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Multivariate Data Analysis Chapter 11 - Structural Equation Modeling

Multivariate Data Analysis Chapter 11 - Structural Equation Modeling. Chapter 11. What Is Structural Equation Modeling? Accommodating Multiple Interrelated Dependence Relationships Incorporating Variables That We Do Not Measure Directly Improving Statistical Estimation

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Multivariate Data Analysis Chapter 11 - Structural Equation Modeling

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  1. Multivariate Data AnalysisChapter 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

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