In dealing with SEM, there are two models involved in the analysis namely: 1. ... Figure 1: The measurement model for Service Quality construct using ten ...
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CHAPTER 2
THE MODELS INVOLVED IN STRUCTURAL EQUATION MODELING (SEM) In dealing with SEM, there are two models involved in the analysis namely: 1.
The measurement model – the model that demonstrates the relationship between measuring items and their underlying latent construct. The researcher needs to assess the measurement model for uni-dimensionality, validity, and reliability prior to modeling the structural model.
2.
The structural model – the model that demonstrates the inter-relationships among constructs as theorized in the study. The constructs are assembled into the structural model based on the hypothesis stated in the theoretical framework.
2.1 THE ROLE OF THEORY IN STRUCTURAL EQUATION MODELING The researcher begins by specifying a theoretical model on the basis of theory. Every construct in the model is conceptualized as a latent, and the researcher is measuring these constructs using multiple items in a questionnaire. These items can be developed by researchers, or adopted from literatures customized to suit the field of present study. The researcher analyzes the measurement model for each construct to assess how well the generated items representing their underlying construct. The analysis is carried out using Confirmatory Factor Analysis (CFA). Through the process of CFA, the issues of construct validity and reliability would be addressed. The researcher examines the factor loading for each item and the fitness indexes for the construct. The item having low factor loading would cause poor fitness indexes for the construct, and should be deleted from measurement model. After deletion the model is re-specified– and the fitness indexes would improve. If low factor loadings items are deleted but the fitness indexes for the construct is still low, then the researcher needs to obtain the Modification Indices (MI). MI indicates the redundancy between a pair of items in a measurement model. High MI means the items are redundant. The researcher needs to delete one of the two redundant items in order to improve the model fit.
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2.2
THE MEASUREMENT MODEL FOR A LATENT CONSTRUCT The example of a measurement model is given in Figure 1. Here, the latent construct is “service
quality” which cannot be measured directly. Instead, the service quality construct is measured using a set of ten items in a questionnaire. The ten measuring items are enclosed in Table 1.
Service Quality is a Latent Construct
Figure 1: The measurement model for Service Quality construct using ten measuring items Table 1: The measuring items for Service Quality construct This university.........
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has an adequate infrastructure facilities
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has a beautiful campus environments
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has a good campus transportation system
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has adequate academic facilities
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has a comfortable cafeteria or food courts
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has good sports facilities
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has conducive rooms in hostels
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SEM Made Simple Zainudin Awang (2015) MPWS Publisher Q8
has with library with adequate materials
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offers a flexible class schedule
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Q10
has an effective information delivery system
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Source: Research Methodology and Data Analysis 2nd Edition by Zainudin Awang (2012)
Another example of a measurement model is given in Figure 2. Here, the latent construct is “customer satisfaction” which cannot be measured directly. Instead, the customer satisfaction construct (presented in Table 2) is measured using a set of five items in a questionnaire.
Latent Construct Measuring Item
Figure 2: The measurement model for Customer Satisfaction construct Table 2: The Measuring Items for Customer Satisfaction Construct As a student of this university, I am…..
Strongly Disagree Q1 satisfied with the system at this university 1 2 3 Q2 satisfied with academic rules and regulations 1 2 3 Q3 satisfied with the process in obtaining references 1 2 3 Q4 satisfied with academic facilities provided 1 2 3 Q5 satisfied with the security system on campus 1 2 3 Source: Research Methodology and Data Analysis 2nd Edition by Zainudin Awang (2012)
4 4 4 4 4
5 5 5 5 5
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Strongly Agree 9 10 9 10 9 10 9 10 9 10
In the measurement model, the researcher models a latent construct and its measuring items. As presented in Figure 2, the latent construct is customer satisfaction and it is measured using item Q1 to Q5. The researcher analyzes a measurement model using CFA to assess the meaningfulness of its items 43
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in measuring the construct. Low factor loading item means that particular item is not meaningful in measuring the construct, and thus need to be deleted. In literatures, one would find the measuring items for latent construct are also called latent indicators, indicator variables, or manifesting variables.
2.3
THE STRUCTURAL MODEL IN AMOS GRAPHIC In the structural model, the researchers assemble the constructs involved in the study. The
positions of these constructs in the structural model would depend on how these constructs are theorized to relate to each other – or in other words, depending on the schematic diagram of the model. The beauty of AMOS is its ability to draw the schematic diagram of a model directly into its graphical interface. Furthermore, the analysis and its corresponding output are presented exactly on the graphic diagram. To put it in a more appealing perspective – with AMOS, what you see is what you get.
2.3.1
The Structural Model: Modeling the Correlational Relationship The example of a structural model is given in Figure 3. This AMOS graphic is presenting the
correlational relationship between service quality construct (with ten response items) and customer satisfaction construct (with five response items). In this structural model (Figure 3), the researcher intends to estimate the correlational relationship between service quality and customer satisfaction. The service quality construct is measured using ten response items, while the customer satisfaction construct is measured using five response items. Remember, the correlational relationship is represented by a double-headed arrow in AMOS graphic interface. This arrow should be drawn in the clockwise direction to link one latent construct to another latent construct.
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Correlational Path
Figure 3: The structural model linking Service Quality to Customer Satisfaction. In AMOS the double-headed arrow is used to estimate the correlation between the two latent constructs.
2.3.2
The Structural Model: Modeling the Causal Relationship
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The example of a structural model for a causal relationship is given in Figure 4. This AMOS graphic is measuring the causal effects of service quality construct (with ten measuring items) on customer satisfaction construct (with five measuring items). Both constructs are latent. The measuring items for service quality construct and customer satisfaction construct are presented in Table 1 and Table 2 respectively.
Causal Path
Figure 4: The structural model linking Service Quality to Customer Satisfaction. The single headed arrow is used to estimate the causal effects of Service Quality on Customer Satisfaction.
In the above structural model (Figure 4), the researchers are interested to determine the causal effect of service quality construct on customer satisfaction construct. Remember: A causal effect is represented by a single-headed arrow. The arrow is drawn from the latent exogenous construct pointing to the latent endogenous construct. The position of the arrow itself indicates the exogenous construct is hypothesized to have significant causal effect on the endogenous construct. Service Quality is a Latent Exogenous Construct Customer Satisfaction is a Latent Endogenous Construct
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2.3.3 The Structural Model: Modeling the Mediator The example of a structural model with a mediator construct is given in Figure 5. This AMOS graphic is presenting the mediating role of customer satisfaction construct. The causal arrow from service quality construct pointing towards customer satisfaction construct indicates this particular study believes that service quality performance has a causal effect on customer satisfaction. In the meantime, another arrow originates from customer satisfaction construct pointing towards the customer loyalty construct indicate that the level of customer satisfaction is believed to have a causal effect on customer loyalty.
Mediator Construct
Endogenous Construct Exogenous Construct
Figure 5: The structural model linking Service Quality, Customer Satisfaction, and Customer Loyalty.
In Figure 5, the researcher is interested to assess the mediating role of Customer Satisfaction in linking Service Quality to Customer Loyalty. Here, Customer Satisfaction is a mediator construct. The researcher is modeling the mediating construct of customer satisfaction (Figure 5). The regression equations involved this structural model: 47
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1. Customer Loyalty is a function of Service Quality 2. Customer Loyalty is a function of Customer Satisfaction 3. Customer Satisfaction is a function of Service Quality
2.4
The Types of Construct in Structural Equation Modeling
Apart from the observed variable, there are a few types of latent construct involved in SEM. Among the types of construct that researchers need to know are Reflective Construct, Formative Construct, and Second Order Construct.
2.4.1 The Reflective Construct As its name implies, the influence of this construct “reflects” on its response items. Thus the singleheaded arrow flows from the construct onto its items. This construct is measured using certain number of items in a questionnaire. Most of the times, researchers are dealing with the Reflective Constructs in the structural model. Among the examples of Reflective Constructs are: i) Customers’ Perceived Quality concerning their service experience – measured using certain number of items in a questionnaire. ii) Customers’ Perceived Usefulness towards certain cosmetic product– measured using certain number of items in questionnaire. iii) Employee’s Knowledge – the knowledge obtained from undergoing certain training programs iv) Employee’s Skills – the perceived skills acquired after undergoing certain training programs v) Employee’s Attitude – the attitude towards task after undergoing certain training programs
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A Reflective Construct: Arrows flow from Construct to the items
Figure 6: The measurement model of the Reflective Constructs in AMOS Graphic
2.4.2 The Formative Construct Formative Construct is a latent construct which is “formed” by certain number of variables. The variables forming the formative construct are directly measured, thus no measurement error is required. Among the examples of latent formative constructs are i) Socio-Economic Status of respondents which is formed by three factors namely Education, Occupation, and Income. ii) Student’s Academic Performance which is formed by three assessments made on the student namely Individual Assessment, Group Assessment and Final Exam. iii) Company Performance which is formed by three financial measures namely Return on Investment (ROI), Return of Assets (ROA) and Return on Equity (ROE)
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The Formative Construct could also become exogenous as well as Endogenous construct in the structural model. The illustration of Formative Constructs in AMOS Graphic is given in the following figure.
Variables formed the construct. No measurement error since the variables are directly observed
Formative Construct: The arrow flows from variables to form the construct
One of the variables must have a reference point 1
Figure 7: Modeling the Formative Construct in AMOS Graphic
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Formative Construct
Reflective Construct Observe Variable
Figure 7a: The model consists of Formative Construct, Reflective Construct, and Observed Variables
2.4.3 The Second Order Construct The second order construct is a construct that consists of a few sub-constructs. Each sub-construct is measured using certain number of items in a questionnaire. Sometimes the second order construct is called the main construct while the sub-constructs are the components of the main construct. Among the examples of second order construct are Training Transfer which consists of three sub-constructs namely Knowledge, Skills, and Attitude. Another example is Service Quality construct which consists of five sub-constructs namely Reliability, Tangibility, Responsiveness, Empathy, and Assurance.
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SEM Made Simple Zainudin Awang (2015) MPWS Publisher Measurement error of the sub-construct Measurement error of the item
The Second Order Construct - Arrow flows from main construct to sub-constructs
First Order Construct or Sub-Construct
Figure 8: Modeling the Second Order Construct of Training Transfer in AMOS Graphic
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Figure 9: Modeling the Second Order Construct of Patients Service Quality in AMOS Graphic
Figure 9a: The output showing factor loading for second order as well as first order construct 53
SEM Made Simple Zainudin Awang (2015) MPWS Publisher Example: The AMOS Graphic can take all types of construct in the model The model in Figure 9 consists of all three types of construct namely formative construct, first order reflective construct and second order reflective construct.
Second order construct HEALTH has two Sub-constructs
First order construct STRESS has eight items
Formative construct SES is measured using three variables
Figure 10: The model in AMOS Graphic which consists of three types of constructs
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