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
Dr. Mohd Sobhi Ishak ([email protected], 012-2015528) Workshop SEM ke-2, Pusat Islam UUM» » 12-13 Januari 2013
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)
Dr. Mohd Sobhi Ishak ([email protected], 012-2015528) Workshop SEM ke-2, Pusat Islam UUM» » 12-13 Januari 2013
CFA for Perceived Usefulness
Standardized Regression
Weights >.7
Example 1
Dr. Mohd Sobhi Ishak ([email protected], 012-2015528) Workshop SEM ke-2, Pusat Islam UUM» » 12-13 Januari 2013
2nd Order CFA
Example 2
Dr. Mohd Sobhi Ishak ([email protected], 012-2015528) Workshop SEM ke-2, Pusat Islam UUM» » 12-13 Januari 2013
Self-
efficacy
Perceived
Ease of Use
Perceived
Usefulness
Perceived
Enjoyment
Intention
to Use
Case Study
Students’ Intention to Use Internet(SIUI)
Dr. Mohd Sobhi Ishak ([email protected], 012-2015528) Workshop SEM ke-2, Pusat Islam UUM» » 12-13 Januari 2013
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
Dr. Mohd Sobhi Ishak ([email protected], 012-2015528) Workshop SEM ke-2, Pusat Islam UUM» » 12-13 Januari 2013
STAGE 2Developing Overall Measurement
Model • Unidimensionality – 1 measured variable for one
construct
▫ No cross loading
• Item per construct – >3 (identification)
Dr. Mohd Sobhi Ishak ([email protected], 012-2015528) Workshop SEM ke-2, Pusat Islam UUM» » 12-13 Januari 2013
Measurement theory (istilah oleh Hair et al. (2010)
Case Study
Note:Measured Variable – 24Latent - 5
Dr. Mohd Sobhi Ishak ([email protected], 012-2015528) Workshop SEM ke-2, Pusat Islam UUM» » 12-13 Januari 2013
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
Dr. Mohd Sobhi Ishak ([email protected], 012-2015528) Workshop SEM ke-2, Pusat Islam UUM» » 12-13 Januari 2013
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
Dr. Mohd Sobhi Ishak ([email protected], 012-2015528) Workshop SEM ke-2, Pusat Islam UUM» » 12-13 Januari 2013
Identify variables with missing
value from the output of :
Analyze>Descriptive
statistics>Frequencies
Dr. Mohd Sobhi Ishak ([email protected], 012-2015528) Workshop SEM ke-2, Pusat Islam UUM» » 12-13 Januari 2013
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
Dr. Mohd Sobhi Ishak ([email protected], 012-2015528) Workshop SEM ke-2, Pusat Islam UUM» » 12-13 Januari 2013
Let’s Draw Measurement ModelData: SEM WORKSHOP Data
Dr. Mohd Sobhi Ishak ([email protected], 012-2015528) Workshop SEM ke-2, Pusat Islam UUM» » 12-13 Januari 2013
1 Click on the
Analysis Properties
Icon
3 Click on the Analysis
Properties Icon > Output Tab >
Tick button
2 Click on Plugins>Standardized RMR
Dr. Mohd Sobhi Ishak ([email protected], 012-2015528) Workshop SEM ke-2, Pusat Islam UUM» » 12-13 Januari 2013
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.
Dr. Mohd Sobhi Ishak ([email protected], 012-2015528) Workshop SEM ke-2, Pusat Islam UUM» » 12-13 Januari 2013
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
Dr. Mohd Sobhi Ishak ([email protected], 012-2015528) Workshop SEM ke-2, Pusat Islam UUM» » 12-13 Januari 2013
3 Check outliers.If p1<.05,
delete cases
Dr. Mohd Sobhi Ishak ([email protected], 012-2015528) Workshop SEM ke-2, Pusat Islam UUM» » 12-13 Januari 2013
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).
Dr. Mohd Sobhi Ishak ([email protected], 012-2015528) Workshop SEM ke-2, Pusat Islam UUM» » 12-13 Januari 2013
• 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.
Dr. Mohd Sobhi Ishak ([email protected], 012-2015528) Workshop SEM ke-2, Pusat Islam UUM» » 12-13 Januari 2013
Standardized
Estimates
Data : SEM WORKSHOP Data clean
Dr. Mohd Sobhi Ishak ([email protected], 012-2015528) Workshop SEM ke-2, Pusat Islam UUM» » 12-13 Januari 2013
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
Dr. Mohd Sobhi Ishak ([email protected], 012-2015528) Workshop SEM ke-2, Pusat Islam UUM» » 12-13 Januari 2013
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.
Dr. Mohd Sobhi Ishak ([email protected], 012-2015528) Workshop SEM ke-2, Pusat Islam UUM» » 12-13 Januari 2013
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
Dr. Mohd Sobhi Ishak ([email protected], 012-2015528) Workshop SEM ke-2, Pusat Islam UUM» » 12-13 Januari 2013
Standardized Residual
The largest residual is
1.889 (PEJ4 & SE3), so no
residuals exceed |4.0|.
Dr. Mohd Sobhi Ishak ([email protected], 012-2015528) Workshop SEM ke-2, Pusat Islam UUM» » 12-13 Januari 2013
Modification Indices
Sort and check the
highest M.I
Dr. Mohd Sobhi Ishak ([email protected], 012-2015528) Workshop SEM ke-2, Pusat Islam UUM» » 12-13 Januari 2013
SIUI Goodness Of FitFit Indices Cutoff Values Before After
Chi-square (x2)
Chi-square (p-value) 1560.07
(p=.000)
373.127
(p=.000)
Degrees of Freedom (df) 242 179
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 2.085
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 .057
Standardized Root Mean Square
Residual (SRMR)
SRMR < 0.08 (Hu & Bentler, 1999) .0778 .0431
Incremental Fit Indices (IFI)
Comparative Fit Index (CFI) CFI > 0.90 (Bryne, 2001; Hair et
al., 2010; Kline 2005; Schumacker
& Lomax, 2010)
.775 .958
Parsimony Fit Indices (PFI)
Parsimony Normed Fit Index (PNFI) PNFI > 0.60 (Garson, 2009) .654 .787
Dr. Mohd Sobhi Ishak ([email protected], 012-2015528) Workshop SEM ke-2, Pusat Islam UUM» » 12-13 Januari 2013
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
Dr. Mohd Sobhi Ishak ([email protected], 012-2015528) Workshop SEM ke-2, Pusat Islam UUM» » 12-13 Januari 2013
• 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
Dr. Mohd Sobhi Ishak ([email protected], 012-2015528) Workshop SEM ke-2, Pusat Islam UUM» » 12-13 Januari 2013
• 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
Dr. Mohd Sobhi Ishak ([email protected], 012-2015528) Workshop SEM ke-2, Pusat Islam UUM» » 12-13 Januari 2013
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.
Dr. Mohd Sobhi Ishak ([email protected], 012-2015528) Workshop SEM ke-2, Pusat Islam UUM» » 12-13 Januari 2013
&Compute for EVERY
constructs !!!
Stats Tools Package (http://statwiki.kolobkreations.com)
Dr. Mohd Sobhi Ishak ([email protected], 012-2015528) Workshop SEM ke-2, Pusat Islam UUM» » 12-13 Januari 2013
• Tested by examining whether the correlations between
the constructs in the measurement model make sense.
• The construct correlations are used to assess this.
Dr. Mohd Sobhi Ishak ([email protected], 012-2015528) Workshop SEM ke-2, Pusat Islam UUM» » 12-13 Januari 2013
Nomological Validity
Check significant of correlations (***:p<0.001 or *p<0.05)
The interconstruct
correlations (see above
Covariances table).
Dr. Mohd Sobhi Ishak ([email protected], 012-2015528) Workshop SEM ke-2, Pusat Islam UUM» » 12-13 Januari 2013
STAGE 5Convert measurement model
to structural model
Add error terms to
endogenous
variablesPlugins > Name
Unobserved Variables
21
Dr. Mohd Sobhi Ishak ([email protected], 012-2015528) Workshop SEM ke-2, Pusat Islam UUM» » 12-13 Januari 2013
Dr. Mohd Sobhi Ishak ([email protected], 012-2015528) Workshop SEM ke-2, Pusat Islam UUM» » 12-13 Januari 2013
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.
Dr. Mohd Sobhi Ishak ([email protected], 012-2015528) Workshop SEM ke-2, Pusat Islam UUM» » 12-13 Januari 2013
Dr. Mohd Sobhi Ishak ([email protected], 012-2015528) Workshop SEM ke-2, Pusat Islam UUM» » 12-13 Januari 2013
SIUI Goodness Of Fit
Measurement Model vs Structural ModelFit Indices Cutoff Values Measurement
Model
Structural
Model
Chi-square (x2)
Chi-square (p-value) 373.127
(p=.000)
375.553
(p=.000)
Degrees of Freedom (df) 179 181
Absolute Fit Indices
Relative Chi-square, 2/df (CMIN/DF) 2:1 or 3:1 2.085 2.075
Root Mean Square Error of
Approximation (RMSEA)
< 0.07 or 0.03 <
RMSEA <.0.08.057 .057
Standardized Root Mean Square
Residual (SRMR)
SRMR < 0.08 .0431 0.0446
Incremental Fit Indices (IFI)
Comparative Fit Index (CFI) CFI > 0.90 .958 .958
Parsimony Fit Indices (PFI)
Parsimony Normed Fit Index (PNFI) PNFI > 0.60 .787 .795
Dr. Mohd Sobhi Ishak ([email protected], 012-2015528) Workshop SEM ke-2, Pusat Islam UUM» » 12-13 Januari 2013
1Click on value to
get an
interpretation
Dr. Mohd Sobhi Ishak ([email protected], 012-2015528) Workshop SEM ke-2, Pusat Islam UUM» » 12-13 Januari 2013
2
Dr. Mohd Sobhi Ishak ([email protected], 012-2015528) Workshop SEM ke-2, Pusat Islam UUM» » 12-13 Januari 2013
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).
Dr. Mohd Sobhi Ishak ([email protected], 012-2015528) Workshop SEM ke-2, Pusat Islam UUM» » 12-13 Januari 2013
• R2 or SMC• It is estimated that the predictors of INT
explain 46.1 percent of its variance
Dr. Mohd Sobhi Ishak ([email protected], 012-2015528) Workshop SEM ke-2, Pusat Islam UUM» » 12-13 Januari 2013
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”
Dr. Mohd Sobhi Ishak ([email protected], 012-2015528) Workshop SEM ke-2, Pusat Islam UUM» » 12-13 Januari 2013
Thats All about Structural Equation
Modeling (SEM)
• Next we’ll moved to mediating and moderating concept. (Part C)