle or oval 'B toare rereented in ath #odel a circle or oval 'B to

BD).BD).

IndicatorIndicator alo re/erred to a ite# or #ani/et alo re/erred to a ite# or #ani/etvaria(le, are the directl4 #eaured ro4 varia(le thatvaria(le, are the directl4 #eaured ro4 varia(le that

contain the raw data. Che4 are rereented in ath #odelcontain the raw data. Che4 are rereented in ath #odel

a rectan!le ' to ?).a rectan!le ' to ?).

PathPath relationhi (etween contruct, and (etween relationhi (etween contruct, and (etweencontruct and their ai!ned indicator, hown a arrow.contruct and their ai!ned indicator, hown a arrow.

In PLS-SEM, the arrow are alwa4 in!le-headed, thuIn PLS-SEM, the arrow are alwa4 in!le-headed, thu

rereentin! directional relationhi. Sin!le-headedrereentin! directional relationhi. Sin!le-headed

arrow are conidered a redictive relationhi, and witharrow are conidered a redictive relationhi, and with

tron! theoretical uort, can (e interreted a caualtron! theoretical uort, can (e interreted a caual#ll rights reser0ed F. Cannot e re/rodued or distriuted without e8/ress written /erission ro



20/30

Error ter#Error ter# Che error ter# 'e.!., e or eG Ehi(it .D) Che error ter# 'e.!., e or eG Ehi(it .D)are connected to the 'endo!enou) contruct andare connected to the 'endo!enou) contruct and

'reectivel4) #eaured varia(le (4 in!le-headed arrow.'reectivel4) #eaured varia(le (4 in!le-headed arrow.

Error ter# rereent the unelained variance when athError ter# rereent the unelained variance when ath

#odel are eti#ated.#odel are eti#ated.

In Ehi(it .D, error ter# e to e? are on thoe indicatorIn Ehi(it .D, error ter# e to e? are on thoe indicator

whoe relationhi !o /ro# the contruct to the indicatorwhoe relationhi !o /ro# the contruct to the indicator

'i.e., reectivel4 #eaured indicator). In contrat, the'i.e., reectivel4 #eaured indicator). In contrat, the/or#ativel4 #eaured indicator to , where the/or#ativel4 #eaured indicator to , where the

relationhi !oe /ro# the indicator to the contruct, do notrelationhi !oe /ro# the indicator to the contruct, do not

have error ter#.have error ter#.

Che tructural #odel alo contain error ter#. In Ehi(itChe tructural #odel alo contain error ter#. In Ehi(it.D, 0 and 0D are aociated with the endo!enou latent.D, 0 and 0D are aociated with the endo!enou latent

varia(le B and BD 'note that error ter# on contruct andvaria(le B and BD 'note that error ter# on contruct and

#eaured varia(le are la(eled di2erentl4). In contrat, the#eaured varia(le are la(eled di2erentl4). In contrat, the

eo!enou latent varia(le that onl4 elain other latenteo!enou latent varia(le that onl4 elain other latent

varia(le in the tructural #odel do not have an error ter#.varia(le in the tructural #odel do not have an error ter#.

..

#ll rights reser0ed F. Cannot e re/rodued or distriuted without e8/ress written /erission ro



21/30

Refective (Scale) Versus FormativeRefective (Scale) Versus Formative

(Index) Operationalization o !onstructs(Index) Operationalization o !onstructs

! central research Auestion in social science research, "articularl1 mareting,! central research Auestion in social science research, "articularl1 mareting,

management & M$S, focuses on the o"erationali6ation of com"le( constructs:management & M$S, focuses on the o"erationali6ation of com"le( constructs:

!re indicators causing or 0eing caused 01!re indicators causing or 0eing caused 01

the latent #aria0le7construct measured 01 themthe latent #aria0le7construct measured 01 them

Construct

$ndicator + $ndicator 5 $ndicator

Construct

$ndicator + $ndicator 5 $ndicator

Changes in the latent #aria0leChanges in the latent #aria0le

directl1 cause changes in thedirectl1 cause changes in the

assigned indicatorsassigned indicators

Changes in one or more ofChanges in one or more of

the indicators causesthe indicators causes

changes in the latent #aria0lechanges in the latent #aria0le


22/30


23/30

Ea#le: 3eective v. For#ative "orld iewEa#le: 3eective v. For#ative "orld iew

Krun=enneKrun=enne

Consum"tion of 0eerConsum"tion of 0eer

Consum"tion of *ineConsum"tion of *ine

Consum"tion of hardConsum"tion of hard

liAuorliAuor


24/30

Basic ifference Bet*een 'eflecti#e andBasic ifference Bet*een 'eflecti#e and

.ormati#e Measurement !""roaches.ormati#e Measurement !""roaches

HHWhereas reflecti#e indicators are essentiall1 interchangea0le -andWhereas reflecti#e indicators are essentiall1 interchangea0le -andtherefore the remo#al of an item does not change the essentialtherefore the remo#al of an item does not change the essential

nature of the underl1ing construct/, *ith formati#e indicatorsnature of the underl1ing construct/, *ith formati#e indicators

Iomitting an indicator is omitting a "art of the construct2JIomitting an indicator is omitting a "art of the construct2J

5A!#M#N*$&$($S:W!NI$4E", 2??1, /. 2715A!#M#N*$&$($S:W!NI$4E", 2??1, /. 271

*he*he reflecti#e measurementreflecti#e measurementa//roaha//roah

ouses onouses on ma(imi6ingma(imi6ingthethe o#erla"o#erla"

etween interhangeale indiatorsetween interhangeale indiators

*he*he formati#e measurementformati#e measurementa//roaha//roah

generall+generall+ minimi6esminimi6esthethe o#erla"o#erla"

etween o/leentar+ indiatorsetween o/leentar+ indiators

ConstructConstruct

domaindomain

ConstructConstruct

domaindomain


25/30

E(ercise: Satisfaction in 9otels as .ormati#eE(ercise: Satisfaction in 9otels as .ormati#e

and 'eflecti#e K"erationali6ed Constructsand 'eflecti#e K"erationali6ed Constructs

$ am comforta0le *ith$ am comforta0le *ith

this hotelthis hotel

$ a""reciate this hotel$ a""reciate this hotel

$ am looing for*ard to$ am looing for*ard to

sta1ing o#ernight insta1ing o#ernight inthis hotelthis hotel

)he rooms)he roomsI furnishingsI furnishings

are goodare good

)he rooms are Auiet)he rooms are Auiet

)he hotel)he hotelIs "ersonnelIs "ersonnel

are friendl1are friendl1

)he hotel)he hotel2s ser#ice is2s ser#ice is

goodgood)he hotel)he hotel2s cuisine is2s cuisine is

goodgood

)he hotel)he hotel2s recreation2s recreation

offerings are goodofferings are good)he rooms are clean)he rooms are clean

)aing e#er1thing into)aing e#er1thing into

account, $ am satisfiedaccount, $ am satisfied

*ith this hotel*ith this hotel

)he hotel is lo*3"riced)he hotel is lo*3"ricedSatisfactionSatisfaction

*ith 9otels*ith 9otels


26/30

4orati0e Construts H *wo *+/es4orati0e Construts H *wo *+/es

1.1. Co/osite 5orati0e onstrutsCo/osite 5orati0e onstrutsHH indiators o/letel+indiators o/letel+

deterine thedeterine the JlatentK onstrut. *he+ share siilarities eauseJlatentK onstrut. *he+ share siilarities eause

the+ deine a o/osite 0ariale ut a+ or a+ not ha0ethe+ deine a o/osite 0ariale ut a+ or a+ not ha0e

one/tual unit+. !n assessing 0alidit+, indiators are notone/tual unit+. !n assessing 0alidit+, indiators are not

interhangeale and should not e eliinated, eause reo0inginterhangeale and should not e eliinated, eause reo0ing

an indiator will li3el+ hange the nature o the latent onstrut.an indiator will li3el+ hange the nature o the latent onstrut.

2.2. Causal onstrutsCausal onstrutsHH indiators ha0e one/tual unit+ in thatindiators ha0e one/tual unit+ in thatall 0ariales should orres/ond to the deinition o the one/t. !nall 0ariales should orres/ond to the deinition o the one/t. !n

assessing 0alidit+ soe o the indiators a+ eassessing 0alidit+ soe o the indiators a+ e

interhangeale, and also an e eliinated.interhangeale, and also an e eliinated.

Bollen, I.#. 52?11, E0aluating Eet, Co/osite, and Causal !ndiators inBollen, I.#. 52?11, E0aluating Eet, Co/osite, and Causal !ndiators in

Strutural Euations Models,Strutural Euations Models, MIS QuarterlyMIS Quarterly, Vol. , No. 2, //. 9-


27/30


28/30

..

Statistial /ower assued 6 =?Statistial /ower assued 6 =?

! di t SEM M d l C t t! di t SEM M d l C t t


29/30

!ndiators or SEM Model Construts!ndiators or SEM Model Construts

E d d 3 i M d lE t d d 3 t ti M d l


30/30

Etended 3eutation ModelEtended 3eutation Model

%ontruct%ontruct

Introduction to PLS-SEM.ppt

Documents