part b stages of sem process

Dr. Mohd Sobhi IshakDepartment of Multimedia TechnologySchool of Multimedia Technology and CommunicationUniversiti Utara [email protected]

Dr. Mohd Sobhi Ishak ([email protected], 012-2015528) Workshop SEM ke-2, Pusat Islam UUM» » 12-13 Januari 2013

STAGE 1

Operationalizes a construct

1. Scales from prior research

2. New scale development

Pretesting

1. EFA (SPSS)

2. CFA for individual construct

Defining Individual Constructs


CFA for Individual Construct

• Data from pretest

• Check construct validity

▫ Standardized loading estimates : >.5 or >.7

▫ Convergent validity : AVE > .5

▫ Discriminant validity : AVE > r2

▫ Construct reliability : >.7

(will be discuss at Stage 4)


CFA for Perceived Usefulness

Standardized Regression

Weights >.7

Example 1


2nd Order CFA

Example 2


Self-

efficacy

Perceived

Ease of Use

Perceived

Usefulness

Perceived

Enjoyment

Intention

to Use

Case Study

Students’ Intention to Use Internet(SIUI)


Observed Indicator

• Self-Efficacy (SE) – 4 item

• Perceived Ease of Use (PEOU) – 4 item

• Perceived Usefulness (PU) – 5 item

• Perceived Enjoyment (PE) – 4 item

• Intention to Use (IU) – 4 item

• Likert Scale – can use different number of scale points (Hair et al., 2010) e.g 1-5, 0-7, etc.

Case Study


STAGE 2Developing Overall Measurement

Model • Unidimensionality – 1 measured variable for one

construct

▫ No cross loading

• Item per construct – >3 (identification)


Measurement theory (istilah oleh Hair et al. (2010)

Case Study

Note:Measured Variable – 24Latent - 5


STAGE 3Designing Empirical Study

Issue 1: Sample Size• Generally requires a larger sample• Hair et al., 2010 suggest :

1. Multivariate Normality :15 respondent for each parameter.

2. Estimation Technique (MLE) : 100 – 4003. >100,150,300, or 500 : depends on number of constructs,

communalities, underidentified constructs (pg. 662)• Klien (2005) suggests:

▫ < 100 Small sample size▫ 100 to 200Medium sample size▫ > 200Large sample size


Issue 2 : Missing Data

• The best way is to resolve missing data issues before estimating

Exercise:

• Handle missing data in SEM WORKSHOP Missing Data.sav


Identify variables with missing

value from the output of :

Analyze>Descriptive

statistics>Frequencies


STAGE 4Assessing Measurement Model Validity

1. Examine Assumption of SEM

a. Multivariate Normality

b. Outliers

2. Examine the Goodness of Fit (GOF) indices

3. Evaluate Construct Validity

a. Covergent Validity

b. Discriminant Validity

c. Nomological Validity


Let’s Draw Measurement ModelData: SEM WORKSHOP Data


1 Click on the

Analysis Properties

Icon

3 Click on the Analysis

Properties Icon > Output Tab >

Tick button

2 Click on Plugins>Standardized RMR


1• Normality

▫ Degree to which the distribution of the sample data corresponds to a normal distribution.

• Outlier▫ An observation that is substantially different from

the other observation (i.e. has an extreme value) on one or more characteristics (variables)

• Multicollinearity▫ Extent to which a construct can be explained by the

other constructs in the analysis. As multicollinearityincreases, it complicates the interpretation of relationships because it is more difficult to ascretainthe effect of any single construct owing to their interrelationship.


2 Mardia's coefficient

of multivariate

kurtosis. If > 5,

check 3

1 Considered normal if

skewness between -3 to

+3. If not,check 2

1 Considered normal

if curtosis

between -7 to +7.

If not,check 2


3 Check outliers.If p1<.05,

delete cases


21. Absolute Fit Measures

▫ indicate how well your estimated model reproduces the observed

data. (GFI, RMSEA, RMR, SRMR)

2. Incremental Fit Measures ▫ indicate how well your estimated model fits relative to some

alternative baseline model. The most common baseline model is

one that assumes all observed variables are uncorrelated, which

means you have all single item scales. (NFI, NNFI, CFI, RFI)

3. Parsimony Fit Measures ▫ indicate if the model you specify is parsimonious. That is,

whether your model can be improved by specifying fewer

estimated parameter paths (specifying a simpler model). (AGFI,

PNFI).


• SEM has no single statistical test that best describes the “strength”

of the model’s predictions.

• Multiple fit indices should be used to assess goodness of fit.

• Hair et al. (2010) suggested:

1. The χ2 and the χ2 / df (normed Chi-square)

2. One goodness of fit index (e.g., GFI, CFI, NFI, TLI)

3. One badness of fit index (e.g., RMSEA, SRMR)

• Selecting a rigid cut-off for the fit indices is like selecting a

minimum R2 for a regression equation – there is no single “magic”

value for the fit indices that separates good from poor models.

• The quality of fit depends heavily on model characteristics

including sample size and model complexity.

Construct Results – Model Fit Diagnostics

CMIN/DF – a value below 2 is preferred but

between 2 and 5 is considered acceptable.

The AGFI is .946 – above

the .90 minimum.

The CFI is 0.984 – it exceeds the minimum (>0.90) for a model of this complexity and sample size.

The GFI is .965 – above the .90 recommended minimum.

This is the “Model Fit”

portion of the output.

GFI = Goodness of Fit Index

AGFI = Adjusted Goodness of Fit Index

PGFI = Parsimonious Goodness of Fit Index

TLI = Tucker- Lewis

CFI = Comparative Fit Index

PNFI = Parsimonious Normed Fit Index

NFI = Normed Fit Index

Chi-square (X2) = likelihood ratio chi-square

CMIN/DF – a value below 2 is preferred but between 2 and 5 is considered acceptable.

Note: If you click on any of the “Fit Indices” it will give guidelines for interpretation and references supporting the guidelines.

RMSEA = Root Mean Squared Error of Approximation – a value of 0.08 or less is considered acceptable (Hair et al., 2010)

Three Types of Models:

1. Default = your model, the relationships you propose and are testing.

2. Saturated model = a model that hypothesizes that everything is related to everything (just-identified).

3. Independence model = hypothesizes that nothing is related to anything.

RMSEA – represents the

degree to which lack of fit is due to misspecification of the model tested versus being due to sampling error.

Note that when we evaluate the measures we use the numbers for the default model.


Standardized

Estimates

Data : SEM WORKSHOP Data clean


SIUI Goodness Of FitFit Indices Cutoff Values Values

Chi-square (x2)

Chi-square (p-value) 1560.074

(p=.000)

Degrees of Freedom (df) 242

Absolute Fit Indices

Relative Chi-square, 2/df

(CMIN/DF)

2:1 (Tabachnick & Fidell, 2007)

3:1 (Hair et al., 2010; Kline, 2005)

6.447

Root Mean Square Error of

Approximation (RMSEA)

< 0.07 (Bryne, 2001, Kline 2005;

Schumacker & Lomax, 2010)

0.03 < RMSEA <.0.08 (Hair et al., 2010)

.127

Standardized Root Mean Square

Residual (SRMR)

SRMR < 0.08 (Hu & Bentler, 1999) .0778

Incremental Fit Indices (IFI)

Comparative Fit Index (CFI) CFI > 0.90 (Bryne, 2001; Hair et al., 2010;

Kline 2005; Schumacker & Lomax, 2010)

.775

Parsimony Fit Indices (PFI)

Parsimony Normed Fit Index (PNFI) PNFI > 0.60 (Garson, 2009) .654


1. Check Path Estimates (Factor Loadings)▫ Standardized regression Weights must >.5 or >.7

(ideal)2. Check Standardized Residual

▫ No Standardized residual exceed I4.0I▫ Those between I2.5I and I4.OI deserve attention if

other diagnostics indicate a problem3. Check Modification Indices

▫ Identify largest and examine MIs for the factor loading*Note – (1) avoid correlated error terms, (2) follow three-indicator rule.


Factor Loadings

These are factor loadings but in AMOS they are called standardized

regression weights.

1. Check Below .5PEJ6 = 0.66PEJ5=.169INT1=. 478

2. Delete the lowest (PEJ6)3. Calculate Estimates again4. Check Standardized Regression Weights again

Note: SIUI - (1) del PEJ6 ; (2) del PEJ5 ; (3) del INT1


Standardized Residual

The largest residual is

1.889 (PEJ4 & SE3), so no

residuals exceed |4.0|.


Modification Indices

Sort and check the

highest M.I


SIUI Goodness Of FitFit Indices Cutoff Values Before After

Chi-square (x2)


(p=.000)

373.127

(p=.000)

Degrees of Freedom (df) 242 179


Relative Chi-square, 2/df (CMIN/DF) 2:1 (Tabachnick & Fidell, 2007)

3:1 (Hair et al., 2010; Kline, 2005)6.447 2.085



< 0.07 (Bryne, 2001, Kline 2005;

Schumacker & Lomax, 2010)

0.03 < RMSEA <.0.08 (Hair et al.,

2010)

.127 .057


Residual (SRMR)

SRMR < 0.08 (Hu & Bentler, 1999) .0778 .0431


Comparative Fit Index (CFI) CFI > 0.90 (Bryne, 2001; Hair et

al., 2010; Kline 2005; Schumacker

& Lomax, 2010)

.775 .958


Parsimony Normed Fit Index (PNFI) PNFI > 0.60 (Garson, 2009) .654 .787


The extent to which a set of measured items

actually reflect the theoretical latent construct

they are designed to measure

Construct Validity

Face ValidityConvergent

ValidityDiscriminant

ValidityNomological

Validity


• The extent to which indicators of a specific construct

“converge” or share a high proportion of variance in common

• There are three measures:

1. Factor loadings (as discussed before)

2. Average Variance extracted (AVE)

3. Reliability

Rules of Thumb

• Standardized loadings estimates should be .5 or higher, and

ideally .7 or higher.

• AVE should be .5 or greater to suggest adequate convergent

validity.

• Reliability should be .7 or higher to indicate adequate

convergence or internal consistency.

A Part of SIUI Standardized Factor Loadings, Variance Extracted, and Reliability Estimates

INT PU PEJ

Item Reliabilities

(l)

Variance

Extracted delta

INT2 0.873 0.762 0.24

INT3 0.742 0.551 0.45

INT4 0.863 0.745 2.057 0.26

PU1 0.744 0.554 0.45

PU2 0.763 0.582 0.42

PU3 0.691 0.477 0.52

PU4 0.711 0.506 0.49

PU5 0.741 0.549 2.668 0.45

PEJ1 0.786 0.618 0.38

PEJ2 0.814 0.663 0.34

PEJ3 0.694 0.482 0.52

PEJ4 0.805 0.648 2.410 0.35

Average

Variance

Extracted 0.686 0.534 0.603

Construct

Reliability 0.867 0.851 0.858

This is the same as the eigen value

in exploratory factor analysis

BNo. of INT

items=3

A

Squared Factor Loadings

(communalities) @ SMC

(l2)

B/A =

2.057/3

The delta is calculated as 1 minus the item reliability, e.g., the

INT2 delta is 1 – .762 = .24

The delta is also referred to as the standardized error variance.

Standardized

Regression Weights

(l)

nAVE

n

i

i 1

2l

Average Variance Extracted

λ= standardized factor loading

i = number of items.

• A good rule of thumb is an AVE of .5 or higher indicates

adequate convergent validity.

• An AVE of less than .5 indicates that on average, there is more

error remaining in the items than there is variance explained by

the latent factor structure you have imposed on the measure.

Calculated Variance Extracted (AVE):

INT Construct = .762 + .551 + .745 = 2.057 / 3 = .6858

PU Construct = .744 + .763 + .691 + .711 + 741 = 2.668 / 5 = .5336

PEJ Construct = .786 + .814 + .694 + .805 = 2.410 / 4 = .6025

The sum of the

squared loadingsSquared loading for

INT4 : .8632 = .745

n

i

n

i

ii

n

i

i

CR

1 1

2

1

2

)()(

)(

l

l

Construct Reliability

• The rule of thumb for a construct reliability estimate is that .7 or

higher suggests good reliability.

• Reliability between .6 and .7 may be acceptable provided that

other indicators of a model’s construct validity are good.

• A high construct reliability indicates that internal consistency

exists.

• This means the measures all are consistently representing

something.

CR (INT) = (.873+.742+.863)2 / [(.873+.742 +.863)2 + (.24 +.45 +.26)] = 0.87

CR (PU) = (.744 +.763 +.691 +.711+741)2 / [(.744 +.763 +.691 +.711+741)2 + (.554 +.582 +.477 +.506+549)] = 0.85

CR (PEJ) = (.786+.814 +.694 +.805)2 / [(.786+.814 +.694 +.805)2 + (.38 +.34 +.52 +.335] = 0.86

The sum of the loadings,

squared

The sum of the

error variance

(delta)

The sum of the loadings,

squared


• The extent to which a construct is truly distinct from

other constructs (i.e unidimensional).

Measures

•All construct average variance extracted (AVE)

estimates should be larger than the corresponding

squared interconstruct correlation estimates (SIC)-

AVE > r2.•No cross loading between observed variables or error

terms


Discriminant Validity

Covariances

between

constructs.

Correlations between

constructs. These are

standardized covariances.

Will be use in calculating

discriminant validity.

Discriminant validity – compares the average

variance extracted (AVE) estimates for each

factor with the squared interconstruct

correlations (SIC) associated with that factor,

as shown below:

AVE SIC (r2)

INT Construct .686 .033, .342

PEJ Construct .534 .342, .036

PU Construct .851 .033, .036

Calculate SIC (Squared Interconstruct

Correlations) from the IC (Innerconstruct

Correlations) obtained from the AMOS

output correlations table (see previous

slide):

IC (r) SIC (r2)

INT-PU .183 .033

INT-PEJ .585 .342

PU-PEJ .190 .036

Discriminant Validity

CONCLUSION: All variance extracted (AVE) estimates in the above

table are larger than the corresponding squared interconstruct

correlation estimates (SIC). This means the indicators have more in

common with the construct they are associated with than they do

with other constructs. Therefore, the three construct of SISU

measurement model demonstrates discriminant validity.


&Compute for EVERY

constructs !!!

Stats Tools Package (http://statwiki.kolobkreations.com)


• Tested by examining whether the correlations between

the constructs in the measurement model make sense.

• The construct correlations are used to assess this.


Nomological Validity

Check significant of correlations (***:p<0.001 or *p<0.05)

The interconstruct

correlations (see above

Covariances table).


STAGE 5Convert measurement model

to structural model

Add error terms to

endogenous

variablesPlugins > Name

Unobserved Variables

21


STAGE 6Assessing Structural Model Validity

1. Examine the Goodness of Fit (GOF) indices▫ Should be essentially the same as with the

Measurement Model.

2. Hypothesis testing▫ Evaluate the significance, direction, and size of

the structural parameter estimates.


SIUI Goodness Of Fit

Measurement Model vs Structural ModelFit Indices Cutoff Values Measurement

Model

Structural

Model

Chi-square (x2)


(p=.000)

375.553

(p=.000)

Degrees of Freedom (df) 179 181


Relative Chi-square, 2/df (CMIN/DF) 2:1 or 3:1 2.085 2.075



< 0.07 or 0.03 <

RMSEA <.0.08.057 .057


Residual (SRMR)

SRMR < 0.08 .0431 0.0446


Comparative Fit Index (CFI) CFI > 0.90 .958 .958


Parsimony Normed Fit Index (PNFI) PNFI > 0.60 .787 .795


1Click on value to

get an

interpretation


2


Structural

Relationship

Unstandardized

parameter

estimate

Standard error t-value

Standardized

parameter

estimate

H1: SEPU -0.278 0.583 -0.477 -0.029

H2: SEPEJ 0.037 0.018 2.022 0.105*

H3: PEOUPU 3.169 0.896 3.537 0.227***

H4: PEOUPEJ 0.284 0.032 8.8 0.553***

H5: PUINT 0.003 0.004 0.604 0.031

H6: PEJINT 0.787 0.153 5.15 0.341***

H7: PEOUINT 0.49 0.079 6.21 0.414***

Note: *** p<0.001, *p<0.05

• H6 hypothesizes that students’ perceived enjoyment is positively

related to their intention to use internet. This was confirmed (β = .341,

p = .000).

• Perceived enjoyment has a significant effect on intention to use internet

(β = .341, p = .000).


• R2 or SMC• It is estimated that the predictors of INT

explain 46.1 percent of its variance


EXTRA …..How to create path diagram from your structural model?

Using Analyze>Data Imputation in AMOS to create composite variables in SPSS

See Youtube “Imputing Composite Variables in AMOS - YouTube_2”


Thats All about Structural Equation

Modeling (SEM)

• Next we’ll moved to mediating and moderating concept. (Part C)

part b stages of sem process

Education