12 chapter 8 second order confirmatory factor analysis

7/26/2019 12 Chapter 8 Second Order Confirmatory Factor Analysis

1/19

A Handbook on SEM 2nd

Edition

Zainudin Awang - Universiti Sultan Zainal Abidin

163

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


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


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

12 chapter 8 second order confirmatory factor analysis

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