exploratory factor analysis 1206420594617863 4

8/10/2019 Exploratory Factor Analysis 1206420594617863 4

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Lecture 5Survey Research & Design in Psychology

James Neill, 2014

Exploratory Factor Analysis



2

Overview

1. What is actor analysis!

2. "ssum#tions$. Ste#s % #rocess

4. 'am#les(. Summary



3

1. Wi)iversity *201$+. " glossary. -nline/

2. eavers et al. *201$+. Practical consierations or using

e'#loratory actor analysis in eucational research. -article nline/

$. 3oitt & 5ramer *2011+.

5h $06 actor analysis6 Sim#liying com#le' ata. -7e't8oo)/

4. a8rigar et al. *1999+.

valuating the use o e'#loratory actor analysis in#sychological research. -article eReserve/

(. 7a8achnic) & iell *2001+.Princi#al com#onents an actor analysis.

-cha#ter eReserve/

Readings



4

What is actor analysis!



5

What is actor analysis!

1. What is actor analysis!

2. Pur#ose$. 3istory

4. 7y#es(. :oels



6

" gala'y is li)e a ;actor< ithin theuniverse.

7he variance o many varia8les, coul 8e largelye'#laine 8y a smaller num8er o unerlyingactors ue to the corelations *or clustering

together+ o several varia8les.



5once#tual moel o actor analysis

" uses correlations

among many items tosort relate varia8lesinto clusters calle

actors.

actor 1

actor 2


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Factor analysis###

• is use to ientiy clusters o intercorrelate varia8les *calle=actors=+.

• is a family

o multivariate statisticaltechni>ues or e'aminingcorrelations amongst varia8les.

? em#irically tests theoretical atastructures.

? is commonly use in #sychometric

instrument evelo#ment.


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%urposes+ 'heory develop(ent

? @nvestigation o the unerlyingcorrelational #attern share 8ythe varia8les in orer to testtheoretical moels e.g., 3o many#ersonality actors are there! @sintelligence general or multi#le!

? 7he goal is to aress atheoretical >uestion *as o##ose

to calculating actor scores+.


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%urposes+ )ata reduction

• Sim#liication o the ata structure 8y revealing a smaller num8er ounerlying actors *#art o

#sychometrics+• 3el#s to eliminate or ientiy items

or im#rovement6

• reunant varia8les• unclear varia8les• irrelevant varia8les

? Aeas to calculating actor scores


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,istory o actor analysis? @nvente 8y 5harles S#earman

*1904+? Bsage ham#ere 8y onerousness o

han calculation? Since the avent o com#uters,usage has thrive, es#. or6

C 7heory e.g., etermining the structure o#ersonality or intelligence

C Practice e.g., 10,000s o #sychological

screening & measurement tests



" E Exploratory Factor Analysis

• e'#lores & summarises unerlying

correlational structure or a ata set5" E -onir(atory Factor Analysis

• tests the correlational structure o a

ata set against a hy#othesisestructure an rates the ;gooness o it<

'wo (ain types o actor analysis



7his *introuctory+ lecture ocuseson Exploratory Factor Analysis*recommene or unergrauate

level+.

-onir(atory Factor Analysis*an Structural >uation :oeling+ isgenerally #reerre, 8ut is moreavance, so is recommene orgrauate%#roessional level.

Exploratory actor analysis



actor 1 actor 2 actor $

-onceptual (odel . /i(ple (odel

? e.g., 12 items may =ta#= $ unerlying actors

? actors consist o relatively

homogeneous varia8les.



Eysenc1s 3 personality actors

'traversion%introversion

Neuroticism Psychoticism

talkativeshy sociable

funanxious

gloomyrelaxed

tense

unconventional

nurturingharshloner

e.g., 12 items hich measure$ unerlying imensions

o #ersonality


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Fuestion 1

-onceptual (odel . /i(ple (odel

Fuestion 2

Fuestion $

Fuestion 4

Fuestion (

actor 1

actor 2

actor $

ach >uestion loas onto only one actor


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Fuestion 1

-onceptual (odel . -o(plex (odel

Fuestion 2

Fuestion $

Fuestion 4

Fuestion (

actor 1

actor 2

actor $

ach >uestions may loa onto more than one actor



19

5once#tual moel C "rea #lot

5orrelation 8eteenG1 an G2

" theoretical actorhich is #artly

measure 8y thecommon as#ects o

G1 an G2



20

Nine factors?(independent

items)

One factor?

Three factors?

3o many actors!



2&

3o many imensions o #ersonalityare there C an hat are they!

Exa(ple+ %ersonality

;ig (<!? Neuroticism

? 'traversion

? "greea8leness

? #enness

? 5onscientiousness

ysenc)=s $!? 'traversion

? Neuroticism

? Psychoticism

How could you decide between 3 or

5 personality factors?



22

@s intelligence 8etter escri8e as6

? one glo8al actor *g+ or

? several s#eciic actors *e.g., ver8al,s#atial, mathematical, social,)inaesthetic+!

Exa(ple+ ntelligence

How could you decide which modelis supported by evidence?



23

'am#le6 Whatare the essentialacial eatures ore'#ression an

communication!

*@vancevic et al., 200$+

'am#le6 ssential acial eatures



24

Si' orthogonal *ine#enent+ actors,re#resent HI.( o the total varia8ility inacial recognition *in orer o im#ortance+

*@vancevic et al., 200$+6

? u##erli#

? eye8ro#osition

? noseith

? eye#osition

? eye%eye8rolength

? aceith

Exa(ple+ Essential acial eatures



25

Assu(ptions



20

Assu(ptions

1. Kar8age@nKar8ageut

2. Sam#le siLe

$. Aevels o measurement4. Normality

(. AinearityI. utliers

H. actora8ility



2

Garage. In. → Garage.

Out

? Screen the ata

? Bse varia8les that theoretically ;go together<



2"

Assu(ption testing+/a(ple si6e

Some guielines6

• :in.6 N M ( cases #er varia8le● e.g., 20 varia8les, shoul have M 100 cases *16(+

• @eal6 N M 20 cases #er varia8le● e.g., 20 varia8les, ieally have M 400 cases *1620+

• 7otal N M 200 #reera8le



2$

Assu(ption testing+/a(ple si6e

5omrey an Aee=s *1992+ guielines6

(0 E very #oor,

100 E #oor,200 E air,

$00 E goo,

(00 E very goo

1000 E e'cellent



30

"ssum#tion testing6 Sam#le siLe

a8rigar et al. *1999+



3&

Assu(ption testing+Level o (easure(ent

• "ll varia8les must 8e suita8le orcorrelational analysis

i.e., they shoul 8e ratio%metric ata or atleast Ai)ert ata ith several interval levels.



32

Assu(ption testing+7or(ality

• " is generally ro8ust to minorviolation o assum#tions onormality.

• @ the varia8les are normally

istri8ute then the solution isenhance.



33

Assu(ption 'esting+Linearity

• ecause " is 8ase oncorrelations 8eteen varia8les, it isim#ortant to chec) there are linearrelations amongst the varia8les*i.e., chec) scatter#lots+



34

Assu(ption testing+Outliers

? " is sensitive to outlying cases

Civariate outliers*e.g., chec) scatter#lots+

C:ultivariate outliers*e.g., :ahalano8is istance+

? @entiy outliers, then remove ortransorm



30

-lassroo( ehaviour ite(s

1. 5annot concentrate O can concentrate

2. 5urious & en>uiring O little curiousity

$. Perseveres O lac)s #erseverance4. @rrita8le O eventem#ere

(. asily e'cite O not easily e'cite

I. Patient O emaningH. asily u#set O contente



3

. 5ontrol O no control

9. Relates armly to others O isru#tive

10.Persistent O rustrate

11. Diicult O easy

12.Restless O rela'e

1$.Aively O settle

14.Pur#oseul O aimless

1(.5oo#erative O is#utes

-lassroo( ehaviour ite(s



38

5lassroom 8ehaviour items

Assu(ption testing+



3$

Assu(ption testing+Factoraility

5hec) the actora8ility o the correlationmatri' *i.e., ho suita8le is the ata oractor analysis!+ 8y one or more o the

olloing methos6? 5orrelation matri' correlations M .$!

? "ntiimage matri' iagonals M .(!

? :easures o sam#ling ae>uacy *:S"s+! C artletts sig.!

C Q: M .( or .I!

"ssum#tion testing6



40

"ssum#tion testing6actora8ility *5orrelations+

-orrelation 8atrix

1.000 .H1H .H(1 .((4 .429

.H1H 1.000 .2I .4H2 .2I2

.H(1 .2I 1.000 .(0H .$11

.((4 .4H2 .(0H 1.000 .I10

.429 .2I2 .$11 .I10 1.000

5N5&N7R"7&S

5BR@BS

P&RS&&R&S

&&N7&:P&R&D

PA"5@D

5orrelation

5N5&N

7R"7&S 5BR@BS

P&RS&

&R&S

&&N7&

:P&R&D PA"5@D

"re there S: correlations over .$! @ so,#rocee ith "

7a)es some eort ith a large num8er ovaria8les, 8ut is the most =accurate=

Assu(ption testing+



4&

? 'amine the iagonal values on the antiimage correlation matri'

? Note varia8les ith correlations lessthan .( or e'clusion rom the analysis Cthey a##ear to lac) suicient correlationith other varia8les

? :eium eort, reasona8ly accurate

Assu(ption testing+Factoraility+ Anti.i(age

correlation (atrix



42

"nti@mage correlation matri'

:a)e sure to loo) at the antiimage5RRA"7@N matri'

Assu(ption testing+



43

? Klo8al iagnostic inicators correlation matri' is actora8le i6

Cartletts test o s#hericity issigniicant an%or

CQaiser:ayer l)in *Q:+ measureo sam#ling ae>uacy M .( or .I

? Fuic)est metho, 8ut least relia8le

Assu(ption testing+Factoraility+ 8easures o

sa(pling ade9uacy



44

"ssum#tion testing6actora8ility

/u((ary+



45

/u((ary+8easures o sa(pling ade9uacy

Dra on one or more o theolloing to hel# etermine theactora8ility o a correlation matri'6

1. Several correlations M .$!

2. "ntiimage correlation matri'

iagonals M .(!$. artletts test signiicant!

4. Q: M .( to .I!*e#ens on hose rule o thum8+



40

/teps : process

/teps : process



4

/teps : process1. 7est assum#tions

2. Select ty#e o analysis$. Determine no. o actors

*igen alues, Scree #lot, variance e'#laine+

4. Select items *chec) actor loaings to ientiy hich items 8elongin hich actor ro# items one 8y one re#eat+

(. Name an eine actorsI. 'amine correlations amongst actors

H. "nalyse internal relia8ility

. 5om#ute com#osite scores

' EFA



4"

'ype o EFA+Extraction (ethod+ %- vs# %AF

7o main a##roaches to "6

? "nalyses shared variance6Princi#le "'is actoring *P"+

? "nalyses all variance6

Princi#le 5om#onents *P5+



4$

%rincipal axis actoring ;%AF<

? Bse to uncover the structure o anunerlying set o p original varia8les

? :ore theoretical

? "nalyses only share variance

*i.e. leaves out uni>ue variance+



5*

%rincipal co(ponents ;%-<

? :ore common

? :ore #ractical

? Bse to reuce ata to a set o actorscores or use in other analyses

? "nalyses all the variance in eachvaria8le



51

7otal variance o a varia8le

Princi#al 5om#onents *P5+Princi#al "'is actoring *P"+



52

? ten there is little ierence in thesolutions or the to #roceures.

? @ unsure, chec) your ata using

8oth techni>ues

? @ you get ierent solutions or the

to methos, try to or) out hyan ecie on hich solution ismore a##ro#riate

%- vs# %AF

- liti



53

-o((unalities

? ach varia8le has a communality E C the #ro#ortion o its variance

e'#laine 8y the e'tracte actors

? Ranges 8eteen 0 an 1

? @ communality or a varia8le is lo

*e.g., T .(, consier e'tracting moreactors or removing the varia8le+



55

5ommunalities 2



50

Explained variance

? " goo actor solution is one thate'#lains the most variance ith

the eest actors

? Realistically, researchers are

ha##y ith (0H( o thevariance e'#laine



57

'#laine variance

$ actors e'#lain H$.(

o the variance in the1( classroom 8ehaviouritems C very useulU

Eigen values ;E=s<



5"

Eigen values ;E=s<

? ach actor has an hich inicates theamount o variance each actor accounts or.

? s or successive actors have loer values.

? Rule o thum86 igen values over 1 areVsta8le *Qaiser=s criterion+.

? s can also 8e e'#resse as s.

? 7otal o all s is the num8er o varia8les.ach varia8le contri8utes a variance o one.s are then allocate to actors accoring toamount o variance e'#laine.



59

'#laine variance

7he s range 8eteen

0.1I an 9.$(. 7oactors satisie Qaiser=scriterion *s M 1+ 8utthe thir is .9$ an it

also a##ears to 8e auseul actor. 7here is aro# to the 4th actor .

/cree plot



0*

/cree plot

? " line gra#h o s.

? De#icts amount o variancee'#laine 8y each actor.

? 5uto6 Aoo) or here aitionalactors ail to a a##recia8ly to thecumulative e'#laine variance.

? 1st actor e'#lains the most variance.

? Aast actor e'#lains the least amount

o variance.

Scree #lot



61

Scree #lot

Aoo) or the =el8o=

3ere it inicates 2 or $ actors

&cree 'lot

Scree #lot



62

Scree #lot

)omponent Number

*

+

,

!

,-

,.

,"

,/

,0

,*

,+

,

,,

,!

-

.

"

/

0

*

+

,

1 i g

e n v a l u e

,!

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/

*

!

Scree #lot

$ actors! actors!

,ow (any actors!



03

,ow (any actors!

" subjective #rocess ... See) to

e'#lain ma'imum variance usingeest actors, consiering6

1. 7heory C hat is #reicte%e'#ecte!

2. igen alues M 1! *Qaisers criterion+

$. Scree Plot C here oes it ro# o!

4. @nter#reta8ility o last actor !

(. 7ry several ierent solutions!*consier " ty#e, rotation, o actors+

I. actors must 8e a8le to 8e meaningullyinter#rete & ma)e theoretical sense!

,ow (any actors!



04

,ow (any actors!

? "im or (0H( o variancee'#laine 8y 1%4 to 1%$ as manyactors as varia8les%items.

? Sto# e'tracting actors hen they nolonger re#resent useul%meaningulclusters o varia8les.

? Qee# chec)ing%clariying the meaning o each actor C ma)e sure to

e'amine the oring o each item.

nitial solution+



05

? actor loaings *As+ inicaterelative im#ortance o each item to

each actor. C@n the initial solution, each actor tries

;selishly< to gra8 ma'imum

une'#laine variance. C "ll varia8les ill ten to loa strongly

on the 1st actor

nitial solution+>nrotated actor structure

nitial solution



00

nitial solution .>nrotated actor structure

? actors areeightecom8inations o

varia8les

? " actor matri'shos varia8lesin ros anactors incolumns

nitial solution



0

1st actor e'tracte6

? est #ossi8le line o 8est it through

the original varia8les? See)s to e'#lain lion=s share o all

variance? " single actor, 8est summary o the

variance in the hole set o items


nitial solution



0"

? ach su8se>uent actor tries toe'#lain the ma'imum amount o

remaining une'#laine variance.? Secon actor is orthogonal to irst

actor see)s to ma'imise its on

eigen value *i.e., tries to go88le u# asmuch o the remaining une'#lainevariance as #ossi8le+




nitial solution+



*

t a so ut o>nrotated actor structure

? Selom see a sim#le unrotate actorstructure

? :any varia8les loa on 2 or more actors

? Some varia8les may not loa highly onany actors *chec)6 lo communality+

? Bntil the As are rotate, they are iicultto inter#ret.

? Rotation o the A matri' hel#s to in a

more inter#reta8le actor structure.

'wo asic types o actor rotation



&

'wo asic types o actor rotation

rthogonal

*SPSS arima'+minimises actor

covariation,#rouces actors hich

are uncorrelate

8li>ue

*SPSS 8limin+allos actors to

covary,allos correlations

8eteen actors

'wo asic types o



2

'wo asic types oactor rotation

1. rthogonalminimises actor covariation,

#rouces actors hich areuncorrelate

2. 8liminallos actors to covary, alloscorrelations 8eteen actors



3

Orthogonal vs# oli9ue rotations

? 5onsier #ur#ose o actor analysis? @ in ou8t, try 8oth

? 5onsier inter#reta8ility? Aoo) at correlations 8eteen

actors in o8li>ue solution

C @ M .$ then go ith o8li>ue rotation*M 10 share variance 8eteenactors+

t t ilit



4

nterpretaility

? "voi 8eing guie 8y actorloaings only C thin) careully 8e guie 8y theory ancommon sense in selectingactor structure.

? Xou must 8e a8le to unerstanan inter#ret a actor i youregoing to e'tract it.

t t ilit



5

nterpretaility

? 3oever, atch out or Vseeinghat you ant to see henevience might suggest a

ierent, 8etter solution.? 7here may 8e more than one

goo solutionU e.g., in #ersonality

C2 actor moel

C( actor moel

C1I actor moel

Factor loadings ? ite( selection



0


" actor structure is mostinter#reta8le hen61. ach varia8le loas strongly *M .40+ on

only one actor 2. ach actor shos $ or more strong

loaings more loaings E greater relia8ility

$. :ost loaings are either high or lo, eintermeiate values.

4. 7hese elements give a Vsim#le actorstructure.

-

Rotated -o(ponent 8atrixa

5 t



R

o t a t e d

a c t o r ( a t r i x

. % -

= a r i (

a x

.I1 .1( .2

.( .$10

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.HH .$H$ .2$H

.HH0 .$HI .$12

.I$ .20$

.2(9 .4$ .22$

.422 .H(I .29(

.2$4 .I4 .(2I

.$9 .(9$ .(10

.$2 .1(( .H9H

.2I .2I .H4

.$I2 .2( .H24

.240 .($0 .II2

.40( .$9I .I22

P&RS&&R&S

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PBRPS&,BA "57@@7X

5N5&N7R"7&S

SBS7"@N&D "77&N7@N

PA"5@D

5"A:

R&A"G&D

5:PA@"N7

S&A,5N7RAA&D

R&A"7&SW"R:AX

5N7&N7&D

5P&R"7@&&&N7&:P&R&D

5::BN@5"7@&

1 2 $

5om#onent

&'traction :etho6 Princi#al 5om#onent "nalysis.

Rotation :etho6 arima' ith Qaiser NormaliLation.

Rotation converge in I iterations.a.

Rotate actor matri' P5 8limin



78

%attern 8atrixa

.920 .1($

.4(

.H4 .10

.I2 .$$

.(9I .192 .1I

.9$

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.$9

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.$14 .II

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R&A"7&SW"R:AX

5N7&N7&D

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5:PA@"N7

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1 2 $

5om#onent

&'traction :etho6 Princi#al 5om#onent "nalysis.

Rotation :etho6 8limin ith Qaiser NormaliLation.

TaskOrientation

&ociability

&ettledness

Rotate actor matri' P5 8limin

$ l t



79

$ #lot



"*

• are min. E 2

• Recommene min. E $

• :a'. E unlimite

• :ore items6

Y Z relia8ility

Y Z =rouneness=Y Aa o iminishing returns

• 7y#ically E 4 to 10 is reasona8le

,ow (any ite(s per actor!



"2


5omrey & Aee=s *1992+ guielineor #rimary *target+ actorloaings6

M .H0 e'cellentM .I$ very goo

M .(( goo

M .4( air

M .$2 #oor




"3


5uto or acce#ta8le loaings6

? Aoo) or ga# in loaings e.g., ..H.I.$.2

? ut also consier hether actorcan 8e inter#rete a8ove 8ut not8elo cuto.

Other considerations+



"4

Other considerations+7or(ality o ite(s

? 5hec) the item escri#tives.

? 7he more normally istri8ute theitem scores, the 8etter theistri8ution o the com#ositescores.

C e.g. i to items have similar actorAoaings an Relia8ility analysis,consier selecting items hich illhave the least s)e an )urtosis.

Factor analysis in practice



"5


? 7o in a goo solution, consier6 C P5%P"

C arima'%8limin

? Range o #ossi8le actor structures,e.g., or 2, $, 4, (, I, an H actors

? 7hus, the researcher oul

normally conuct many initial "s8eore eciing on a #ro8a8lestructure.




"0

• liminate #oor items one at a time,retesting the #ossi8le solutions

• 5hec) actor structure across su8

grou#s *e.g., gener+ i there issuicient ata *avance+

• Xou ill #ro8a8ly come u# ith a

ierent solution rom someoneelseU

• 5hec)%consier relia8ility analysis

*ne't lecture+




"

Exa(ple

Exa(ple+ -ondo( use



""

Exa(ple+ -ondo( use

? 7he 5onom Bse Selicacy

Scale *5BSS+ as aministere to44H multicultural college stuents*ar)ley & urns, 2000+.

? P5 " ith a arima' rotation.

? 7hree actors ere e'tracte6

1. "##ro#riation

2. Se'ually 7ransmitte Diseases

$. Partners= Disa##roval




"$


20/3 feel confident 3 could gracefully remove and dispose of acondom after sexual intercourse

2/,

3 feel confident 3 could remember to carry a condom 4ith

me should 3 need one

2/03 feel confident 3 could purchase condoms 4ithout feelingembarrassed

2"03 feel confident in my ability to put a condom on myself ormy partner

F5Factor ,6 7ppropriation # ac8uisition and useof a condom (α E .HI+




$*

2.!

3 4ould not feel confident suggesting using condoms 4ith ane4 partner because 3 4ould be afraid he or she 4ould think3 thought they had a sexually transmitted disease

2./

3 4ould not feel confident suggesting using condoms 4ith ane4 partner because 3 4ould be afraid he or she 4ould think3 have a sexually transmitted disease

2"

3 4ould not feel confident suggesting using condoms 4ith ane4 partner because 3 4ould be afraid he or she 4ould think

39ve had a past homosexual experience

F5Factor 6 &exually Transmitted :iseases #

&tigma associated 4ith &T:s (α E .$+





$&

20.

3f my partner and 3 4ere to try to use a condom and did notsucceed; 3 4ould feel embarrassed to try to use one again(e2g2 not being able to unroll condom; putting it on

back4ards or a4k4ardness)

2/03f 3 4ere unsure of my partner9s feelings about usingcondoms 3 4ould not suggest using one

2"+3f 3 4ere to suggest using a condom to a partner; 3 4ould feelafraid that he or she 4ould reect me

F5

Factor +6 'artner9s reaction # students9 partners9 feelings about condoms (α E .

II+




$2

/u((ary

/u((ary+ What is actor analysis



$3

/u((ary+ What is actor analysis

? actor analysis is a amily omultivariate correlational ataanalysis methos or summarising

clusters o covariance.? " summarises correlations amongst items.

? 7he common clusters *calleactors+ are summary inicators ounerlying uLLy constructs.

/u((ary+ Assu(ptions



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? Sam#le siLe

C ( cases #er varia8les*ieally 20 cases #er varia8le+

C N M 200? ivariate & multivariate outliers

? actora8ility o correlation matri'*:easures o Sam#ling "e>uacy+

? Normality enhances the solution

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$5

1. 7est assum#tions

2. Select ty#e o analysis$. Determine no. o actors

*igen alues, Scree #lot, variance e'#laine+

4. Select items *chec) actor loaings to ientiy hich items 8elongin hich actor ro# items one 8y one re#eat+

(. Name an eine actors

I. 'amine correlations amongst actors

H. "nalyse internal relia8ility

5om#ute com#osite scores

Ne't

lecture

/u((ary+ 'ypes o FA



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/u((ary+ 'ypes o FA

? P"6 7heoretical ata e'#loration

Cuses share variance

? P56 Data reuction Cuses all variance

? 5onsier trying 8oth ays

C "re solutions ierent! Why!

/u((ary+ Rotation



$

/u((ary+ Rotation

? rthogonal *arima'+

C #er#enicular vectors

? 8li>ue *8limin+ C angle vectors

? 5onsier trying 8oth ays C "re solutions ierent! Why!

/ F t t ti



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No. o actors to e'tract!

? @ns#ect s

C loo) or M 1 or suen ro#*ins#ect scree #lot+

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? @nter#reta8ility % theory

/u((ary+ Factor extraction

Reerences



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1. ar)ley, 7. W. Jr., & urns, J. A. *2000+.actor analysis o the 5onom Bse Selicacy Scale among multicultural college stuents

. Health Education Research, 15 *4+, 4(49.2. 5omrey, ". A. & Aee, 3. . *1992+. A first course in factor analysis. 3illsale, NJ6

rl8aum.

$. 3oitt, D. & 5ramer, D. *2011+. 5ha#ter $06 actor analysis6 Sim#liying com#le'ata. @n Introduction to statistics in psychology *##. $I2$H9+ *(th e.+. 3arlo, BQ6Pearson.

4. @vancevic, ., Qaine, ". Q., :5Ainin, .", & Sune, J. *200$+.actor analysis o essential acial eatures. @n the #roceeings o the 2(th@nternational 5onerence on @normation 7echnology @nteraces *@7@+, ##. 1H191,5avtat, 5roatia.

(. a8rigar, A. R., Wegener, D. 7., :ac5allum, R. 5., & Strahan, . J. *1999+.

valuating the use o e'#loratory actor analysis in #sychological research.sychological !ethods, "*$+, 2H2299.

I. rancis, K. *200H+. Introduction to ### for $indo%s& v. 15.' and 1".' %ith Notesfor #tudent%are *(th e.+. Syney6 Pearson ucation.

H. 7a8achnic), . K. & iell, A. S. *2001+. Princi#al com#onents an actor analysis.

@n (sing multivariate statistics. *4th e., ##. (2 I$$+. Neeham 3eights, :"6

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