12 chapter 8 second order confirmatory factor analysis
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CHAPTER
THE SECOND ORDER CONFIRMATORY
FACTOR ANALYSIS (CFA)
The Second Order CFA is a statistical method employed by the researcher to confirm that the theorized
construct in a study loads into certain number of underlying sub-constructs or components. For
example, the theory posits that service quality construct consist of five underlying sub-constructs and
each sub-construct is measured using certain number of items using a questionnaire. The researcher
might want to estimate the effect of main construct on its sub-constructs. Here, the main construct has
become second order construct while the sub-constructs become the first order construct.
8.1 THE STEPS IN PERFORMING SECOND ORDER CFA
Step 1: Draw the Main Construct of the model followed by its Sub-Constructs.
Using the one sided arrow, link the Main Construct to all Sub-Constructs. Put the residual for
every Sub-Construct since the Sub-Construct has an arrow pointing into it from the Main Construct(Figure A). Put a parameter 1 on one of the arrows of the Sub-Construct as a reference point if there
are more than two sub-constructs in the model. However if the Main Constructs has only two Sub-
Constructs, then both Sub-Constructs must have parameter 1.The above condition only applies if the
researcher is doing second order CFA separately for every construct. However, if one is doing the
Pooled CFA, the above requirement does not apply at all meaning only one reference point is needed
regardless of the number of components in a construct.
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Figure A: The CFA for Second Order Construct namely Corporate Entrepreneurship
Step 2: Run the Second Order CFA for the main construct on its sub-constructs
In this step, the researcher estimate the causal effects from the main construct to all its sub-
constructs. The objective here is to estimate the factor loading of main construct on its sub-constructs in
order to confirm that the theorized second order construct loads into the respective sub-constructs. As
usual, the CFA procedure would also estimate the factor loading for every item.
The result of second order CFA of Figure A is given in Figure B. Using the output in Figure B,
the researcher could begin the analysis procedure for CFA using the same steps outlined for first order
CFA regarding fitness indexes, deleting the low factor loading items, and modification indices.
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Figure B: The CFA result shows the factor loading for items as well as for sub-constructs
8.2 PERFORMING SECOND ORDER CFA FOR A SINGLE CONSTRUCT
In this study, the researcher intends to validate the main construct namely Training Transfer. This
construct has three sub-constructs namely Knowledge, Skills, and Attitude. The three latent sub-
constructs are measured using certain number of items.
The researcher draws the main construct (Training Transfer) and three sub-constructs (Knowledge,
Skills, and Attitude). The main construct is linked to the sub-constructs using one sided arrow to show
the causal effect. Thus, each sub-construct must have a residual since it has an arrow pointing in from
the main construct. One of the sub-constructs must have a reference point 1. Finally every sub-
construct has their respective items.
Second Orderfactor loadin
First Order factor loading
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Figure 1: Estimating the factor loading for a single construct namely Training Transfer
In the above diagram, Training Transfer is the main construct while Knowledge, Skills, and Attitude
are three sub-constructs. In second order CFA, the main construct Training Transfer will become
second order construct and the three sub-constructs will become the first order constructs.
The Second Order CFA results are presented in Figure 2.
The model is estimating the
effects of Training Transfer on
its sub-constructs. Thus, the
residual is required
Main Construct
Sub-Construct
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Figure 2: The factor loading for second order as well as the first order construct
First of all, observe that all fitness indexes have achieved the required level. Thus, no item deletion and
modification is required. The results showed that Training Transfer loads well on its three sub-
constructs. The factor loading of Training Transfer on Knowledge, Skills, and Attitude are 0.91, 0.97,
and 0.84 respectively. Furthermore, the R2for all sub-constructs are high (0.83, 0.93, and 0.70), which
reflect the contribution of Training Transfer on its three sub-constructs is good. In other word, the
theory that Training Transfer consists of three sub-constructs is well supported.
One might want to examine the significance of the main construct on every sub-construct in the model.
For this purpose, he needs to obtain the output of Regression Path Coefficient (as shown in Figure 3)
and the results from the Text-Output (as shown in Table 1).
Factor loading for
second order construct
Factor loading for first
order construct
R2for second
order constructR2for first
order construct
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Figure 3: The regression path coefficient of Training Transfer on its sub-constructs
Table 1: The regression path coefficient and its significance
Estimate S.E. C.R. P Results
Attitude
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8.3 PERFORMING THE POOLED CFA SECOND ORDER AND ITS
REPORTING PROCEDURE
Figure 1: The Pooled CFA - both first and second order constructs are in one measurement model
The output of the Pooled-CFA Second Order will be:
i. The Factor Loading for every sub-construct
ii. Factor Loading for items of the sub-construct
iii. The correlation between constructs (double headed arrow)
The reporting procedure is given in Table 2
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Table 2: The CFA Results for the Measurement Model for all Main and Sub Constructs
Construct Item Factor
Loading
CR
(above 0.6)
AVE
(above 0.5)
CorporateEntrepreneurship
Innovation .814 0.746 0.500Pro Activeness .709
Risk Taking .554
Innovation Q60 .696 0.928 0.649
Q59 .760
Q58 .679
Q57 .863
Q56 .872
Q55 .850
Q54 .814
Q53 .790
Q52 .794
Q51 .754
Pro activeness Q37 .696 0.838 0.567
Q38 .760
Q39 .679
Q40 .863
Risk Taking Q19 .787 0.939 0.689
Q20 .846
Q21 .875
Q22 .802
Q23 .819
Q24 .842
Q25 .835
Financial
Performance
Q6 .779 0.914 0.641
Q7 .821
Q8 .876
Q9 .806
Q10 .791
Q11 .722
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Figure 3: The Regression Path Coefficient of the model
The testing of hypothesis for the effect of Corporate Entrepreneurship on Financial Performance
H1: Corporate Entrepreneurshiphas a significant and direct effect on Financial Performance
Table 4: The Regression Path Coefficient and its Significance
Construct Path Construct Estimate S.E. C.R. P Result
Financial Performance
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8.4 PERFORMING THE SECOND ORDER CFA FOR SERVICE
QUALITY (SERVQUAL) MODEL
The famous SERVQUAL model developed by Parasuraman et al. (1985, 1988) has 22 items in five
dimensions named as Tangibility, Reliability, Responsiveness, Assurance, and Empathy. Shown in
Figure 1 are the components and their respective items. A study was carried out in 2015 using the same
items as proposed by the author (Parasuraman et al., 1988). One of the objectives of this particular
study was to re-examine and re-confirm that the measurement model for Service Quality construct with
five dimensions still holds. Thus this study needs to employ CFA to achieve its objective. The CFA
procedure was carried out as shown in Figure 2 and the results are shown in Figure 3.
Figure 1: The Measurement Model for Service Quality construct
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Figure 2: The output for Measurement Model after CFA
The Fitness Indexes in Figure 3 do not meet the required level as recommended by the literature even
though all factor loadings are above the threshold of 0.6. Thus, the researcher needs to examine the
Modification Indexes (MI) to identify the correlated items and make an appropriate modification to the
model in order to improve the fit.
Table 1 present the Modification Indices for the measurement model. Amos output in Table 1 presented
the Modification Indices (MI) based on the covariance between a pair of measurement error. The
symbol e represents the measurement error while R represents the residual of a component. Indetermining which item to modify, one should look for high MI (greater than 15) which correlates
between a pair of measurement errors: [ei ej ].
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Table 1: The Modification Indices (MI)
M.I. Par Change Notes
e10 R2 16.623 .119 Correlation between Measurement error and residual
e5 e14 16.558 .203 Correlation between Measurement error of differentcomponent
e4 R2 25.797 -.142 Correlation between Measurement error and residual
e4 e20 18.818 .220 Correlation between Measurement error of different component
e2 e5 17.416 .182 Correlation between Measurement error of the same component
e1 R3 18.136 .145 Correlation between Measurement error and residual
From the list in Table 1, the correlated pair between e2 and e5 is selected, and the modification to
the measurement model is made as shown in Figure 4.
Figure 3: The modification is made based the MI shown in Table 1.
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The Fitness Indexes achieved the required level after the modification is made. Once the Fitness
Indexes have been achieved, the study needs to compute the value of CR and AVE for every construct
as well as every component of the construct as shown in Table 2.
Table 2: The CR and AVE for the main construct and its components
Construct Item Factor
Loading
CR
(above 0.6)
AVE
(above 0.5)
Service Quality Empathy .97 0.871 0.971
Assurance .96
Tangibility .83
Reliability .93
Responsiveness .97
Empathy emp1 .85 0.886 0.610
emp2 .74
emp3 .73
emp4 .81
emp5 .77
Assurance asu1 .75 0.869 0.625
asu2 .81
asu3 .82
asu4 .78
Tangibility tan1 .84 0.870 0.626
tan2 .83
tan3 .76
tan4 .73
Reliability rel1 .73 0.897 0.635
rel2 .79
rel3 .80
rel4 .82
rel5 .84
Responsiveness res1 .78 0.865 0.617
res2 .78
res3 .82
res4 .76
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8.5 The Reexamination of Perceived Service Quality (PSQ) Model
Through Second Order CFA
There were six service quality components in PSQ Model which was developed few years ago for the
customers in Muslim countries. The current study is trying to re-examine the robustness of the model
after certain period of time to see whether the structure of components are still intact or certain items
are no longer meaningful in measuring their respective components. This particular study is being
motivated by the opinion that certain variables might have changed after certain period of time due to
changes in socio-economic status of the target population, especially with regard to the customers
perception towards services. The study employed the Second Order Confirmatory Factor Analysis(CFA) to achieve the above objective the construct consists of several sub-constructs.
Firstly, the researcher needs to execute CFA for the first order constructs. The purpose here is to ensure
that the underlying components are mutually exclusive or the discriminant validity is achieved. The
result obtained from CFA is shown in Figure 1.
Secondly, the researcher needs to examine the Fitness Indexes to determine whether they achieve the
required level. If not, then examine the factor loading for every item measuring the component. Delete
one item at a time with lowest factor loading (less than 0.6) to be deleted first and run again the model
until the Fitness Indexes achieved the required level. If it is still not achieved, then obtain the output for
Modification Indices (MI).
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.
Figure 1: The CFA for PSQ Components. The figure at the double-headed arrow indicates the correlation between
components while the figure at the single-headed arrow measure the factor loading of the items
The output shows the correlation between components is below the threshold of 0.85 reflecting the non-
existence of redundancy among the components measuring the PSQ construct. All factor loading values
are above the threshold 0.6 indicating all items are still meaningful in measuring the respective
components. All Fitness Indexes have achieved the required level which indicates the validity of the
constructs forming PSQ Model.
The output in Table 1 shows all diagonal values (in bold) are higher than the values in their respective
rows and columns indicating discriminant validity among the PSQ components.
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Table 1: The Discriminant Validity Index Summary for PAKSERV PSQ Construct
Tangibility Reliability Sincerity Assurance Familiarity Personalization
Tangibility 0.858
Reliability 0.64 0.857
Sincerity 0.58 0.45 0.838
Assurance 0.54 0.62 0.55 0.840
Familiarity 0.59 0.58 0.55 0.56 0.823
Personalization 0.51 0.57 0.56 0.52 0.62 0.838
Figure 2: The Measurement Model for PAKSERV PSQ Model
The values in Table 2 further confirm the validity and reliability of the PSQ Model.
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Table 2: The Validity and Reliability Indexes for PAKSERV PSQ Model
Construct Item Factor
Loading
CR
(above 0.6)
AVE
(above 0.5)
Perceived
Service Quality
Tangibility .77 0.885 0.563
Reliability .77
Sincerity .71
Assurance .74
Familiarity .78
Personalization .73
Tangibility g1 .87 0.933 0.736
g2 .85
g3 .85
g4 .86g5 .86
Reliability f1 .86 0.917 0.735
f2 .86
f3 .86
f4 .85
Sincerity d1 .84 0.904 0.702
d2 .82
d3 .82
d4 .87
Assurance c1 .84 0.923 0.706c2 .86
c3 .85
c4 .82
c5 .83
Familiarity b1 .84 0.863 0.678
b2 .81
b3 .82
Personalization
a1 .86 0.904 0.702
a2 .84
a3.86a4 .79
Figure 3 illustrates the regression coefficient of the construct on every sub-construct. The significance
of this regression coefficient is shown in Table 3.
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Figure 3: The Regression Path Coefficient for Every Component in the PSQ Model
Table 3: The Regression Path Coefficient and it Significance for PSQ Model
Component Path Construct Estimate S.E. C.R. P Results
Tangibility