In Amos Graphic, the rectangles represent the observed variables while the .... The conversion of a research framework into AMOS Graphic will be illustrated ...
A Handbook on SEM 2nd Edition Zainudin Awang - Universiti Sultan Zainal Abidin
Overview of Structural Equation Modeling (SEM) Academicians, researchers, as well as postgraduate students are developing theories concerning the relationships among certain hypothetical constructs. They are modeling their theorized relationships 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 A.
The path diagram of the model for the study is developed based on theories. From here, the researcher comes out with his theoretical framework for the study.
Figure A: The Path 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 rectangles represent the observed variables while the ellipses represent the atent constructs. The schematic diagram of theoretical framework in Figure A is converted into Amos Graphic as shown in Figure B. 1
A Handbook on SEM 2nd Edition Zainudin Awang - Universiti Sultan Zainal Abidin
In Figure B, the researcher determines 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 B are identified as follows: 1. Financial Position is a latent construct. This type of construct is called Formative Construct. This construct is ―formed‖ by observed variables namely Company Leverage, Annual Growth, Performance Ratio, and Company Taxation. These data are obtained from the annual report (secondary source). In this model, Financial Position construct is measured indirectly using four measures. Thus, no measurement error required. 2. Risk Taking Propensity is also a latent construct. This construct is called Second Order
Construct since it consists of three sub-constructs namely Comp1, Comp2, and Comp3. And for each sub-construct, there are few items namely R11, R12, and CR13 for Comp1, R21, R22, and R23 for Comp2, and R31, R32, and R33 for Comp3. These items are included in a questionnaire. Thus, the measurement errors are required for every item since it is measuring respondent’s perception about risk (Figure B). 3. Attitude towards Risk is also a Second Order construct. This construct consists of two first sub-constructs 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. Thus, the measurement error is also required for every items being measured since it is measuring respondent’s attitude towards risk (Figure B). 4. Demand for Insurance is an observed variable. Sometime this variable is termed as a
directly measured variable. The value is obtained directly from secondary data. Thus, it is represented using a rectangle and no measurement error involved.
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 A, Figure B, and Figure C.
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A Handbook on SEM 2nd Edition Zainudin Awang - Universiti Sultan Zainal Abidin
Figure B: The Path Diagram is converted into Amos Graphic.
Figure B shows the measuring items for all constructs and variables involved in a model. In Amos Graphic, ellipses represent latent constructs while rectangles represent the measured variables. The measures for formative construct (Leverage, Growth, Bankruptcy, and TaxConsideration) have no measurement errors since they are exact values. While the measures for reflective constructs (R11-R13, R21-R23, R31-R33, St11-St14, St21-St24, and Int1-Int6) have measurement errors since they are respondent’s perception score. All dependent variables and endogenous constructs (indicated through an ―arrow-pointing in‖) must have an error in equation. Note: An arrow originating from an Independent Variable pointing towards a Dependent Variable completes one equation, thus it needs an error in equation or residual. Once the data is obtained, the researcher would pluck these data into their respective variable indicated by rectangles. The data input is made through ―click and drag‖ procedure. 3
A Handbook on SEM 2nd Edition Zainudin Awang - Universiti Sultan Zainal Abidin
Figure C shows the output produced by Amos Graphic after data input was made and the model was executed. The output in Figure C is ready for interpretation.
Figure C: The Amos Graphic showing the respective path coefficient, factor loading and R2
Why One Needs to Employ SEM? SEM is a Second Generation multivariate analysis technique developed due to some limitations in the traditional Ordinary Least Squares (OLS) especially when dealing with latent constructs. In the above example (Figure B), Financial Positions, Risk-Taking Propensity, Attitude towards Risk, and Intention to Protect are latent constructs. Latent constructs are unobserved variables. They are measured indirectly using multiple items in a questionnaire. The analysis for 4
A Handbook on SEM 2nd Edition Zainudin Awang - Universiti Sultan Zainal Abidin
latent constructs is no longer appropriate with traditional OLS, and the researchers should switch to SEM so as to keep pace with the advancement in research methodology. In fact, SEM is developed to cater limitations in OLS, and among them are latent constructs and modeling the inter-relationship among constructs simultaneously in a model. AMOS is an acronym for Analysis of Moments Structures. This is one of the newest software developed for Structural Equation Modeling (SEM). The researchers could employ AMOS Graphic to model and analyze the inter-relationships among latent constructs effectively, accurately, and efficiently. More importantly, the multiple equations of inter-relationships in a model are computed simultaneously.
Why One Should Employ Amos Graphic? As has been said earlier, researchers could convert their theoretical framework directly into AMOS graphic for analysis. More importantly, using Amos Graphic interface, researchers can create path diagrams using drawing tools, rather than by writing equations or by typing commands. Even the researchers could validate the measurement model of a latent construct using Confirmatory Factor Analysis (CFA). Once CFA is completed, the researcher could move into modeling the Structural Equation Modeling (SEM). Thus, analyzing and testing the theory using AMOS is fast, efficient, and user friendly.
The conversion of a research framework into AMOS Graphic will be illustrated using the following example. The theoretical framework in Figure 1 consists of four constructs namely Entrepreneurial Orientation (EO), Marketing Orientation (MO), Organizational Innovation (OI), and Business Performance (BP). Construct EO and MO have two sub-constructs each. The subconstructs are measured using certain number of items in a questionnaire. Meanwhile, Construct OI and BP are measured using five items and four items respectively. An example of a researcher’s theoretical framework and the corresponding hypotheses is given in Figure 1.
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A Handbook on SEM 2nd Edition Zainudin Awang - Universiti Sultan Zainal Abidin
Figure 1: The theoretical framework showing the path hypotheses to be tested in the study
The framework in Figure 1 indicates several hypotheses to be tested in the study. Hypotheses H 1, H2, H3, and H5 are testing for causal effects. Hypothesis H4 is intended to test the mediation effects; while another hypothesis namely H6 is testing the moderation effect in the model. The procedure for hypothesis testing would be made easy in SEM using AMOS Graphic. The researcher only needs to convert the theoretical model into AMOS Graphic. Once converted, the inter-relationship among constructs could be analyzed. Now, let see how the theoretical framework in Figure 1 is converted into AMOS Graphic as shown in Figure 2.
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A Handbook on SEM 2nd Edition Zainudin Awang - Universiti Sultan Zainal Abidin
Figure 2: The research framework converted into AMOS Graphic. Table 1: The hypotheses to be tested in the study H1
Entrepreneurial Orientation has positive and significant effect on Marketing Orientation
H2
Entrepreneurial Orientation has positive and significant effect on Organizational Innovation
H3
Entrepreneurial Orientation has positive and significant effect on Business Performance
H4
Marketing Orientation has positive and significant effect on Organizational Innovation
H5
Marketing Orientation has positive and significant effect on Business Performance
H6
Organizational Innovation has positive and significant effect on Business Performance
H7
Marketing Orientation mediates the relationship between Entrepreneurial Orientation and Business Performance
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A Handbook on SEM 2nd Edition Zainudin Awang - Universiti Sultan Zainal Abidin H8
Organizational Innovation mediates the relationship between Marketing Orientation and Business Performance
Figure 3: The output shown the path coefficient and other values after the model is executed
AMOS Graphic could find models that best fit data at hand The researcher should take advantage from the results of previous researches by specifying constraints on a certain parameter in the model. Researchers can fit multiple models in a single analysis. Amos Graphic examines every pair of the models where one model can be obtained by placing parameter restrictions on the other. Amos could also identify the pair of redundant items in a measurement model which jeopardize the fitness of the model. The researcher could either constrain a pair of redundant items in a measurement model, or delete the item altogether from the model in order to improve the fitness of the model. 8
A Handbook on SEM 2nd Edition Zainudin Awang - Universiti Sultan Zainal Abidin
Examples where AMOS Graphic is employed in research: Now let’s go through some practical examples to familiarize how AMOS Graphic is being employed to model and analyze research problems. Do not worry if you found the applications to be too difficult for you to understand at this stage because we will go back to basic and begin our journey from ground zero beginning chapter 1. 1)
In the field of psychological research — AMOS Graphic could be employed to model and evaluate the role of medical counseling in helping the healing process of patients undergoing treatment in a hospital. The above objective could be modeled using AMOS Graphic as shown in Figure 3. In Figure 3, the amount of medication administered is an independent variable. Note - The independent variable is the variable that can be manipulated by the researcher. The degree of wellness is a dependent variable since it is the outcome of independent variable. The medical counseling is a moderator variable. The study is intended to evaluate the moderation effects of medical counseling in the relationship between amount of medication administered by the doctor and the degree of wellness experienced by the patients. Both variables in the model namely the amount of medication and degree of wellness are directly measured. In the model (Figure 3), the degree of wellness could also be latent construct if it is measured through a set of questionnaire given to the patients to measure how they feel after taking certain amount of medication and going through certain period of medical counseling.
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A Handbook on SEM 2nd Edition Zainudin Awang - Universiti Sultan Zainal Abidin
All variables involved in the model are directly observed
Figure 3: Modeling the moderator variable “medical counseling intervention” in the relationship between Amount of Medication and Degree of Wellness of hospital patients. 2)
In the field of medical and healthcare research — AMOS Graphic could be employed to determine the influence of Corporate Image of drugs manufacturers and Cost of Medicines on the doctors’ Willingness to Prescribe generic drugs to their patients. The above problem is modeled in AMOS Graphic as shown in Figure 4. In the study, the Manufacturer Image and Willingness to Prescribe are latent constructs measured through a set of questionnaire, while the Cost of Medicine is a directly measured variable. The directly measured variable is also termed as an observed variable.
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A Handbook on SEM 2nd Edition Zainudin Awang - Universiti Sultan Zainal Abidin
Manufacturer Image and Willingness to Prescribe are latent constructs
Cost of Medicine is a directly measured variable
Figure 4: Modeling the causal effects of Manufacturer Image and Cost of Medicine on Doctors’ Willingness to Prescribe. 3)
In the field of social science — AMOS Graphic could be employed to determine the effects of respondents’ Socio-Economic Status (SES) on their Stress and Health Condition. The above problem could be modeled in AMOS Graphic as shown in Figure 5. In the model (Figure 5), SES is an independent latent construct measured using three variables namely education, occupation, and income. Another latent construct namely stress is measured using eight items in a questionnaire. The other latent construct namely health is measured using two sub-constructs namely mental health (5 items) and physical health (5 items). 11
A Handbook on SEM 2nd Edition Zainudin Awang - Universiti Sultan Zainal Abidin
SES is a formative construct
Stress is a reflective first order construct
Health is a reflective second order construct measured by mental and physical health
Figure 5: Modeling the effects of SES on Health with Stress as a mediator construct 4)
In the field of educational research — AMOS Graphic could be employed to evaluate how infrastructure facilities, academic facilities, academic instructors, and program schedules are influencing students’ academic performance in a university. The above problem is modeled in Figure 6. In the model, the variable student academic performance is a latent construct. This construct is measured using three variables namely individual performance (observed score), group performance (observed score), and final examination (observed score). In this case, the academic performance is called a formative construct since it is formed by the observed score instead of the items in a questionnaire.
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A Handbook on SEM 2nd Edition Zainudin Awang - Universiti Sultan Zainal Abidin
Academic Performance is a Formative Construct
Figure 6: Modeling the multiple regression equations with latent constructs 5)
In the field of academic research – AMOS Graphic could be employed to assess how Students’ Satisfaction mediates the relationship between University Reputation and the Loyalty of outgoing undergraduates to continue into postgraduate study. Figure 7 illustrate how the Students’ Satisfaction construct is modeled as a mediator in the relationship between University Reputation and Students Loyalty.
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A Handbook on SEM 2nd Edition Zainudin Awang - Universiti Sultan Zainal Abidin
University Reputation and Students Loyalty are Second Order constructs
Main construct is University Reputation. Subconstructs are Faculties, programs, and Collaboration. Main construct is Students Loyalty. Sub-constructs are Repurchase and Recommend
Figure 7: Modeling the Students’ Loyalty towards a university 6)
In the field of market research — AMOS Graphic could be employed to model the effects of Corporate Reputation of manufacturers on the Competitiveness of their products in the market. The study hypothesizes that the higher the corporate reputation of an organization, the products will be more competitive. Corporate Reputation is a second order construct. It is measured through three first order constructs namely Company reputation, Product Reputation, and Personnel Reputation.
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A Handbook on SEM 2nd Edition Zainudin Awang - Universiti Sultan Zainal Abidin
In this model - Main construct is Corporate Reputation while sub-constructs are Company, Product, and Personnel. All sub domains are measured using questionnaires.
Corporate Reputation is a second order construct. Its first order constructs are Company, product, and Personnel
Figure 8: Modeling the impact of manufacturers Corporate Reputation on the Competitiveness of their products in the market.
7)
In the field of institutional research — AMOS Graphic is employed to study the significance of Organizational Climate in a workplace as a moderator in the relationship between Employees’ Job Satisfaction and their Work Commitment (Figure 9). In Figure 9, the researcher is theorizing that the effects of Job Satisfaction on Work Commitment would depend on the level of Organizational Climate in an organization. 15
A Handbook on SEM 2nd Edition Zainudin Awang - Universiti Sultan Zainal Abidin
Independent Construct
Dependent Construct
Moderator
Figure 9: Modeling the Organizational Climate in an organization as a moderator in the relationship between employees Job Satisfaction and their Work Commitment
In Figure 9, the construct Organizational Climate is a moderator in the Job Satisfaction and Work Commitment relationship. However, in Figure 10, the same construct namely Organizational Climate could also be used as a mediator in the same study (Refer to Figure 10). In Figure 10, the researcher is theorizing that Job Satisfaction among employees should trigger positive work climate in an organization (Organizational Climate) and with good working climate, the intended Work Commitment among employees could be achieved.
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A Handbook on SEM 2nd Edition Zainudin Awang - Universiti Sultan Zainal Abidin
Mediator
Independent Construct
Dependent Construct
Figure 10: Modeling the Organizational Climate as a mediator linking employees’ Job Satisfaction and their Work Commitment.
After going through some research examples where AMOS Graphic is employed to model the stated research framework, now we move into Chapter 1 to begin our learning process on SEM using AMOS Graphics.
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