SEM: Testing a Structural ModelSEM: Testing a Structural Model

LEARNING OBJECTIVESLEARNING OBJECTIVESUpon completing this chapter, you should be able to Upon completing this chapter, you should be able to

do the following:do the following:• Distinguish a measurement model from a structural Distinguish a measurement model from a structural

model.model.• Describe the similarities between SEM and other Describe the similarities between SEM and other

multivariate techniques.multivariate techniques.• Depict a model with dependence relationships using Depict a model with dependence relationships using

a path diagram.a path diagram.• Test a structural model using SEM.Test a structural model using SEM.• Diagnose problems with the SEM results.Diagnose problems with the SEM results.

SEM: Testing a Structural ModelSEM: Testing a Structural Model

• What is it?What is it?

• Why use it?Why use it?

Structural Equations Modeling Structural Equations Modeling OverviewOverview

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

Structural Equations Modeling DefinedStructural Equations Modeling Defined

An Overview of Theory Testing with SEMAn Overview of Theory Testing with SEM

The testing of theoretical models using SEM The testing of theoretical models using SEM

focuses on two issues:focuses on two issues:

• The overall and relative model fit.The overall and relative model fit.

• The size, direction and significance of the The size, direction and significance of the

structural parameter estimates, depicted structural parameter estimates, depicted

with one-headed arrows on a path diagram.with one-headed arrows on a path diagram.

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

Expanded Theoretical ModelExpanded Theoretical Model

Structural Equations Modeling StagesStructural Equations Modeling Stages

Stage 1: Defining Individual Constructs Stage 1: Defining Individual Constructs

Stage 2: Developing the Overall Measurement ModelStage 2: Developing the Overall Measurement Model

Stage 3: Designing a Study to Produce Empirical Stage 3: Designing a Study to Produce Empirical ResultsResults

Stage 4: Assessing the Measurement Model ValidityStage 4: Assessing the Measurement Model Validity

Stage 5: Specifying the Structural ModelStage 5: Specifying the Structural Model

Stage 6: Assessing Structural Model ValidityStage 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 TheoryStages in Testing Structural Theory

Key Issues . . . Key Issues . . .

• One-Step vs. Two-Step ApproachesOne-Step vs. Two-Step Approaches

• Completing Stages 5 and 6 to test the Completing Stages 5 and 6 to test the

structural theorystructural theory

Stage 5: Specifying the Structural Stage 5: Specifying the Structural ModelModel

Key Issues . . . Key Issues . . .

• Unit of analysisUnit of analysis

• Model specification using a path diagramModel specification using a path diagramo Measurement modelMeasurement modelo Structural modelStructural modelo Recursive vs. nonrecursive modelsRecursive vs. nonrecursive models

• Designing the studyDesigning the study

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

Stage 5: A Non-recursive ModelStage 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.

Rules of Thumb 14–1 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:

o replacing the two-headed arrows from CFA with single headed arrows representing a cause and effect type relationship, or

o 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.

Rules of Thumb 14–1 continued . . .Rules of Thumb 14–1 continued . . .

Specifying the Structural Model• Non-recursive models involving cross-sectional data should be avoided in

most instances:o It is difficult to produce a set of conditions that could support a test of a

reciprocal relationship with cross-sectional data. o 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.

o The loading estimate between the variable and the latent construct is set (fixed) to the square root of the best estimate of its reliability.

o The corresponding error term is set (fixed) to 1.0 minus the reliability estimate.

Stage 6: Assessing the Stage 6: Assessing the Structural Model ValidityStructural Model Validity

Key Issues . . . Key Issues . . .

• Understanding structural model fit from CFA fitUnderstanding structural model fit from CFA fit

• Comparing CFA fit and SEM fitComparing CFA fit and SEM fit

• Examining hypothesized dependence Examining hypothesized dependence

relationshipsrelationships

• Examining the model diagnosticsExamining the model diagnostics

Theoretically-Based HBAT Theoretically-Based HBAT Employee Retention SEM ModelEmployee Retention SEM Model

JS

OC

SI

EP

AC

Hypotheses: H1: EP + JS H2: EP + OC H3: AC +JS H4: AC +OC H5: JS + OC H6: JS + SI H7: OC +SI

Note: observable indicator variables are not shown to simplify the model.

Copyright © 2010 Pearson Education, Inc., publishing as Prentice-Hall.

HBAT CFA/SEM Constructs and Indicator VariablesOrganizational 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 IntentionsSI1 = 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-WorkersAC1 = 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 PerceptionsEP1 = 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 SatisfactionJS1 = 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.

Variable Description Variable TypeJS1 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). MetricOC3 I have a sense of loyalty to HBAT (0-10, Agree-Disagree). MetricOC4 I am proud to tell others that I work for HBAT (0-10, Agree-Disagree). MetricEP2 The place I work in is designed to help me do my job better (0-10, Agree-Disagree). MetricEP3 There are few obstacles to make me less productive in my workplace (0-10, Ag-Disa). MetricAC1 How happy are you with the work of your coworkers? (5-pt. Happy-Unhappy) MetricEP4 What term best describes your work environment? (7-pt. Hectic-Soothing?) MetricJS2 When you think of your job, how satisfied do you feel? (7-pt) MetricJS3 How satisfied are you with your current job with HBAT? (7-pt) MetricAC2 How do you feel about your coworkers? (7-pt. Unfavorable-Favorable) MetricSI1 I am not actively searching for another job. (5-pt. Agree/Disagree) MetricJS4 How satisfied are you with HBAT as an employer? (5-pt. Not vs. Very Much) MetricSI2 I seldom look at the job listings on Monster.com. (5-pt. Agree-Disagree) MetricJS5 Please indicate your satisfaction with your current job. (0-100% Satisfied) MetricAC3 How often do you do things with your coworkers on your days off? (5-pt. Never-Often) MetricSI3 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) NonmetricX24 Your geographic location – in USA or outside USA? (0 = Outside/1 = USA)

NonmetricX25 Your age in years ___? MetricX26 How long have you worked for HBAT – years and months? Metric

Description of HBAT CFA-SEM Database VariablesDescription of HBAT CFA-SEM Database Variables

Attitudes Attitudes toward toward

CoworkersCoworkers

JS4

JS3

JS5

JS2

JS1

OC1OC2 OC3

OC4

AC3AC2 AC4AC1

SI2

SI3

SI1

SI4

EP2EP1 EP3

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.

EP4

Organizational Organizational CommitmentCommitment

Staying Staying IntentionsIntentions

Job Job SatisfactionSatisfaction

Environmental Environmental PerceptionsPerceptions

Measurement Theory Model for HBAT 5 Construct CFAMeasurement Theory Model for HBAT 5 Construct CFA

Theoretically-Based HBAT Theoretically-Based HBAT Employee Retention SEM ModelEmployee Retention SEM Model

JS

OC

SI

EP

AC

Hypotheses: H1: EP + JS H2: EP + OC H3: AC +JS H4: AC +OC H5: JS + OC H6: JS + SI H7: OC +SI

Endogeneous Endogeneous VariableVariable

Exogeneous Exogeneous VariableVariable

Endogeneous Endogeneous VariableVariable

Note: model Note: model is recursive.is recursive.

Note: observable indicator variables are not shown to simplify the model..

Possible “Competing” HBAT Possible “Competing” HBAT Employee Retention SEM ModelEmployee Retention SEM Model

JS

OC

SI

EP

AC

Hypotheses: H1: EP + JS H2: EP + OC H3: AC +JS H4: AC +OC H5: JS + OC H6: JS + SI H7: OC +SI

Hypothesized new Hypothesized new relationship to test.relationship to test.

SEM Learning CheckpointSEM Learning Checkpoint

1.1. How does SEM differ from CFA?How does SEM differ from CFA?

2.2. Explain the difference between a one-step and a Explain the difference between a one-step and a two-step approach.two-step approach.

3.3. What is the difference between endogenous and What is the difference between endogenous and exogenous constructs?exogenous constructs?

4.4. How are the hypothesized relationships in SEM How are the hypothesized relationships in SEM different?different?

5.5. What are some typical problems you can encounter What are some typical problems you can encounter with SEM and how do you deal with them?with SEM and how do you deal with them?

6.6. What are the three SEM GOF measures and how What are the three SEM GOF measures and how do they differ?do they differ?