Structural equation modeling : foundations and extensions / David Kaplan.

Format:

Book

Author/Creator:

Kaplan, David, 1955-

Series:

Advanced quantitative techniques in the social sciences ; 10.

Advanced quantitative techniques in the social sciences ; v. 10

Language:

English

Subjects (All):

Social sciences--Mathematical models.

Social sciences.

Social sciences--Statistical methods.

Physical Description:

xviii, 215 pages : illustrations ; 24 cm.

Place of Publication:

Thousand Oaks, Calif. : Sage Publications, [2000]

Summary:

With detailed, empirical examples, this exciting book presents an advanced treatment of the foundations of structural equation modeling (SEM) and demonstrates how SEM can provide a unique lens on problems in the social and behavioral sciences.

The author begins with an introduction to recursive and non-recursive models, estimation, testing, and the problem of measurement in observed variables. Then Kaplan explores the issue of group differences in structural models, statistical assumptions in structural modeling (from sampling to missing data and specification error), the assessment of statistical power and model modification in the context of model evaluation, and SEM applied to complex data structures such as those obtained from clustered random sampling.

Contents:

1. Structural Equation Modeling: An Introduction to Its History and Current Practice 1

1.1. Psychometric Origins of Structural Equation Modeling 1

1.2. Biometric and Econometric Origins of Structural Equation Modeling 3

1.3. Simultaneous Equation Modeling Among Latent Variables 5

1.4. Modern Developments 6

1.5. The "Conventional" Practice of Structural Equation Modeling 7

1.6. A Note on the Substantive Examples 10

2. Path Analysis: Modeling Systems of Structural Equations Among Observed Variables 13

2.1. A Substantive Example: Specification of Path Models 14

2.1.1. Recursive and Nonrecursive Models 16

2.1.2. Reduced Form and Covariance Structure Specifications 18

2.2. Identification of Path Models 19

2.2.1. Definition of Identification 20

2.2.2. Some Common Identification Rules 20

2.3. Estimation of Model Parameters 24

2.3.1. Maximum Likelihood 25

2.3.2. Generalized Least Squares 28

2.3.3. A Note on Scale Invariance and Scale Freeness 30

2.4. Model and Parameter Testing 31

2.5. Interpretation of Model Parameters 34

2.5.1. Effect Decomposition 35

2.5.2. Standardized Solutions 36

3. Factor Analysis 40

3.1. Model Specification and Assumptions 41

3.2. The Nature of Unique Variables 43

3.3. Identification and Rotation in the Unrestricted Factor Model 43

3.4. Statistical Estimation in the Unrestricted Model 46

3.4.1. Maximum Likelihood and Generalized Least Squares Methods 46

3.5. The Restricted Factor Model: Confirmatory Factor Analysis 48

3.5.1. Identification in the Restricted Model 49

3.5.2. Testing in the Restricted Model 50

4. Structural Equation Models in Single and Multiple Groups 54

4.1. Specification of the General Structural Equation Model 55

4.2. Identification of Structural Equation Models 56

4.3. Testing and Interpretation in Structural Equation Models 58

4.3.1. Standardized Solutions in the Full Model 59

4.4. Multiple Group Modeling: No Mean Structure 63

4.4.1. Multiple Group Specification and Testing 63

4.5. Multiple Group Specification: Bringing in the Means 68

4.5.1. Mean Structure Specification and Testing 68

4.5.2. Identification and Estimation of the Mean Structure Model 68

4.6. An Alternative Model for Estimating Group Differences 70

4.6.2. Extensions of the MIMIC Model 72

4.7. Issues of Causal Inference in Multiple Group Models 73

4.7.1. The Problem of Factorial Invariance 74

4.7.2. Latent Variable ANCOVA Approaches to Modeling Selection 75

4.7.3. A Propensity Score Approach to Modeling Selection 76

5. Statistical Assumptions Underlying Structural Equation Modeling 79

5.1. Sampling Assumptions 79

5.2. Non-Normality 80

5.2.1. Effects of Non-Normality on Normal Theory-Based Estimation 81

5.2.2. Estimators for Continuous Non-Normal Data 81

5.2.3. Estimators for Categorical Variables 82

5.2.4. Recent Developments in Estimation Under Non-Normality 85

5.3. Missing Data 87

5.3.1. A Nomenclature for Missing Data 87

5.3.2. Available Case Approaches to Missing Data 88

5.3.3. Model-Based Approaches to Missing Data 89

5.3.4. MAR-Based Approaches for Modeling Missing Data 93

5.3.5. An Example of Structural Equation Modeling with Missing Data 94

5.4. Specification Error 96

5.4.1. The Basic Problem of Specification Error 96

5.4.2. Studies on the Problem of Specification Error 97

5.4.3. Implications of Specification Error Propagation for the Practice of Structural Equation Modeling 99

5.5. An Additional Assumption: Exogeneity 99

5.5.1. Parameters of Interest 100

5.5.2. Variation Free 100

5.5.3. A Definition of Weak Exogeneity 101

5.5.4. Some Examples of the Exogeneity Problem 101

5.5.5. Weak Exogeneity in Structural Equation Models 103

5.5.6. An Indirect Test of Weak Exogeneity in Structural Equation Modeling 103

5.5.7. Weak Exogeneity and the Practice of Structural Equation Modeling 104

6. Evaluating and Modifying Structural Equation Models 106

6.1. Evaluating Overall Model Fit: Alternative Fit Indices 107

6.1.1. Measures Based on Comparative Fit to a Baseline Model 107

6.1.2. Measures Based on Errors of Approximation 110

6.1.3. Measures That Assess Cross-Validation Adequacy 114

6.1.4. Summary of Alternative Fit Indices for the Science Achievement Model 118

6.2. Model Modification and Statistical Power 119

6.2.1. Sample Size, Power, and Expected Parameter Change 121

6.2.2. Model Modification and Cross-Validation 122

6.2.3. Factors Influencing Model Modification and Power 127

6.3. The Conventional Practice of Model Evaluation and Modification 127

7. Multilevel Structural Equation Modeling 130

7.1. Basic Concepts in Multilevel Regression Analysis 131

7.1.1. The Intercepts- and Slopes-as-Outcomes Model 132

7.2. Basic Ideas in Multilevel Structural Equation Modeling 134

7.2.1. Parameter Estimation in Multilevel Structural Models 135

7.3. Multilevel Factor Analysis 136

7.4. Multilevel Path Analysis 140

8. Latent Growth Curve Modeling 149

8.1. Growth Curve Modeling: A Motivating Example and Basic Ideas 150

8.1.1. Growth Curve Modeling from the Multilevel Modeling Perspective 151

8.1.2. Growth Curve Modeling from the Structural Modeling Perspective 153

8.1.3. Multivariate Growth Curve Modeling 159

8.2. Extension of Growth Curve Modeling 163

8.2.1. Binary Outcome Measures 164

8.2.2. Intervention Studies 164

8.2.3. Evaluating Growth Curve Models Using Forecasting Statistics 165

9. Epilogue: Toward a New Approach to Structural Equation Modeling and Directions for Future Research 171

9.1. Revisiting the Conventional Approach to Structural Equation Modeling 173

9.2. The Conventional Approach to Econometric Practice 175

9.2.1. Components of the Textbook Approach to Econometrics 176

9.3. The Probabilistic Reduction Approach 177

9.3.1. The Historical Background of the Probabilistic Reduction Approach 177

9.4. Elements of the Probabilistic Reduction Approach 180

9.4.1. The Data Generating Process 180

9.4.2. The Theoretical Model 182

9.4.3. The Estimable Model 182

9.4.4. The Statistical Model 182

9.4.5. The Empirical Social Science Model 185

9.4.6. Recap: Modeling Steps Using the Probabilistic Reduction Approach 185

9.5. Implications of the Probabilistic Reduction Approach for the Development and Practice of Structural Equation Modeling 187

9.5.1. Incorporation of Latent Variables 188

9.5.2. The Role of Assessing Assumptions 188

9.5.3. Alternative Estimation Procedures 189

9.5.4. The Importance of Goodness of Fit 189

9.5.5. Beyond Goodness of Fit 190

9.6. Summary: The Future of Structural Equation Modeling 191.

Notes:

Includes bibliographical references (pages 193-204) and indexes.

ISBN:

0761914072

OCLC:

44868851