1. SEM: Testing a Structural Model

2. SEM: Testing a Structural Model
LEARNING OBJECTIVES
Upon completing this chapter, you should be able to do the following:
Distinguish a measurement model from a structural model.
Describe the similarities between SEM and other multivariate techniques.
Depict a model with dependence relationships using a path diagram.
Test a structural model using SEM.
Diagnose problems with the SEM results.

3. Structural Equations Modeling Overview
What is it?
Why use it?

4. Structural Equations Modeling Defined
Structural Equations Modeling is a process for testing a structural theory. A structural theory is a conceptual representation of the hypothesized structural relationships between constructs. It can be expressed in terms of a structural model that represents the theory with a set of structural equations and is usually depicted with a visual diagram.

5. An Overview of Theory Testing with SEM
The testing of theoretical models using SEM focuses on two issues:
The overall and relative model fit.
The size, direction and significance of the structural parameter estimates, depicted with one-headed arrows on a path diagram.

6. Visual Representation (Path Diagram) of a Simple Structural Theory

7. Expanded Theoretical Model

8. Structural Equations Modeling Stages
Stage 1: Defining Individual Constructs
Stage 2: Developing the Overall Measurement Model
Stage 3: Designing a Study to Produce Empirical Results
Stage 4: Assessing the Measurement Model Validity
Stage 5: Specifying the Structural Model
Stage 6: Assessing Structural Model Validity
Note: We test measurement theory during stages 1 – 4 and structural theory in stages 5 – 6.

9. Stages in Testing Structural Theory
Key Issues
One-Step vs. Two-Step Approaches
Completing Stages 5 and 6 to test the structural theory

10. Stage 5: Specifying the Structural Model
Key Issues
Unit of analysis
Model specification using a path diagram
Measurement model
Structural model
Recursive vs. nonrecursive models
Designing the study

11. Stage 5: Converting a Measurement (CFA) Model into a Structural Model

12. Stage 5: A Non-recursive Model
Job Satisfaction is both a predictor of and a result of Job Search. Job Search is both a predictor of and a result of Job Satisfaction. Therefore, the model is non-recursive.

13. Specifying the Structural Model
Rules of Thumb 14–1
Specifying the Structural Model
CFA is limited in its ability to examine the nature of relationships between constructs beyond simple correlations.
A structural model should be tested after CFA has validated the measurement model.
The structural relationships between constructs can be created by:
replacing the two-headed arrows from CFA with single headed arrows representing a cause and effect type relationship, or
removing the two-headed curved arrows connecting constructs that are not hypothesized to be directly related.
Recursive SEM models cannot be associated with fewer degrees of freedom than a CFA model involving the same constructs and variables.

14. Specifying the Structural Model
Rules of Thumb 14–1 continued
Specifying the Structural Model
Non-recursive models involving cross-sectional data should be avoided in most instances:
It is difficult to produce a set of conditions that could support a test of a reciprocal relationship with cross-sectional data.
Non-recursive models yield more problems with statistical identification.
When a structural model is being specified, it should use the CFA factor pattern corresponding to the measurement theory and allow the coefficients for the loadings and the error variance terms to be estimated along with the structural model coefficients.
Measurement paths and error variance terms for single item “constructs” should be set based on the best knowledge available.
The loading estimate between the variable and the latent construct is set (fixed) to the square root of the best estimate of its reliability.
The corresponding error term is set (fixed) to 1.0 minus the reliability estimate.

15. Stage 6: Assessing the Structural Model Validity
Key Issues
Understanding structural model fit from CFA fit
Comparing CFA fit and SEM fit
Examining hypothesized dependence relationships
Examining the model diagnostics

17. Theoretically-Based HBAT Employee Retention SEM ModelEP JS SI OC
Hypotheses:
H1: EP + JS
H2: EP + OC
H3: AC +JS
H4: AC +OC
H5: JS + OC
H6: JS +  SI
H7: OC +SI AC
Note: observable indicator variables are not shown to simplify the model.

18. HBAT CFA/SEM Constructs and Indicator Variables
Organizational Commitment
OC1 = My work at HBAT gives me a sense of accomplishment.
OC2 = I am willing to put in a great deal of effort beyond that normally expected to help HBAT
be successful.
OC3 = I have a sense of loyalty to HBAT.
OC4 = I am proud to tell others that I work for HBAT.
Staying Intentions
SI1 = I am not actively searching for another job.
SI2 = I seldom look at the job listings on monster.com.
SI3 = I have no interest in searching for a job in the next year.
SI4 = How likely is it that you will be working at HBAT one year from today?
Attitudes Towards Co-Workers
AC1 = How happy are you with the work of your coworkers?
AC2 = How do you feel about your coworkers?
AC3 = How often do you do things with your coworkers on your days off?
AC4 = Generally, how similar are your coworkers to you?
Environmental Perceptions
EP1 = I am very comfortable with my physical work environment at HBAT.
EP2 = The place I work in is designed to help me do my job better.
EP3 = There are few obstacles to make me less productive in my workplace.
EP4 = What term best describes your work environment at HBAT?
Job Satisfaction
JS1 = All things considered, I feel very satisfied when I think about my job.
JS2 = When you think of your job, how satisfied do you feel?
JS3 = How satisfied are you with your current job at HBAT?
JS4 = How satisfied are you with HBAT as an employer?
JS5 = Please indicate your satisfaction with your current job with HBAT by placing a percentage in the blank, with 0% = not satisfied at all and 100% = highly satisfied.
Copyright © 2010 Pearson Education, Inc., publishing as Prentice-Hall.

19. Description of HBAT CFA-SEM Database Variables
Variable Description Variable Type
JS1 I feel satisfied when I think about my job. (0-10, Agree-Disagree) Metric
OC1 My work at HBAT give me a sense of accomplishment (0-10, Agree-Disagree) Metric
OC2 I am willing to put in a great deal of effort . . to help HBAT (0-10, Agree-Disagree) Metric
EP1 I am comfortable with my work environment at HBAT (0-10, Agree-Disagree) Metric
OC3 I have a sense of loyalty to HBAT (0-10, Agree-Disagree). Metric
OC4 I am proud to tell others that I work for HBAT (0-10, Agree-Disagree). Metric
EP2 The place I work in is designed to help me do my job better (0-10, Agree-Disagree) Metric
EP3 There are few obstacles to make me less productive in my workplace (0-10, Ag-Disa). Metric
AC1 How happy are you with the work of your coworkers? (5-pt. Happy-Unhappy) Metric
EP4 What term best describes your work environment? (7-pt. Hectic-Soothing?) Metric
JS2 When you think of your job, how satisfied do you feel? (7-pt) Metric
JS3 How satisfied are you with your current job with HBAT? (7-pt) Metric
AC2 How do you feel about your coworkers? (7-pt. Unfavorable-Favorable) Metric
SI1 I am not actively searching for another job. (5-pt. Agree/Disagree) Metric
JS4 How satisfied are you with HBAT as an employer? (5-pt. Not vs. Very Much) Metric
SI2 I seldom look at the job listings on Monster.com. (5-pt. Agree-Disagree) Metric
JS5 Please indicate your satisfaction with your current job. (0-100% Satisfied) Metric
AC3 How often do you do things with your coworkers on your days off? (5-pt. Never-Often) Metric
SI3 I have no interest in searching for a job in the next year. (5-pt. Agree-Disagree) Metric
AC4 Generally, how similar are your coworkers to you? (6-pt. Different-Similar) Metric
SI4 How likely is it that you will be working at HBAT one year from today? (5-pt) Metric
X22 Your work type – full time or part time? (0 = Full Time/1 = Part Time) Nonmetric
X23 Your gender – male or female? (0 = Female/1 = Male) Nonmetric
X24 Your geographic location – in USA or outside USA? (0 = Outside/1 = USA) Nonmetric
X25 Your age in years ___? Metric
X26 How long have you worked for HBAT – years and months? Metric

20. Measurement Theory Model for HBAT 5 Construct CFA
OC2
OC3
OC1
OC4
Organizational Commitment
JS1
JS2
SI1
Job Satisfaction
JS3
Staying Intentions
SI2
JS4
SI3
JS5
SI4
Attitudes toward Coworkers
Environmental Perceptions
AC1
AC2
AC3
AC4
EP1
EP2
EP3
EP4
Note: Measured variables are shown as a box with labels corresponding to those shown in the HBAT questionnaire. Latent constructs are an oval. Each measured variable has an error term, but the error terms are not shown. Two headed connections indicate covariance between constructs. One headed connectors indicate a causal path from a construct to an indicator (measured) variable. In CFA all connectors between constructs are two-headed covariances / correlations.

21. Note: model is recursive.
Theoretically-Based HBAT
Employee Retention SEM Model
Note: model is recursive.
Endogeneous Variable EP
Endogeneous Variable JS SI OC
Hypotheses:
H1: EP + JS
H2: EP + OC
H3: AC +JS
H4: AC +OC
H5: JS + OC
H6: JS +  SI
H7: OC +SI AC
Exogeneous Variable
Note: observable indicator variables are not shown to simplify the model.

24. Hypothesized new relationship to test.
Possible “Competing” HBAT
Employee Retention SEM Model
Hypothesized new relationship to test. EP JS SI OC
Hypotheses:
H1: EP + JS
H2: EP + OC
H3: AC +JS
H4: AC +OC
H5: JS + OC
H6: JS +  SI
H7: OC +SI AC

28. SEM Learning Checkpoint
How does SEM differ from CFA?
Explain the difference between a one-step and a two-step approach.
What is the difference between endogenous and exogenous constructs?
How are the hypothesized relationships in SEM different?
What are some typical problems you can encounter with SEM and how do you deal with them?
What are the three SEM GOF measures and how do they differ?