SEM: Testing a Structural Model

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.

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

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.

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.

Visual Representation (Path Diagram) of a Simple Structural Theory

Expanded Theoretical Model

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.

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

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

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

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.

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.

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.

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

Theoretically-Based HBAT Employee Retention SEM Model 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 Note: observable indicator variables are not shown to simplify the model.

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.

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

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.

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.

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

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?