# Meta-Analysis: A Structural Equation Modeling Approach

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Presents a novel approach to conducting meta-analysis using structural equation modeling.

Structural equation modeling (SEM) and meta-analysis are two powerful statistical methods in the educational, social, behavioral, and medical sciences. They are often treated as two unrelated topics in the literature. This book presents a unified framework on analyzing meta-analytic data within the SEM framework, and illustrates how to conduct meta-analysis using the metaSEM package in the R statistical environment.

Meta-Analysis: A Structural Equation Modeling Approach begins by introducing the importance of SEM and meta-analysis in answering research questions. Key ideas in meta-analysis and SEM are briefly reviewed, and various meta-analytic models are then introduced and linked to the SEM framework. Fixed-, random-, and mixed-effects models in univariate and multivariate meta-analyses, three-level meta-analysis, and meta-analytic structural equation modeling, are introduced. Advanced topics, such as using restricted maximum likelihood estimation method and handling missing covariates, are also covered.  Readers will learn a single framework to apply both meta-analysis and SEM.  Examples in R and in Mplus are included.

This book will be a valuable resource for statistical and academic researchers and graduate students carrying out meta-analyses, and will also be useful to researchers and statisticians using SEM in biostatistics. Basic knowledge of either SEM or meta-analysis will be helpful in understanding the materials in this book.

Preface xiii

Acknowledgments xv

List of abbreviations xvii

List of figures xix

List of tables xxi

1 Introduction 1

1.1 What is meta-analysis? 1

1.2 What is structural equation modeling? 2

1.3 Reasons for writing a book on meta-analysis and structural equation modeling 3

1.4 Outline of the following chapters 6

1.5 Concluding remarks and further readings 8

2 Brief review of structural equation modeling 13

2.1 Introduction 13

2.2 Model specification 14

2.3 Common structural equation models 18

2.4 Estimation methods, test statistics, and goodness-of-fit indices 25

2.5 Extensions on structural equation modeling 38

2.6 Concluding remarks and further readings 42

3 Computing effect sizes for meta-analysis 48

3.1 Introduction 48

3.2 Effect sizes for univariate meta-analysis 50

3.3 Effect sizes for multivariate meta-analysis 57

3.4 General approach to estimating the sampling variances and covariances 60

3.5 Illustrations Using R 68

3.6 Concluding remarks and further readings 78

4 Univariate meta-analysis 81

4.1 Introduction 81

4.2 Fixed-effects model 83

4.3 Random-effects model 87

4.4 Comparisons between the fixed- and the random-effects models 93

4.5 Mixed-effects model 96

4.6 Structural equation modeling approach 100

4.7 Illustrations using R 105

4.8 Concluding remarks and further readings 116

5 Multivariate meta-analysis 121

5.1 Introduction 121

5.2 Fixed-effects model 124

5.3 Random-effects model 127

5.4 Mixed-effects model 134

5.5 Structural equation modeling approach 136

5.6 Extensions: mediation and moderation models on the effect sizes 140

5.7 Illustrations using R 145

5.8 Concluding remarks and further readings 174

6 Three-level meta-analysis 179

6.1 Introduction 179

6.2 Three-level model 183

6.3 Structural equation modeling approach 188

6.4 Relationship between the multivariate and the three-level meta-analyses 195

6.5 Illustrations using R 200

6.6 Concluding remarks and further readings 210

7 Meta-analytic structural equation modeling 214

7.1 Introduction 214

7.2 Conventional approaches 218

7.3 Two-stage structural equation modeling: fixed-effects models 223

7.4 Two-stage structural equation modeling: random-effects models 233

7.5 Related issues 235

7.6 Illustrations using R 244

7.7 Concluding remarks and further readings 273

8 Advanced topics in SEM-based meta-analysis 279

8.1 Restricted (or residual) maximum likelihood estimation 279

8.2 Missing values in the moderators 289

8.3 Illustrations using R 294

8.4 Concluding remarks and further readings 309

9 Conducting meta-analysis with Mplus 313

9.1 Introduction 313

9.2 Univariate meta-analysis 314

9.3 Multivariate meta-analysis 327

9.4 Three-level meta-analysis 346

9.5 Concluding remarks and further readings 353

A A brief introduction to R, OpenMx, and metaSEM packages 356

A.1 R 357

A.2 OpenMx 362

A.3 metaSEM 364

References 368

Index 369

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