دانلود کتاب Bayesian Structural Equation Modeling

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Cover Half Title Page Series Page Title Page Copyright Dedication Series Editor’s Note Preface Acknowledgments Contents Part I. Introduction 1. Background 1.1 Bayesian Statistical Modeling: The Frequency of Use 1.2 The Key Impediments within Bayesian Statistics 1.3 Benefits of Bayesian Statistics within SEM 1.3.1 A Recap: Why Bayesian SEM? 1.4 Mastering the SEM Basics: Precursors to Bayesian SEM 1.4.1 The Fundamentals of SEM Diagrams and Terminology 1.4.2 LISREL Notation 1.4.3 Additional Comments about Notation 1.5 Datasets Used in the Chapter Examples 1.5.1 Cynicism Data 1.5.2 Early Childhood Longitudinal Survey–Kindergarten Class 1.5.3 Holzinger and Swineford (1939) 1.5.4 IPIP 50: Big Five Questionnaire 1.5.5 Lakaev Academic Stress Response Scale 1.5.6 Political Democracy 1.5.7 Program for International Student Assessment 1.5.8 Youth Risk Behavior Survey 2. Basic Elements of Bayesian Statistics 2.1 A Brief Introduction to Bayesian Statistics 2.2 Setting the Stage 2.3 Comparing Frequentist and Bayesian Estimation 2.4 The Bayesian Research Circle 2.5 Bayes’ Rule 2.6 Prior Distributions 2.6.1 The Normal Prior 2.6.2 The Uniform Prior 2.6.3 The Inverse Gamma Prior 2.6.4 The Gamma Prior 2.6.5 The Inverse Wishart Prior 2.6.6 The Wishart Prior 2.6.7 The Beta Prior 2.6.8 The Dirichlet Prior 2.6.9 Different Levels of Informativeness for Prior Distributions 2.6.10 Prior Elicitation 2.6.11 Prior Predictive Checking 2.7 The Likelihood (Frequentist and Bayesian Perspectives) 2.8 The Posterior 2.8.1 An Introduction to Markov Chain Monte Carlo Methods 2.8.2 Sampling Algorithms 2.8.3 Convergence 2.8.4 MCMC Burn-In Phase 2.8.5 The Number of Markov Chains 2.8.6 A Note about Starting Values 2.8.7 Thinning a Chain 2.9 Posterior Inference 2.9.1 Posterior Summary Statistics 2.9.2 Intervals 2.9.3 Effective Sample Size 2.9.4 Trace-Plots 2.9.5 Autocorrelation Plots 2.9.6 Posterior Histogram and Density Plots 2.9.7 HDI Histogram and Density Plots 2.9.8 Model Assessment 2.9.9 Sensitivity Analysis 2.10 A Simple Example 2.11 Chapter Summary 2.11.1 Major Take-Home Points 2.11.2 Notation Referenced 2.11.3 Annotated Bibliography of Select Resources Appendix 2.A: Getting Started with R Part II. Measurement Models and Related Issues 3. The Confirmatory Factor Analysis Model 3.1 Introduction to Bayesian CFA 3.2 The Model and Notation 3.2.1 Handling Indeterminacies in CFA 3.3 The Bayesian Form of the CFA Model 3.3.1 Additional Information about the (Inverse) Wishart Prior 3.3.2 Alternative Priors for Covariance Matrices 3.3.3 Alternative Priors for Variances 3.3.4 Alternative Priors for Factor Loadings 3.4 Example 1: Basic CFA Model 3.5 Example 2: Implementing Near-Zero Priors for Cross-Loadings 3.6 How to Write Up Bayesian CFA Results 3.6.1 Hypothetical Data Analysis Plan 3.6.2 Hypothetical Results Section 3.6.3 Discussion Points Relevant to the Analysis 3.7 Chapter Summary 3.7.1 Major Take-Home Points 3.7.2 Notation Referenced 3.7.3 Annotated Bibliography of Select Resources 3.7.4 Example Code for Mplus 3.7.5 Example Code for R 4. Multiple-Group Models 4.1 A Brief Introduction to Multiple-Group Models 4.2 Introduction to the Multiple-Group CFA Model (with Mean Differences) 4.3 The Model and Notation 4.4 The Bayesian Form of the Multiple-Group CFA Model 4.5 Example 1: Using a Mean-Difference, Multiple-Group CFA Model to Assess for School Differences 4.6 Introduction to the MIMIC Model 4.7 The Model and Notation 4.8 The Bayesian Form of the MIMIC Model 4.9 Example 2: Using the MIMIC Model to Assess for School Differences 4.10 How to Write Up Bayesian Multiple-Group Model Results with Mean Differences 4.10.1 Hypothetical Data Analysis Plan 4.10.2 Hypothetical Results Section 4.10.3 Discussion Points Relevant to the Analysis 4.11 Chapter Summary 4.11.1 Major Take-Home Points 4.11.2 Notation Referenced 4.11.3 Annotated Bibliography of Select Resources 4.11.4 Example Code for Mplus 4.11.5 Example Code for R 5. Measurement Invariance Testing 5.1 A Brief Introduction to MI in SEM 5.1.1 Stages of Traditional MI Testing 5.1.2 Challenges within Traditional MI Testing 5.2 Bayesian Approximate MI 5.3 The Model and Notation 5.4 Priors within Bayesian Approximate MI 5.5 Example: Illustrating Bayesian Approximate MI for School Differences 5.5.1 Results for the Conventional MI Tests 5.5.2 Results for the Bayesian Approximate MI Tests 5.5.3 Results Comparing Latent Means across Approaches 5.6 How to Write Up Bayesian Approximate MI Results 5.6.1 Hypothetical Data Analysis Plan 5.6.2 Hypothetical Analytic Procedure 5.6.3 Hypothetical Results Section 5.6.4 Discussion Points Relevant to the Analysis 5.7 Chapter Summary 5.7.1 Major Take-Home Points 5.7.2 Notation Referenced 5.7.3 Annotated Bibliography of Select Resources 5.7.4 Example Code for Mplus 5.7.5 Example Code for R Part III. Extending the Structural Model 6. The General Structural Equation Model 6.1 Introduction to Bayesian SEM 6.2 The Model and Notation 6.3 The Bayesian Form of SEM 6.4 Example: Revisiting Bollen’s (1989) Political Democracy Example 6.4.1 Motivation for This Example 6.4.2 The Current Example 6.5 How to Write Up Bayesian SEM Results 6.5.1 Hypothetical Data Analysis Plan 6.5.2 Hypothetical Results Section 6.5.3 Discussion Points Relevant to the Analysis 6.6 Chapter Summary 6.6.1 Major Take-Home Points 6.6.2 Notation Referenced 6.6.3 Annotated Bibliography of Select Resources 6.6.4 Example Code for Mplus 6.6.5 Example Code for R Appendix 6.A: Causal Inference and Mediation Analysis 7. Multilevel Structural Equation Modeling 7.1 Introduction to MSEM 7.1.1 MSEM Applications 7.1.2 Contextual Effects 7.2 Extending MSEM into the Bayesian Context 7.3 The Model and Notation 7.4 The Bayesian Form of MSEM 7.5 Example 1: A Two-Level CFA with Continuous Items 7.5.1 Implementation of Example 1 7.5.2 Example 1 Results 7.6 Example 2: A Three-Level CFA with Categorical Items 7.6.1 Implementation of Example 2 7.6.2 Example 2 Results 7.7 How to Write Up Bayesian MSEM Results 7.7.1 Hypothetical Data Analysis Plan 7.7.2 Hypothetical Results Section 7.7.3 Discussion Points Relevant to the Analysis 7.8 Chapter Summary 7.8.1 Major Take-Home Points 7.8.2 Notation Referenced 7.8.3 Annotated Bibliography of Select Resources 7.8.4 Example Code for Mplus 7.8.5 Example Code for R Part IV. Longitudinal and Mixture Models 8. The Latent Growth Curve Model 8.1 Introduction to Bayesian LGCM 8.2 The Model and Notation 8.2.1 Extensions of the LGCM 8.3 The Bayesian Form of the LGCM 8.3.1 Alternative Priors for the Factor Variances and Covariances 8.4 Example 1: Bayesian Estimation of the LGCM Using ECLS–K Reading Data 8.5 Example 2: Extending the Example to Include Separation Strategy Priors 8.6 Example 3: Extending the Framework to Assessing MI over Time 8.7 How to Write Up Bayesian LGCM Results 8.7.1 Hypothetical Data Analysis Plan 8.7.2 Hypothetical Results Section 8.7.3 Discussion Points Relevant to the Analysis 8.8 Chapter Summary 8.8.1 Major Take-Home Points 8.8.2 Notation Referenced 8.8.3 Annotated Bibliography of Select Resources 8.8.4 Example Code for Mplus 8.8.5 Example Code for R 9. The Latent Class Model 9.1 A Brief Introduction to Mixture Models 9.2 Introduction to Bayesian LCA 9.3 The Model and Notation 9.3.1 Introducing the Issue of Class Separation 9.4 The Bayesian Form of the LCA Model 9.4.1 Adding Flexibility to the LCA Model 9.5 Mixture Models, Label Switching, and Possible Solutions 9.5.1 Identifiability Constraints 9.5.2 Relabeling Algorithms 9.5.3 Label Invariant Loss Functions 9.5.4 Final Thoughts on Label Switching 9.6 Example: A Demonstration of Bayesian LCA 9.6.1 Motivation for This Example 9.6.2 The Current Example 9.7 How to Write Up Bayesian LCA Results 9.7.1 Hypothetical Data Analysis Plan 9.7.2 Hypothetical Results Section 9.7.3 Discussion Points Relevant to the Analysis 9.8 Chapter Summary 9.8.1 Major Take-Home Points 9.8.2 Notation Referenced 9.8.3 Annotated Bibliography of Select Resources 9.8.4 Example Code for Mplus 9.8.5 Example Code for R 10. The Latent Growth Mixture Model 10.1 Introduction to Bayesian LGMM 10.2 The Model and Notation 10.2.1 Concerns with Class Separation 10.3 The Bayesian Form of the LGMM 10.3.1 Alternative Priors for Factor Means 10.3.2 Alternative Priors for the Measurement Error Covariance Matrix 10.3.3 Alternative Priors for the Factor Covariance Matrix 10.3.4 Handling Label Switching in LGMMs 10.4 Example: Comparing Different Prior Conditions in an LGMM 10.5 How to Write Up Bayesian LGMM Results 10.5.1 Hypothetical Data Analysis Plan 10.5.2 Hypothetical Results Section 10.5.3 Discussion Points Relevant to the Analysis 10.6 Chapter Summary 10.6.1 Major Take-Home Points 10.6.2 Notation Referenced 10.6.3 Annotated Bibliography of Select Resources 10.6.4 Example Code for Mplus 10.6.5 Example Code for R Part V. Special Topics 11. Model Assessment 11.1 Model Comparison and Cross-Validation 11.1.1 Bayes Factors 11.1.2 The Bayesian Information Criterion 11.1.3 The Deviance Information Criterion 11.1.4 The Widely Applicable Information Criterion 11.1.5 Leave-One-Out Cross-Validation 11.2 Model Fit 11.2.1 Posterior Predictive Model Checking 11.2.2 Missing Data and the PPC Procedure 11.2.3 Testing Near-Zero Parameters through the PPPP 11.3 Bayesian Approximate Fit 11.3.1 Bayesian Root Mean Square Error of Approximation 11.3.2 Bayesian Tucker-Lewis Index 11.3.3 Bayesian Normed Fit Index 11.3.4 Bayesian Comparative Fit Index 11.3.5 Implementation of These Indices 11.4 Example 1: Illustrating the PPC and the PPPP for CFA 11.5 Example 2: Illustrating Bayesian Approximate Fit for CFA 11.6 How to Write Up Bayesian Approximate Fit Results 11.6.1 Hypothetical Data Analysis Plan 11.6.2 Hypothetical Results Section 11.6.3 Discussion Points Relevant to the Analysis 11.7 Chapter Summary 11.7.1 Major Take-Home Points 11.7.2 Notation Referenced 11.7.3 Annotated Bibliography of Select Resources 11.7.4 Example Code for Mplus 11.7.5 Example Code for R 12. Important Points to Consider 12.1 Implementation and Reporting of Bayesian Results 12.1.1 Priors Implemented 12.1.2 Convergence 12.1.3 Sensitivity Analysis 12.1.4 How Should We Interpret These Findings? 12.2 Points to Check Prior to Data Analysis 12.2.1 Is Your Model Formulated "Correctly"? 12.2.2 Do You Understand the Priors? 12.3 Points to Check after Initial Data Analysis, but before Interpretation of Results 12.3.1 Convergence 12.3.2 Does Convergence Remain after Doubling the Number of Iterations? 12.3.3 Is There Ample Information in the Posterior Histogram? 12.3.4 Is There a Strong Degree of Autocorrelation in the Posterior? 12.3.5 Does the Posterior Make Substantive Sense? 12.4 Understanding the Influence of Priors 12.4.1 Examining the Influence of Priors on Multivariate Parameters (e.g., Covariance Matrices) 12.4.2 Comparing the Original Prior to Other Diffuse or Subjective Priors 12.5 Incorporating Model Fit or Model Comparison 12.6 Interpreting Model Results the "Bayesian Way" 12.7 How to Write Up Bayesian Results 12.7.1 (Hypothetical) Results for Bayesian Two-Factor CFA 12.8 How to Review Bayesian Work 12.9 Chapter Summary and Looking Forward Glossary References Author Index Subject Index About the Author