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Chapter 1 Introduction to Model Selection 1

1.1 Introduction 1

1.2 Bayes Factor 5

1.3 Other Methods 13

1.4 Lv Measure for Model Selection 16

1.5 Outline of the Book 18

Chapter 2 Bayesian Model Selection for Nonlinear Latent Variable Models 20

2.1 Introduction 20

2.2 Brief Review of the Lv Measure 21

2.3 Model Description 23

2.4 Lv Measure for Nonlinear Structural Equation Models 25

2.5 A Simulation Study 35

2.6 A Real Example 47

2.7 Discussion 51

Chapter 3 Bayesian Model Selection for Latent Variable Models with Mixed Continuous and Categorical Data 53

3.1 Introduction 53

3.2 Model Description 54

3.3 Lv Measure for Nonlinear SEMs with Mixed Continuous and Ordered Categorical Data 56

3.4 A Simulation Study 66

3.5 A Real Example 73

3.6 Discussion 78

Chapter 4 Bayesian Model Selection of Two-Level Latent Variable Models 79

4.1 Introduction 79

4.2 Model Description 81

4.3 Lv Measure for Two-Level Structural Equation Models 84

4.4 A Simulation Study 92

4.5 A Real Example 102

4.6 Discussion 106

Chapter 5 Bayesian Model Selection for Latent Variable Models with Finite Mixtures 107

5.1 Introduction 107

5.2 Model Description 109

5.3 Lv Measure for Finite Mixture SEMs 111

5.4 A Simulation Study 121

5.5 A Real Example 126

5.6 Discussion 129

Chapter 6 Bayesian Model Selection of Latent Variable Model With Non-Ignorable Missing Data 130

6.1 Introduction 130

6.2 NSEMs with Non-Ignorable Missing Data 132

6.3 Lv Measure for NSEM with Non-Ignorable Missing Data 134

6.4 Illustrative Examples 143

6.5 Discussion 149

References 157

Appendix A Variable Description in Real Examples 164