Multivariate Data Analysis Chapter 11 Structural Equation Modeling

Multivariate Data Analysis Chapter 11 - Structural Equation Modeling

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

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

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

Stages in Structural Equation Modeling n Stage 1: Developing a Theoretically Based Model – Assess role in modeling strategy – Specify theoretical model • Specify casual relationships • Avoid specification error n 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

Stages in Structural Equation Modeling (Cont. ) n 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

Stages in Structural Equation Modeling (Cont. ) n 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

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

Stages in Structural Equation Modeling (Cont. ) n 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

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

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

A Confirmatory Factor Analysis (Cont. ) n 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

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

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

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

Estimating a Path Model with SEM (Cont. ) n 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

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

Appendix 11 A - A Mathematical Representation in LISREL Notation n From a Path Diagram to LISREL Notation n – 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 n References n

Appendix 11 B - Overall Goodness-of-Fit Measures for Structural Equation Modeling (Cont. ) n 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

Appendix 11 B - Overall Goodness-of-Fit Measures for Structural Equation Modeling (Cont. ) n Incremental Fit Measures – – n 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

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