Meta-analysis : a structural equation modeling approach /

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 lite...

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Bibliographic Details
Main Author: Cheung, Mike W. L. (Author)
Corporate Authors: Alumni and Friends Memorial Book Fund, Wiley InterScience (Online service)
Format: Book
Language:English
Published: Chichester, England ; West Sussex, England : Wiley, 2015
Chichester, West Sussex, United Kingdom : 2015
Subjects:
Meta-analysis
Research > Statistical methods
Sampling (Statistics)
Statistics
Electronic books
Table of Contents:
  • 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
  • 1.3.1 Benefits to users of structural equation modeling and meta-analysis 6
  • 1.4 Outline of the following chapters 6
  • 1.4.1 Computer examples and data sets used in this book 8
  • 1.5 Concluding remarks and further readings 8
  • References 9
  • 2 Brief review of structural equation modeling 13
  • 2.1 Introduction 13
  • 2.2 Model specification 14
  • 2.2.1 Equations 14
  • 2.2.2 Path diagram 15
  • 2.2.3 Matrix representation 15
  • 2.3 Common structural equation models 18
  • 2.3.1 Path analysis 18
  • 2.3.2 Confirmatory factor analysis 19
  • 2.3.3 Structural equation model 21
  • 2.3.4 Latent growth model 22
  • 2.3.5 Multiple-group analysis 23
  • 2.4 Estimation methods, test statistics, and goodness-of-fit indices 25
  • 2.4.1 Maximum Likelihood estimation 25
  • 2.4.2 Weighted least squares 26
  • 2.4.3 Multiple-group analysis 28
  • 2.4.4 Likelihood ratio test and Wald test 28
  • 2.4.5 Confidence intervals on parameter estimates 29
  • 2.4.6 Test statistics versus goodness-of-fit indices 34
  • 2.5 Extensions on structural equation modeling 38
  • 2.5.1 Phantom variables 38
  • 2.5.2 Definition variables 39
  • 2.5.3 Full information maximum likelihood estimation 41
  • 2.6 Concluding remarks and further readings 42
  • References 42
  • 3 Computing effect sizes for meta-analysis 48
  • 3.1 Introduction 48
  • 3.2 Effect sizes for univariate meta-analysis 50
  • 3.2.1 Mean differences 50
  • 3.2.2 Correlation coefficient and its Fisher's z transformation 55
  • 3.2.3 Binary variables 56
  • 3.3 Effect sizes for multivariate meta-analysis 57
  • 3.3.1 Mean differences 57
  • 3.3.2 Correlation matrix and its Fisher's z transformation 59
  • 3.3.3 Odds ratio 60
  • 3.4 General approach to estimating the sampling variances and covariances 60
  • 3.4.1 Delta method 61
  • 3.4.2 Computation with structural equation modeling 64
  • 3.5 Illustrations Using R 68
  • 3.5.1 Repeated measures 69
  • 3.5.2 Multiple treatment studies 71
  • 3.5.3 Multiple-endpoint studies 73
  • 3.5.4 Multiple treatment with multiple-endpoint studies 75
  • 3.5.5 Correlation matrix 77
  • 3.6 Concluding remarks and further readings 78
  • References 78
  • 4 Univariate meta-analysis 81
  • 4.1 Introduction 81
  • 4.2 Fixed-effects model 83
  • 4.2.1 Estimation and hypotheses testing 83
  • 4.2.2 Testing the homogeneity of effect sizes 85
  • 4.2.3 Treating the sampling variance as known versus as estimated 85
  • 4.3 Random-effects model 87
  • 4.3.1 Estimation and hypothesis testing 88
  • 4.3.2 Testing the variance component 90
  • 4.3.3 Quantifying the degree of the heterogeneity of effect sizes 92
  • 4.4 Comparisons between the fixed- and the random-effects models 93
  • 4.4.1 Conceptual differences 93
  • 4.4.2 Statistical differences 94
  • 4.5 Mixed-effects model 96
  • 4.5.1 Estimation and hypotheses testing 97
  • 4.5.2 Explained variance 98
  • 4.5.3 A cautionary note 99
  • 4.6 Structural equation modeling approach 100
  • 4.6.1 Fixed-effects model 100
  • 4.6.2 Random-effects model 101
  • 4.6.3 Mixed-effects model 102
  • 4.7 Illustrations using R 105
  • 4.7.1 Odds ratio of atrial fibrillation between bisphosphonate and non-bisphosphonate users 105
  • 4.7.2 Correlation between organizational commitment and salesperson job performance 108
  • 4.8 Concluding remarks and further readings 116
  • References 117
  • 5 Multivariate meta-analysis 121
  • 5.1 Introduction 121
  • 5.1.1 Types of dependence 121
  • 5.1.2 Univariate meta-analysis versus multivariate meta-analysis 122
  • 5.2 Fixed-effects model 124
  • 5.2.1 Testing the homogeneity of effect sizes 125
  • 5.2.2 Estimation and hypotheses testing 126
  • 5.3 Random-effects model 127
  • 5.3.1 Structure of the variance component of random effects 128
  • 5.3.2 Nonnegative definite of the variance component of random effects 129
  • 5.3.3 Estimation and hypotheses testing 131
  • 5.3.4 Quantifying the degree of heterogeneity of effect sizes 132
  • 5.3.5 When the sampling covariances are not known 133
  • 5.4 Mixed-effects model 134
  • 5.4.1 Explained variance 135
  • 5.5 Structural equation modeling approach 136
  • 5.5.1 Fixed-effects model 136
  • 5.5.2 Random-effects model 137
  • 5.5.3 Mixed-effects model 138
  • 5.6 Extensions: mediation and moderation models on the effect sizes 140
  • 5.6.1 Regression model 141
  • 5.6.2 Mediating model 143
  • 5.6.3 Moderating model 144
  • 5.7 Illustrations using R 145
  • 5.7.1 BCG vaccine for preventing tuberculosis 146
  • 5.7.2 Standardized mean differences between males and females on life satisfaction and life control 156
  • 5.7.3 Mediation and moderation models 161
  • 5.8 Concluding remarks and further readings 174
  • References 174
  • 6 Three-level meta-analysis 179
  • 6.1 Introduction 179
  • 6.1.1 Examples of dependent effect sizes with unknown degree of dependence 180
  • 6.1.2 Common methods to handling dependent effect sizes 180
  • 6.2 Three-level model 183
  • 6.2.1 Random-effects model 183
  • 6.2.2 Mixed-effects model 187
  • 6.3 Structural equation modeling approach 188
  • 6.3.1 Two representations of the same model 189
  • 6.3.2 Random-effects model 191
  • 6.3.3 Mixed-effects model 193
  • 6.4 Relationship between the multivariate and the three-level meta-analyses 195
  • 6.4.1 Three-level meta-analysis as a special case of the multivariate meta-analysis 195
  • 6.4.2 Approximating a multivariate meta-analysis with a three-level meta-analysis 196
  • 6.4.3 Three-level multivariate meta-analysis 198
  • 6.5 Illustrations using R 200
  • 6.5.1 Inspecting the data 201
  • 6.5.2 Fitting a random-effects model 202
  • 6.5.3 Obtaining the likelihood-based confidence interval 203
  • 6.5.4 Testing τ²₍₃₎ = 0 204
  • 6.5.5 Testing τ²₍₂₎ = 0 205
  • 6.5.6 Testing τ²₍₂₎ = &tau²₍₃₎ 205
  • 6.5.7 Testing types of proposals (grant versus fellowship) 206
  • 6.5.8 Testing the effect of the year of application 207
  • 6.5.9 Testing the country effect 209
  • 6.6 Concluding remarks and further readings 210
  • References 211
  • 7 Meta-analytic structural equation modeling 214
  • 7.1 Introduction 214
  • 7.1.1 Meta-analytic structural equation modeling as a possible solution for conflicting research findings 215
  • 7.1.2 Basic steps for conducting a meta-analytic structural equation modeling 217
  • 7.2 Conventional approaches 218
  • 7.2.1 Univariate approaches 218
  • 7.2.2 Generalized least squares approach 221
  • 7.3 Two-stage structural equation modeling: fixed-effects models 223
  • 7.3.1 Stage 1 of the analysis: pooling correlation matrices 224
  • 7.3.2 Stage 2 of the analysis: fitting structural models 227
  • 7.3.3 Subgroup analysis 233
  • 7.4 Two-stage structural equation modeling: random-effects models 233
  • 7.4.1 Stage 1 of the analysis: pooling correlation matrices 234
  • 7.4.2 Stage 2 of the analysis: fitting structural models 235
  • 7.5 Related issues 235
  • 7.5.1 Multiple-group structural equation modeling versus meta-analytic structural equation modeling 236
  • 7.5.2 Fixed-effects model: two-stage structural equation modeling versus generalized least squares 237
  • 7.5.3 Alternative random-effects models 239
  • 7.5.4 Maximum likelihood estimation versus restricted (or residual) maximum likelihood estimation 242
  • 7.5.5 Correlation coefficient versus Fisher's z score 242
  • 7.5.6 Correction for unreliability 243
  • 7.6 Illustrations using R 244
  • 7.6.1 A higher-order confirmatory factor analytic model for the Big Five model 244
  • 7.6.2 A regression model on SAT (Math) 258
  • 7.6.3 A path model for cognitive ability to supervisor rating 266
  • 7.7 Concluding remarks and further readings 273
  • References 274
  • 8 Advanced topics in SEM-based meta-analysis 279
  • 8.1 Restricted (or residual) maximum likelihood estimation 279
  • 8.1.1 Reasons for and against the maximum likelihood estimation 280
  • 8.1.2 Applying the restricted (or residual) maximum likelihood estimation in SEM-based meta-analysis 281
  • 8.1.3 Implementation in structural equation modeling 283
  • 8.2 Missing values in the moderators 289
  • 8.2.1 Types of missing mechanisms 289
  • 8.2.2 Common methods to handling missing data 290
  • 8.2.3 Maximum likelihood estimation 291
  • 8.3 Illustrations using R 294
  • 8.3.1 Restricted (or residual) maximum likelihood estimation 295
  • 8.3.2 Missing values in the moderators 300
  • 8.4 Concluding remarks and further readings 309
  • References 310
  • 9 Conducting meta-analysis with Mplus 313
  • 9.1 Introduction 313
  • 9.2 Univariate meta-analysis 314
  • 9.2.1 Fixed-effects model 314
  • 9.2.2 Random-effects model 317
  • 9.2.3 Mixed-effects model 322
  • 9.2.4 Handling missing values in moderators 325
  • 9.3 Multivariate meta-analysis 327
  • 9.3.1 Fixed-effects model 328
  • 9.3.2 Random-effects model 333
  • 9.3.3 Mixed-effects model 337
  • 9.3.4 Mediation and moderation models on the effect sizes 340
  • 9.4 Three-level meta-analysis 346
  • 9.4.1 Random-effects model 346
  • 9.4.2 Mixed-effects model 351
  • 9.5 Concluding remarks and further readings 353
  • References 354

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