3.Measurement Model

8/22/2019 3.Measurement Model

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Introduction to Structural Equation Modelling

Joaqun Alds-ManzanoUniversitat de ValnciaDepartment of Marketing

* [email protected]

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Measurement Model Reliability & Validity


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Psychometric properties: Reliability

Reliability An instrument is said to be reliableif it is shown to provide consistent

scores upon repeated administration, upon administration by alternateforms, and so forth.

But test-retest is not usually a feasible way to establish a scale reliability(time and economic constraints) so we rely in testing internalconsistency.

Internal consistency is the extent to which the individual items thatconstitute a test correlate with one another or with the test total

If items are highly correlated, that indicates a common LV is causingthem, not that is the LV we were trying to measure, so:

Reliability is a necessary but not sufficient condition to validity We use three reliability indicators:

Cronbachs alpha (Cronbach, 1951) Composite Reliability (Fornell & Larcker, 1981) Average Variance Extracted (Fornell & Larcker, 1981)

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Cronbachs Starting point: covariance matrix among indicators Its standardization is the correlation matrix Total scale variance: sum of C elements Total variance=Common variance + Specific variance (unique)

Common variance: Variance among items provoked by the latentvariable (shared by the items). If LV changes, items change.

Specific variance: caused by item measurement errors: C matrixdiagonal

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C =

!1

2!

12!

13! !

1k

!12

!2

2!

23! !

2k

!13

!23

!3

2! !

3k

" " " # "

!1k

!2k

!3k ! !k

2

!

"

#######

$

%

&&&&&&&


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Cronbachs

ais the part of the total variance that can be attributed to the latent variable(common variance)

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X1

X2

X3

Y

e1

e2

e3

Common variance sourceUnique variance source

! =

"y

2! !

i

2

"!

y

2=1!

!i

2

"!

y

2

Total variance: sum of all theelements of the covariancematrix Specific (unique) variance: sum ofthe elements in the diagonal of thecovariance matrix

Unique variance source

Unique variance source


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Cronbachs We must correct the effect of the different number of elements in the

numerator and denominator of the previous expression, as we have k2elements in the matrix but only kin its diagonal

So k2-kelements can be found in the numerator and kin the denominator.So to make the ratio express relative magnitudes and not the number ofcases, we correct by k2/ (k2k) that si k/(k-1)

a can also be expressed in terms of correlations more than variances andcovariances (Crocker y Algina, 1986):

where r is the average correlation among scale items

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! =

k

k!1 1!"i

2

""y2#

$%&

'(

! =k"

1+ k!1( )"


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Cronbachs Benchmark values for Cronbachs:

Nunnally & Bernstein (1994; p.265-6): a.70 Carmines & Zeller (1979; p.51): a.80

Estimates in excess of .90 are suggestive of item redundancy or inordinatescale length (ORourke, Hatcher & Stepanski, 2005)

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Psychometric properties: Reliability Cronbachs . An annotated example (ORourke, Hatcher & Stepanski, 2005)

HELPING OTHERS X1. Went out of my way to do a favour for a co-worker. 1 2 3 4 5 6 7 X2. Went out of my way to do a favour for a relative. 1 2 3 4 5 6 7 X3. Went out of my way to do a favour for a friend. 1 2 3 4 5 6 7 FINANCIAL GIVING

X4. Gave money to a religious charity. 1 2 3 4 5 6 7 X5. Gave money to a charity not associated with a religion 1 2 3 4 5 6 7 X6. Gave money to a panhandler. 1 2 3 4 5 6 7

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Helpingothers

Financialgiving

X1

X2

X3

X4

X5

X6


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Cronbachs . An annotated example (ORourke, Hatcher & Stepanski, 2005) I want to test the reliability of Helping others construct but I make a

mistake and add item X4 to the X1-X3 list

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CovarianceMatrix

X1X2X3X4

X11,9465X2,76331,2245

X31,2106,52241,4792

X4-,2604,1061-,05393,2147

CorrelationMatrix

X1X2X3X4

X11,0000

X2,49441,0000

X3,7134,38821,0000

X4-,1041,0535-,02471,0000

RELIABILITYANALYSIS-SCALE(ALPHA)

MeanStdDevCases1.X15,18001,395250,0

2.X25,40001,106650,0

3.X35,52001,216250,0

4.X43,64001,793050,0


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Cronbachs . An annotated example (ORourke, Hatcher & Stepanski, 2005)

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NofStatisticsforMeanVarianceStdDevVariables

Scale19,740012,44123,52724

ItemMeansMeanMinimumMaximumRangeMax/MinVariance4,93503,64005,52001,88001,5165,7652

ItemVariancesMeanMinimumMaximumRangeMax/MinVariance

1,96621,22453,21471,99022,6253,7821Inter-item

CovariancesMeanMinimumMaximumRangeMax/MinVariance,3814-,26041,21061,4710-4,6489,2783

Inter-item

CorrelationsMeanMinimumMaximumRangeMax/MinVariance

,2535-,1041,7134,8176-6,8534,0969

Total scale variance

Average correlation among items


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Cronbachs . An annotated example (ORourke, Hatcher & Stepanski, 2005)

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ReliabilityCoefficients4items

Alpha=,4904Standardizeditemalpha=,5759

! =4

31!

7,8649

12, 4412

"#$

%&'= 0,4904

! =4! 0,2535

1+ 4 "1( )! 0,2535= 0,5759

!i

2=1,9465+1,2245+1, 4792 + 3,2147 = 7,8649!


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Cronbachs . An annotated example (ORourke, Hatcher & Stepanski, 2005) I realize I committed a mistake, What happens if I delete X4? Sensibility analysis to item deletion

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Item-totalStatistics

ScaleScaleCorrectedMeanVarianceItem-SquaredAlpha

ifItemifItemTotalMultipleifItem

DeletedDeletedCorrelationCorrelationDeleted

X114,56007,0678,4620,5753,2439X214,34008,4331,4331,2574,3189

X314,22007,6037,5007,5127,2403

X416,10009,6429-,0374,0295,7766


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Composite reliability Takes into account all the LVs in the measurement model A CFA must be performed to get the necessary information A CR is calculated for each LV (Fornell y Larcker, 1981):

Being Lij the standardized loading of each of thejindicators of the LVi Var(Eij) is the variance of the error tem of each indicator that can be

calculated as follows:

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Var Eij( ) =1!Lij2

CR

L

L Var E

ij

j

ijj

ijj

=

+

( )

-

- -

2

2


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Psychometric properties: Reliability Composite reliability: An annotated example

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STANDARDIZEDSOLUTION:V1=V1=.963*F1+.270E1

V2=V2=.514*F1+.858E2V3=V3=.741*F1+.671E3

V4=V4=.945*F2+.326E4V5=V5=.657*F2+.754E5V6=V6=.673*F2+.740E6

Helpingothers

Financialgiving

X1

X2

X3

X4

X5

X6


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Psychometric properties: Reliability Composite reliability: An annotated example

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CR1=

Lijj

!"

#$%

&'

2

Lijj

!"#$%&'

2

+ Var Eij( )j

!=

2,218( )2

2,218( )2

+1,259

= 0, 796 CR2=

2,275( )2

2,275( )2

+1, 222

= 0,809

Benchmark:Same as Cronbachs a


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Average Variance Extracted (AVE) Average variance that the LV can explain of all its indicators (Fornell y

Larcker, 1981):

Being all the notation known but ki that is the number of indicators of theith LV

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AVEi =

Lijj

!2

Lijj!

2

+ Var Eij( )j!=

Lijj

!2

ki


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Psychometric properties: Reliability Average Variance Extracted (AVE)

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AVE1 =

Lijj

!2

Lijj!

2

+ Var Eij( )j!

=1, 741

1, 741+1,259

= 0,580 AVE2 =1, 778

1, 778+1,222

= 0,592

Benchmark:AVE > .50


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Psychometric properties: Validity

Validity Construct validity is the extent to which a set of measured items actually

reflect the theoretical latent construct they are designed to measure.

Types of validity: Face validity: the extent to which the content of the items is consistent

with the construct definition, based solely on the researchersjudgment

Convergent validity: the extent to which indicators of a specificconstruct converge or share a high proportion of variance incommon.

Discriminant validity: the extent to which a construct is truly distinctfrom other constructs

Nomological validity: examines whether the correlations between theconstructs in the measurement theory make sense

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Published results from previous studies. Pre-test or pilot study findings

With CFA SEM

information


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Psychometric properties: Validity Validity. An annotated example (Rusbult, 1980; Hatcher, 1994)

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Convergent validity: Model goodness-of-fit must be adequate (same as for the rest of validity

criteria)

Check Lagrange multipliers as some indicators may be being caused formore than one LV (bad item design)

Loadings must be significant. Loadings size must be adequate:

Ideally 0.70 and higher. If some of them are not, the average of theloadings for each factor should be .70 or higher (Hair, Anderson,Tatham & Black, 1998)

At least .60 (Bagozzi y Yi, 1988) The rationale of the .70 benchmark is that .702 implies that approximately

50% of the item variance will be explained by the LV. Lower values implythat most of the variance in the indicator is error variance.

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Convergent validity. An annotated example (Rusbult, 1980; Hatcher, 1994). Estimating a CFA (measurement model)

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Psychometric properties: Validity Convergent validity. An annotated example (Rusbult, 1980; Hatcher, 1994)

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/SPECIFICATIONSVARIABLES=19;CASES=240;METHOD=ML;

ANALYSIS=COVARIANCE;MATRIX=COR;

/EQUATIONS

V1=*F1+E1;V2=*F1+E2;

V3=*F1+E3;

V4=*F1+E4;

V5=*F2+E5;

V6=*F2+E6;

V7=*F2+E7;V8=*F3+E8;

V9=*F3+E9;

V10=*F3+E10;V11=*F4+E11;

V12=*F4+E12;V13=*F4+E13;

V14=*F5+E14;

V15=*F5+E15;

V16=*F5+E16;

V17=*F6+E17;V18=*F6+E18;

V19=*F6+E19;

/VARIANCES

F1TOF6=1;

E1TOE19=*;/COVARIANCES

F1TOF6=*;/PRINT

FIT=ALL;

GOODNESSOFFITSUMMARYFORMETHOD=ML

INDEPENDENCEMODELCHI-SQUARE=2459.673ON171DEGREESOF

FREEDOM

INDEPENDENCEAIC=2117.67331INDEPENDENCECAIC=1351.48405

MODELAIC=-26.32656MODELCAIC=-640.17410

CHI-SQUARE=247.673BASEDON137DEGREESOFFREEDOM

PROBABILITYVALUEFORTHECHI-SQUARESTATISTICIS.00000

THENORMALTHEORYRLSCHI-SQUAREFORTHISMLSOLUTIONIS

234.506.

FITINDICES

-----------BENTLER-BONETTNORMEDFITINDEX=.899

BENTLER-BONETTNON-NORMEDFITINDEX=.940

COMPARATIVEFITINDEX(CFI)=.952

BOLLEN(IFI)FITINDEX=.952

MCDONALD(MFI)FITINDEX=.794LISRELGFIFITINDEX=.906

LISRELAGFIFITINDEX=.870

ROOTMEAN-SQUARERESIDUAL(RMR)=.237

STANDARDIZEDRMR=.047

ROOTMEAN-SQUAREERROROFAPPROXIMATION(RMSEA)=.05890%CONFIDENCEINTERVALOFRMSEA(.046,.069)

Model GoF


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CUMULATIVEMULTIVARIATESTATISTICSUNIVARIATEINCREMENT----------------------------------------------------------------

HANCOCK'SSEQUENTIAL

STEPPARAMETERCHI-SQUARED.F.PROB.CHI-SQUAREPROB.D.F.PROB.

----------------------------------------------------------1V4,F622.5801.00022.580.0001371.000

2V2,F239.0732.00016.493.0001361.0003V1,F244.6873.0005.614.0181351.000

4V17,F249.7454.0005.058.0251341.000

5V2,F554.6475.0004.902.0271331.0006V8,F159.2016.0004.554.0331321.000

Lagrange Multiplier test

Should we add the relationship? No face validity (unless substantive reasons)Should we associate it only to F6? Significant loading on F1, same problemWe should delete it and run the model again


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Psychometric properties: Validity onvergent validity. An annotated example (Rusbult, 1980; Hatcher, 1994)

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GOODNESSOFFITSUMMARYFORMETHOD=ML

INDEPENDENCEMODELCHI-SQUARE=2167.771ON153DEGREESOFFREEDOM

INDEPENDENCEAIC=1861.77095INDEPENDENCECAIC=1176.23320MODELAIC=-59.12792MODELCAIC=-596.80459



THENORMALTHEORYRLSCHI-SQUAREFORTHISMLSOLUTIONIS174.047.

FITINDICES

-----------BENTLER-BONETTNORMEDFITINDEX=.917

BENTLER-BONETTNON-NORMEDFITINDEX=.961COMPARATIVEFITINDEX(CFI)=.970

BOLLEN(IFI)FITINDEX=.970

MCDONALD(MFI)FITINDEX=.881

LISRELGFIFITINDEX=.925

LISRELAGFIFITINDEX=.893ROOTMEAN-SQUARERESIDUAL(RMR)=.197

STANDARDIZEDRMR=.042

ROOTMEAN-SQUAREERROROFAPPROXIMATION(RMSEA)=.046

90%CONFIDENCEINTERVALOFRMSEA(.032,.059)

GoF of revised model 1


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V1=V1=2.201*F1+1.000E1.129

17.079@V2=V2=2.398*F1+1.000E2

.157

15.301@V3=V3=2.551*F1+1.000E3

.13618.733@

V5=V5=1.596*F2+1.000E5.105

15.162@

V6=V6=1.830*F2+1.000E6.113

16.236@

V7=V7=1.800*F2+1.000E7.109

16.513@V8=V8=.944*F3+1.000E8

.094

9.991@V9=V9=.893*F3+1.000E9

.0949.455@

V10=V10=1.294*F3+1.000E10

.11411.383@

V11=V11=2.143*F4+1.000E11.171

12.516@

V12=V12=2.326*F4+1.000E12.178

13.082@V13=V13=1.093*F4+1.000E13

.157

6.977@

Are loadings significant?

V14=V14=1.773*F5+1.000E14.124

14.333@

V15=V15=1.569*F5+1.000E15

.13611.523@

V16=V16=1.032*F5+1.000E16

.1228.486@

V17=V17=1.368*F6+1.000E17.130

10.493@

V18=V18=1.493*F6+1.000E18

.12711.771@

V19=V19=1.591*F6+1.000E19.141

11.247@


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Convergent validity. An annotated example (Rusbult, 1980; Hatcher, 1994)

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Loadings size

V1=V1=.885*F1+.465E1.784

V2=V2=.824*F1+.566E2.680

V3=V3=.937*F1+.351E3.877

V5=V5=.828*F2+.561E5.685

V6=V6=.866*F2+.500E6.750

V7=V7=.875*F2+.483E7.766

V8=V8=.666*F3+.746E8.444

V9=V9=.634*F3+.773E9.402

V10=V10=.751*F3+.661E10.563

V11=V11=.826*F4+.564E11.682

V12=V12=.864*F4+.503E12.747

V13=V13=.463*F4+.886E13.215

V14=V14=.843*F5+.537E14.711

V15=V15=.707*F5+.707E15.500

V16=V16=.551*F5+.835E16.303

V17=V17=.684*F6+.730E17.467

V18=V18=.760*F6+.650E18.577

V19=V19=.728*F6+.685E19.530


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Discriminant validity Three criteria:

Chi-square difference test (Anderson y Gerbing, 1988) Confidence interval test (Anderson y Gerbing, 1988) Average Variance Extracted test (Fornell y Larcker, 1981)

Must be applied for each pair of factors!!! For time constraint reasons, in this example we will apply them just to the two

factors that exhibit higher correlations (and can more feasibly havediscriminant validity problems)

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IIIF4-F4-.224*I

IF2-F2.071II-3.148@I

II

IF5-F5.635*IIF2-F2.052I

I12.181@III

IF6-F6-.375*IIF2-F2.069I

I-5.424@I

IIIF4-F4-.092*I

IF3-F3.082I

I-1.131III

IF5-F5.516*IIF3-F3.069I

I7.479@I

IIIF6-F6-.424*I

IF3-F3.075II-5.633@I

II

IF5-F5.008*IIF4-F4.079I

I.102III

IF6-F6.255*I

IF4-F4.076II3.340@I

IIIF6-F6-.300*I

IF5-F5.077I

I-3.895@III


Discriminant validity. An annotated example (Rusbult, 1980; Hatcher, 1994)

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Problematic factor

MAXIMUMLIKELIHOODSOLUTION(NORMALDISTRIBUTIONTHEORY)

COVARIANCESAMONGINDEPENDENTVARIABLES---------------------------------------

STATISTICSSIGNIFICANTATTHE5%LEVELAREMARKEDWITH@.

VF

------IF2-F2.609*I

IF1-F1.047II12.867@I

II

IF3-F3.440*IIF1-F1.066I

I6.624@I

IIIF4-F4-.016*I

IF1-F1.073II-.220I

II

IF5-F5.714*IIF1-F1.044I

I16.107@III

IF6-F6-.223*I

IF1-F1.073II-3.046@I

IIIF3-F3.534*I

IF2-F2.062I

I8.549@I


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Discriminant validity. An annotated example (Rusbult, 1980; Hatcher, 1994) Chi-square difference test (Anderson & Gerbing, 1988)

The CFA for the measurement model is estimated again, but thecovariance between the two problematic factors is fixed to 1 (F1 & F5)

The chi-square of the original measurement model CFA is subtracted fromthe chi-square of this restricted CFA. The same is done with their degreesof freedom.

This difference (should be positive) is distributed as a Chi-square with asmany degrees of freedom as the difference between the two models df.

If this statistic (the chi-square difference) is significant, it will indicate thatrestricting the correlation to be 1, significantly worsens the model fit andis not a reasonable assumption.

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29









MODELAIC=9.13766MODELCAIC=-533.01965




Measurement model

CFAwhere/COVF1,F5=1


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Chi-square difference: 251,138180,872=70,266 Degrees of freedom difference: 1 Critical value:

p


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Discriminant validity. An annotated example (Rusbult, 1980; Hatcher, 1994) Confidence interval test (Anderson & Gerbing, 1988)

A confidence interval for the correlation estimation is built: correlationestimation 2 SE (standard errors)

If value 1 forms part of the confidence intervaI, discriminant validity cannotbe assumed

Interval: Lower extreme: 0.714 - 20,044=0.626 Upper extreme: 0.714 + 20,044=0.802

Value 1 does not belong to the CI, no threaten to discriminant validity

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IF4-F4-.016*I

IF1-F1.073I

I-.220I

IIIF5-F5.714*I

IF1-F1.044I

I16.107@I

II


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Discriminant validity. An annotated example (Rusbult, 1980; Hatcher, 1994) AVE test(Fornell y Larcker, 1981)

AVE for each pair of factors is calculated (You did it to check reliability! Sono extra work)

The AVEs of the two evaluated factors are compared to the squaredcorrelation between them

If both AVEs are higher than the squared correlation, no evidence ofdiscriminant validity problems is found

Squared correlation: 0.7142=0.510

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IF4-F4-.016*I

IF1-F1.073I

I-.220I

II

IF5-F5.714*I

IF1-F1.044II16.107@I

II


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Psychometric properties: Validity Discriminant validity. An annotated example (Rusbult, 1980; Hatcher, 1994) AVE test(Fornell y Larcker, 1981)

Although AVE for F5 is slightly lower than the squared correlation, previousresults would lead us to conclude that no relevant discriminant validityproblems are present

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AVEF1=

2,340

2,340 + 0, 660= 0, 780

AVEF5=

1,514

1,514 +1, 486

= 0,504


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Nomological validity: Usually it is tested by examining whether the correlations between the

constructs in the measurement model make sense. The construct correlationsare used to assess this.

In my opinion a more sensible (although more exigent) way, is comparing themeasurement model and the structural model fit.

Structural model adds the theoretical value (structural part) to justmeasurement, so it should have a better fit.

If our final structural model (without non-significant relationships and with thenew relationships we could have added on a theory basis) exhibits a betterdegree of fit than the only measurement model, or at least are notdistinguishable, nomological validity can be assumed.

Chi-square difference test is used to evaluate goodness of fit.

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IIIF4-F4-.224*I

IF2-F2.071II-3.148@I

II

IF5-F5.635*IIF2-F2.052I

I12.181@III

IF6-F6-.375*IIF2-F2.069I

I-5.424@I

IIIF4-F4-.092*I

IF3-F3.082I

I-1.131III

IF5-F5.516*IIF3-F3.069I

I7.479@I

IIIF6-F6-.424*I

IF3-F3.075II-5.633@I

II

IF5-F5.008*IIF4-F4.079I

I.102III

IF6-F6.255*I

IF4-F4.076I

[email protected]*I

IF5-F5.077I

I-3.895@III


Nomological validity. An annotated example (Rusbult, 1980; Hatcher, 1994)

35

MAXIMUMLIKELIHOODSOLUTION(NORMALDISTRIBUTIONTHEORY)

COVARIANCESAMONGINDEPENDENTVARIABLES---------------------------------------

STATISTICSSIGNIFICANTATTHE5%LEVELAREMARKEDWITH@.

VF

------IF2-F2.609*I

IF1-F1.047II12.867@I

II

IF3-F3.440*IIF1-F1.066I

I6.624@I

IIIF4-F4-.016*I

IF1-F1.073II-.220I

II

IF5-F5.714*IIF1-F1.044I

I16.107@III

IF6-F6-.223*I

IF1-F1.073II-3.046@I

IIIF3-F3.534*I

IF2-F2.062I

I8.549@I


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Psychometric properties: Validity Validity. An annotated example (Rusbult, 1980; Hatcher, 1994)

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Psychometric properties: Validity Nomological validity. An annotated example (Rusbult, 1980; Hatcher, 1994)

37

Structural model 1

/TITLE/SPECIFICATIONS

VARIABLES=19;CASES=240;

METHOD=ML;

ANALYSIS=COVARIANCE;MATRIX=COR;

/MATRIX

/STANDARDDEVIATIONS

/EQUATIONSV1=*F1+E1;

V2=*F1+E2;

V3=F1+E3;

V5=*F2+E5;

V6=*F2+E6;

V7=F2+E7;

V8=*F3+E8;

V9=*F3+E9;

V10=F3+E10;

V11=*F4+E11;

V12=F4+E12;V13=*F4+E13;

V14=F5+E14;

V15=*F5+E15;

V16=*F5+E16;

V17=*F6+E17;

V18=F6+E18;

V19=*F6+E19;

F1=*F2+*F5+*F6+D1;

F2=*F3+*F4+D2;

/VARIANCESF3TOF6=*;

E1TOE3=*;

E5TOE19=*;

D1TOD2=*;

/COVARIANCES

F3TOF6=*;

/WTEST

/LMTEST

/PRINTFIT=ALL;

/END


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Nomological validity. An annotated example (Rusbult, 1980; Hatcher, 1994)

38













Measurement model

Structural model 1


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Nomological validity. An annotated example (Rusbult, 1980; Hatcher, 1994) Chi-square structural model 1: 216.75 (df124) Chi-square measurement model: 180.87 (df120) Structural model 1 chi-square greater than measurement model (worst

fit), but is the difference significant?

Chi-square difference: 35.88 Degrees of freedom difference: 4 Critical value p


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Nomological validity. An annotated example (Rusbult, 1980; Hatcher, 1994) What relationships are not necessary (not significant) and are worsening

our fit?

Are there any theory based relationships that could be added? Can Wald and Lagrange help us?

40

MULTIVARIATELAGRANGEMULTIPLIERTESTBYSIMULTANEOUSPROCESSINSTAGE1CUMULATIVEMULTIVARIATESTATISTICSUNIVARIATEINCREMENT

----------------------------------------------------------------

HANCOCK'S

SEQUENTIALSTEPPARAMETERCHI-SQUARED.F.PROB.CHI-SQUAREPROB.D.F.PROB.

----------------------------------------------------------1F2,F534.1811.00034.181.0001241.000

2V1,F244.9242.00010.743.0011231.000

3V2,F551.6743.0006.750.0091221.000

WALDTEST(FORDROPPINGPARAMETERS)MULTIVARIATEWALDTESTBYSIMULTANEOUSPROCESS

CUMULATIVEMULTIVARIATESTATISTICSUNIVARIATEINCREMENT

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STEPPARAMETERCHI-SQUARED.F.PROBABILITYCHI-SQUAREPROBABILITY

-------------------------------------------------------------1F5,F4.0071.935.007.935

2F1,F6.8512.653.845.358

3F4,F32.6843.4431.833.176


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Wald suggests two covariances to be deleted (F5,F4) y (F4,F3), but only oneregression coefficient is not significant F1 to F6.

Lagrange suggests adding a regression coefficient between F2 and F5. Only ifwe can find substantive theory to support this, this step should be done

Model is re-estimated

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INDEPENDENCEAIC=1861.77095INDEPENDENCECAIC=1176.23320MODELAIC=-59.12792MODELCAIC=-596.80459










Measurement model

Structural model 2


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Chi-square structural model 2: 183.19 (df124)

Chi-square measurement model: 180.87 (df

120) Structural model 2 chi-square is greater than the measurement model one

(worst fit), but is the difference significant?

Chi-square difference: 2.32 Degrees of freedom difference: 4 Critical value for p


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Psychometric properties: Validity Model nomologically valid

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Psychometric properties: Validity Example of presentation in a paper (Bign, Alds, Ruiz y Sanz, 2008)

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Appendix

Variable Indicator F actor loading Robust t-value CA CR AVE

P er ce iv ed u se ful nes s US EF UL 2 0 .7 40 * * 19.03 0.87 0.87 0.57US EF UL 3 0 .7 80 * * 20.86US EF UL 4 0 .7 60 * * 19.59US EF UL 5 0 .7 32 * * 18.01US EF UL 6 0 .7 58 * * 19.51

Perceived ease of use EASE1 0.750 * * 16.99 0.74 0.75 0.43EASE3 0.600 * * 12.04EASE4 0.646 * * 14.01

EASE6 0.629 * * 12.88Innovativeness INN1 0.701 * * 8.81 0.78 0 .80 0.67

INN2 0.920 * * 10.67Attitud e to onl in e shopp in g ATT I4 0.743 * * 16.82 0.81 0.81 0.59

ATTI5 0.873 * * 20.29ATTI7 0.678 * * 14.03

I nf or ma ti on de pen den cy DE P1 0 .8 40 * * 18.27 0.73 0.74 0.59DEP3 0.685 * * 13.24

S-B x2 (94 df) 252.31 (p , 0.01); NFI 0.90; NNFI 0.92; CFI 0.94; IFI 0.94;RMSEA 0.06

Notes: *p , 0.05; * *p , 0.01. CA Cronbachs a; CR composite reliability; AVE averagevariance extracted

Table AI.Validation of the finalmeasurement model

reliability and convergentvalidity

Online shoppinginformation

667


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Psychometric properties: Validity Example of presentation in a paper (Bign, Alds, Ruiz y Sanz, 2008)

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1 2 3 4 5

1. Perceived usefulness 0.75 0.60 * * 0.20 * * 0.65 * * 0.62 * *

2. Perceived ease of use [0.51;0.69] 0.66 0.33 * * 0.47 * * 0.55 * *

3. Innovativeness [0.09;0.32] [0.19;0.46] 0.82 0.17 * * 0.084. Attitude to online shopping [0.59;0.71] [0.36;0.58] [0.05;0.29] 0.77 0.44* *

5. Online information dependency [0.53;0.72] [0.43;0.67] [-0.04;0.21] [0.33;0.55] 0.77

Notes: *p, 0.05; * *p, 0.01. Diagonal represents the square root of the average variance extracted;while above the diagonal the shared variance (squared correlations) are represented. Below thediagonal the 95 per cent confidence interval for the estimated factors correlations is provided

Table AII.Validation of the finalmeasurement model

discriminant validity

Documents

3.Measurement Model