1. Multivariate Data Analysis Chapter 11 - Structural Equation Modeling

2. Chapter 11 What Is Structural Equation Modeling? Accommodating Multiple Interrelated Dependence Relationships Incorporating Variables That We Do Not Measure Directly –Improving Statistical Estimation –Representing Theoretical Concepts –Specifying Measurement Error

3. A Simple Example of SEM The Research Question Setting Up the Structural Equation Model for Path Analysis An Application of Path Analysis Summary

4. The Role of Theory in Structural Equation Modeling Developing a Modeling Strategy –Confirmatory Modeling Strategy –Competing Models Strategy –Model Development Strategy

5. Stages in Structural Equation Modeling Stage 1: Developing a Theoretically Based Model –Assess role in modeling strategy –Specify theoretical model Specify casual relationships Avoid specification error Stage 2: Constructing a Path Diagram of Causal Relationships –Elements of a Path Diagram –Examples of Path Diagrams –Basic Terminology (exogenous, endogenous) –Assumptions of Path Diagrams

6. Stages in Structural Equation Modeling (Cont.) Stage 3: Converting the Path Diagram into a Set of Structural Equations and Specifying the Measurement Model –Structural Model –Measurement Model Correspondence to Factor Analysis Specifying the Measurement Model Determining the Number of Indicators Accounting for Construct Reliability –Empirically Estimating Reliabilities –Specifying the Reliabilities »Single-item Measures »Use of Validated Scales or Measures »Two-stage Analysis »Methods of Specifying the Reliability –Correlations Among Constructs and Indicators

7. Stages in Structural Equation Modeling (Cont.) Stage 4: Choosing the Input Matrix Type and Estimating the Proposed Model –Inputting Data 3 Assumptions Missing Data Covariances versus Correlations and Types Used Sample Size –Model Misspecification –Model Size –Departures From Normality –Estimation Procedure –Model Estimation Estimation Technique (OLS, MLE, WLS, GLS, ADF) Estimation Processes –Direct Estimation –Bootstrapping –Simulation –Jackknifing Computer Programs –Solving the "Not Positive Definite" Problem

8. Stages in Structural Equation Modeling (Cont.) Stage 5: Assessing the Identification of the Structural Model –Degrees of Freedom –Rules for Identification –Diagnosing Identification Problems –Sources and Remedies of Identification Problems

9. Stages in Structural Equation Modeling (Cont.) Stage 6: Evaluating Goodness-of-Fit Criteria –Offending Estimates –Overall Model Fit –Measurement Model Fit Composite Reliability Variance Extracted –Structural Model Fit –Comparison of Competing or Nested Models

10. Stages in Structural Equation Modeling (Cont.) Stage 7: Interpreting and Modifying the Model –Standardized Versus Unstandardized Solutions –Model Respecification A Process of Model Respecification Empirical Indicators of Possible Respecification A Recap of the Seven-Step Process

11. A Confirmatory Factor Analysis Stage 1: Developing a Theoretically Based Model Stage 2: Constructing a Path Diagram of Causal Relationships Stage 3: Converting the Path Diagram into a Set of Structural Equations and Specifying the Measurement Model Stage 4: Choosing Input Matrix Type and Obtaining Model Estimates –Inputting Data –Model Estimation Stage 5: Assessing the Identification of the Structural Model

12. A Confirmatory Factor Analysis (Cont.) Step 6: Evaluating Goodness-of-Fit Criteria –Offending Estimates –Model Respecification –Overall Model Fit: Revised Model Absolute Fit Measures Incremental Fit Measures Parsimonious Fit Measures –Measurement Model Fit

13. A Confirmatory Factor Analysis (Cont.) Stage 7: Interpreting and Modifying the Model –Interpretation –Model Respecification Higher-Order Factor Analysis Models Summary

14. Estimating a Path Model with SEM Stage 1: Developing a Theoretically Based Model Stage 2: Constructing a Path Diagram of the Causal Relationships Stage 3: Converting the Path Diagram into Structural Equations and Specifying the Measurement Model –Specifying Structural Equations –Specifying the Measurement Model –Correlations Among Constructs and Indicators

15. Estimating a Path Model with SEM (Cont.) Stage 4: Choosing Input Matrix Type and Estimating Model –Inputting the Data –Model Estimation Stage 5: Assessing the Identification of the Structural Model

16. Estimating a Path Model with SEM (Cont.) Stage 6: Evaluating Goodness-of-Fit Criteria –Offending Estimates –Overall Model Fit Absolute Fit Measures Incremental Fit Measures Parsimonious Fit Indices –Measurement Model Fit –Structural Model Fit –Competing Models

17. Estimating a Path Model with SEM (Cont.) Stage 7: Interpreting and Modifying the Model Interpretation Model Respecification –Normalized Residual Analysis –Modification Indices Overview of the Seven Step Process

18. Appendix 11A - A Mathematical Representation in LISREL Notation LISREL Notation From a Path Diagram to LISREL Notation –Constructing Structural Equations from the Path Diagram Denoting the Correspondence of Indicators and Constructs Specifying the LISREL Structural and Measurement Model Equations Specifying the Structural Equation Correlations Measurement Model (Indicator) Correlations Summary References

19. Appendix 11B - Overall Goodness-of-Fit Measures for Structural Equation Modeling (Cont.) Measures of Absolute Fit –Likelihood-Ratio Chi-Square Statistic –Noncentrality and Scaled Noncentrality Parameters –Goodness-of-Fit Index –Root Mean Square Residual –Root Mean Square Error of Approximation –Expected Cross-Validation Index –Cross-Validation Index

20. Appendix 11B - Overall Goodness-of-Fit Measures for Structural Equation Modeling (Cont.) Incremental Fit Measures –Adjusted Goodness-of-Fit Index –Tucker-Lewis Index –Normed Fit Index –Other Incremental Fit Measures Parsimonious Fit Measures –Parsimonious Normed Fit Index –Parsimonious Goodness-of-Fit Index –Normed Chi-Square –Akaike Information Criterion

21. Appendix 11B - Overall Goodness-of-Fit Measures for Structural Equation Modeling (Cont.) A Review of Structural Model Goodness-of-Fit Measures Summary References Annotated Articles