Table Of ContentStructural Equation Modeling Using AMOS
Preface
In the era of advanced technology, vast amount of data concerning science, social
science, and economy are gathered and transmitted efficiently worldwide. Thus,
academicians as well as practitioners need to analyze those data so that it will be
meaningful for decision makers, policy makers, and the like. As everybody knows,
making quick and accurate decision is crucial for the growth and survival of an
organization, especially in the borderless world where competitions are fierce. Thus,
employing the advanced research methodology in data analysis often differentiates
between success and failure of an organization. Structural Equation Modeling, or
popularly known as SEM, is one of the newest methods of multivariate data analysis
developed specifically to overcome the limitations experienced in the previous
methodology namely the Ordinary Least Square (OLS) regressions.
SEM, which is often termed as the Second Generation Method, could entertain latent
constructs with multiple indicators as well as the usual observed variables into the model
concurrently and, more importantly, the inter-relationship among them are analyzed
simultaneously. This book is suitable for the beginners since it explains the basic concept
of SEM and how it works together with easy to understand examples. The book also
introduces the application of the most popular SEM software namely AMOS Graphic. As
the chapter moves on, it provides practical examples where SEM with AMOS Graphic is
employed to model and solve the problems in postgraduate studies. Among the statistical
analysis procedure explained in detail include the testing of hypothesis for Path Model
(direct effect), testing the mediation effect of a Mediator (direct as well as indirect effect),
and testing the moderation effect of a Moderator (interference effect) in the model.
Zainudin Awang, PhD
Table of Contents Page
Overview: Structural Equation Modeling (SEM) using AMOS 1
Why One Needs to Employ SEM? 4
Examples Where AMOS Graphic is Employed in Research 8
Chapter 1
1.0 Introduction to Structural Equation Modeling (SEM) 17
1.1 The Concept of SEM and How it Works 17
1.2 The Advantages of SEM Compared to OLS 18
1.3 Converting Regression Models into AMOS Graphic 20
1.4 The Concept of Latent Construct in Research 22
1. 5 The Minimum Sample Size Required in using SEM 24
1.6 Introduction to AMOS Software 24
1.7 The Variable Terms in SEM using AMOS 25
1.8 Modeling the Observed and Unobserved variables in AMOS Graphic 27
1.9 Modeling Multiple Variables in AMOS Graphic 32
1.10 Modeling the Mediator Variable in AMOS Graphic 34
1.11 Modeling the Moderator Variable in AMOS Graphic 40
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Chapter 2
2.0 The Models Involved in Structural Equation Modeling 46
2.1 The Role of Theory in Structural Equation Modeling 46
2.2 The Measurement Model for a Construct 47
2.3 The Structural Model in AMOS Graphic 50
2.3.1 The Structural Model: Modeling the Correlational Relationship 50
2.3.2 The Structural Model: Modeling the Causal Relationship 52
2.3.3 The Structural Model: Modeling the Mediator 53
2.4 The Types of Constructs in Structural equation Modeling 55
2.4.1 The Reflective Construct 55
2.4.2 The Formative Construct 56
2.4.3 The Second Order Construct 59
Chapter 3
3.0 Validating the Measurement Model using CFA 61
3.1 Evaluating the Fitness a Model: The Measurement and Structural 63
Model
3.2 The Steps Involved in Validating the Measurement Model 68
3.3 The Confirmatory Factor Analysis (CFA) 69
3.31 Validating the Pooled Measurement Model 72
3.32 The Measurement Model for Pooled Latent Constructs 73
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3.33 Assessing the Validity and Reliability for a Pooled Measurement 78
Model
3.4 The Assessment of Normality Distribution for the Data 80
Chapter 4
4.0 Analyzing the SEM Structural Model in AMOS Graphic 84
4.1 The Steps Involved in Performing Structural Equation Modeling 84
4.2 Performing the Structural Equation Modeling Analysis 85
4.2.1 Interpreting the AMOS Text Output: The Standardized Regression 91
Weights
4.2.2 Interpreting the AMOS Test Output: The Regression Weights 92
4.2.3 Interpreting the AMOS Test Output: The Standardized Residual 94
Covariance
4.3 An Example of More Complicated Amos Output 95
Chapter 5
5.0 Analyzing the Relationships between Variables in a Model 99
5.1 Analyzing the Relationships between Observed Variables 99
5.2 Analyzing the Relationships between Latent Constructs 101
5.3 Analyzing the Causal Effects for Observed Variables 104
5.4 Analyzing the Causal Effects for Simple Latent Constructs 105
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5.5 Analyzing the Causal Effects for Multiple Latent Constructs 107
5.6 Path Analysis: Analyzing the Mediation Effects in a Model 112
Chapter 6
6.0 Analyzing the Mediating Variable in a Model 118
6.1 Analyzing the Mediating Effects for Observed Variables 120
6.2 Analyzing the Mediating Effects for Latent Constructs 124
6.3 Analyzing the Mediator in a Complex Model 129
6.4 Mediation Test: Confirming the Test Results through Bootstrapping 134
6.5 Computing the Effect Size in a Mediation Test 136
Chapter 7
7.0 Analyzing the Moderating Variable in a Model 144
7.1 The Schematic Diagram for Moderator Variable in a Model 145
7.2 Modeling the Interaction effects for Observed variables 147
7.3 Scale of Measurement for the Moderator Variable 148
7.4 Modeling the Moderating Effects for Observed Variable 149
7.5 Analyzing the Moderating Effects for Observed Variable 151
7.6 Modeling the Moderating Effects for Latent Constructs 154
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7.7 Analyzing the Moderator for Latent Constructs: The Multi-Group 155
CFA
7.8 Comparing the Group Effect for Moderator Variable 172
Chapter 8
8.0 The Second Order Confirmatory factor Analysis 176
8.1 The Steps Involved in Performing Second Order CFA 176
8.2 Performing Second Order CFA for Training Transfer Constructs 177
8.3 Performing Second Order CFA for Job Satisfaction Constructs 181
8.4 Performing Second Order CFA for Technological Innovation 191
Constructs
Chapter 9
9.0 The Application of AMOS Graphic in Postgraduate Researches 199
9.1 Modeling the Loyalty of banking Customers 199
9.2 Modeling the Loyalty of Outgoing Undergraduates towards 201
University for Postgraduates
9.3 Modeling Customer Loyalty towards their Service Provider 209
9.4 Modeling Investor Loyalty towards Listed Companies 212
9.5 Modeling the Effects of Entrepreneurial Orientation on Business 213
performance
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9.6 Modeling the Effects of University reputation on Students Loyalty 214
9.7 Modeling the Effects of Individual Factors, Transfer Climate, and 215
Training Design on Training Transfer in an Organization
9.8 Modeling Motivation to Transfer as a Mediator in The Transfer 221
Training Model
Bibliography 224
Index 228
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Overview of Structural Equation Modeling (SEM)
Academicians, researchers, as well as postgraduate students, are debating theories
concerning the relationships among certain hypothetical constructs. They are modeling
this theorized relationship with the intention to test their theoretical model with the
empirical data from the field. The example of a Theoretical Framework is given in Figure
1.
Figure 1: The Schematic Diagram Showing the Theoretical Framework of a Study
The schematic diagram in Figure A is converted into AMOS Graphic and
analyzed using empirical data. In AMOS Graphic, the rectangle represents the directly
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observed variables, while the ellipse represents the unobserved variable or latent
constructs. The schematic diagram of theoretical framework in Figure 1 is converted into
AMOS Graphic as shown in Figure 2.
In Figure 2, the researcher needs to determine the types of variables and
constructs involved in the model and how the study is going to measure them. The types
of latent construct and variables involved in Figure 2 are identified as follows:
1. Financial position is a latent construct. The type of this latent construct is called
Formative Construct. This Formative Construct is formed by four variables namely
Leverage, Growth, Bankruptcy, and Tax Consideration. The data for these variables
are obtained directly from the annual reports. The type of variables here are measured
or observed variables.
2. Risk Taking Propensity is another latent construct. The type of latent construct in
this case is called Second Order Construct. This Second Order Construct consists of
three first order constructs or dimensions namely Comp1, Comp2, and Comp3. The
variables for Comp1 (R11, R12, CR13), Comp2 (R21, R22, R23), and Comp3 (R31,
R32, R33) are measured using items in a questionnaire.
3. Attitude towards Risk is another Second Order construct. This construct consists of
two first order constructs or dimensions namely Att1 and Att2. The latent construct
Att1 and Att2 are measured using four items in a questionnaire (St11, St12, St13,
St14) and (St21, St22, St23, St24), respectively.
4. Demand for Insurance is an observed variable. Sometimes, this variable is termed as
a directly measured variable. The value is obtained from secondary data.
For the sake of providing the overall picture of what to expect from the book, the
author would demonstrate the process from the beginning (theoretical framework)
until the output is obtained for analysis through Figure 1, Figure 2, and Figure 3.
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Figure 2: The Schematic Diagram is Converted into AMOS Graphic
Figure 2 shows the measuring items for all constructs and variables involved in a
model. In AMOS Graphic, ellipses represent latent constructs, while rectangles represent
input variables. Once the data are obtained, the researcher would input these data into
their respective variable indicated by rectangles. The data input is made through “click
and drag” procedure.
Figure 3 shows the output produced by AMOS Graphic after data input was made
and the model was executed. This output is ready for interpretation and hypothesis
testing.
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