What is assumed?
There are two ways of learning about structural equation modeling (SEM).The one I have chosen for this book is best described by an old advertising tag for a sport shoe company:"Just do it".My approach could be called kinetic learning because it is based on the tactile experience of learning about SEM by using Stata to estimate and interpret models. This means youshould have Stataopen while youread this book; otherwise, this book might help you go to sleep if you try to read it without simultaneously working through it on your computer.By contrast,if you do work through the examples in the book by running the commands as you are reading,I hope you develop the same excitement that I have for SEM.
The alternative approach to learning SEM is to read books that are much more theoretical and may not even illustrate the mechanics of estimating models. These kinds of books are important,and reading them will enrich your understanding of SEM. This book is not meant to replace those books, but simply to get you started.My intent is for you to work your way through this book sequentially, but I recognize that some readers will want to skip around.I am hopeful that after you have been through this book once, you will want to return to specific chapters to reference techniques covered there. To facilitate this, each chapter includes some repetition of the most salient concepts covered in prior chapters. There is also a detailed index at the end of the book.

Dedication v

List of tables xiii

List of figures xv

List of boxes xix

Preface xxi

Acknowledgments xxvii

1 Introduction to confirmatory factor analysis 1

1.1 Introduction 1

1.2 The"do not even think about it"approach 2

1.3 The principal component factor analysis approach 3

1.4 Alpha reliability for our nine-item scale 7

1.5 Generating a factor score rather than a mean or summative score 9

1.6 What can CFA add? 11

1.7 Fitting a CFA model 14

1.8 Interpreting and presenting CFA results 17

1.9 Assessing goodness of fit 21

      1.9.1 Modification indices 26

      1.9.2 Final model and estimating scale reliability 29

1.10 A two-factor model 33

      1.10.1 Evaluating the depression dimension 34

      1.10.2 Estimating a two-factor model 37

1.11 Parceling 45

1.12 Extensions and what is next 45

1.13 Exercises 46

1.A Using the SEM Builder to run a CFA 49

      1.A.1 Drawing the model 49

      1.A.2 Estimating the model 53

2 Using structural equation modeling for path models 59

2.1 Introduction 59

2.2 Path model terminology 59

      2.2.1 Exogenous predictor,endogenous outcome,and endogenous mediator variables 60

      2.2.2 A hypothetical path model 61

2.3 A substantive example of a path model 65

2.4 Estimating a model with correlated residuals 72

      2.4.1Estimating direct,indirect,and total effects 73

      2.4.2 Strengthening our path model and adding covariates 80

2.5 Auxiliary variables 83

2.6 Testing equality of coefficients 84

2.7 A cross-lagged panel design 86

2.8 Moderation 89

2.9 Nonrecursive models 95

      2.9.1Worked example of a nonrecursive model 97

      2.9.2 Stability of a nonrecursive model 100

      2.9.3 Model constraints 101

      2.9.4 Equality constraints 103

2.10 Exercises 105

2.A Using the SEM Builder to run path models 108

3 Structural equation modeling 115

3.1 Introduction 115

3.2 The classic example of a structural equation model 115

3.2.1Identification of a full structural equation model 117

3.2.2Fitting a full structural equation model 119

3.2.3 Modifying our model 125

3.2.4 Indirect effects 128

3.3 Equality constraints 129

3.4 Programming constraints 131

3.5 Structural model with formative indicators 141

      3.5.1Identification and estimation of a composite latent variable 143

      3.5.2Multiple indicators, multiple causes model 147

3.6 Exercises 150

4 Latent growth curves 153

4.1 Discovering growth curves 153

4.2 A simple growth curve model 154

4.3 Identifying a growth curve model 157

      4.3.1An intuitive idea of identification 157

      4.3.2 Identifying a quadratic growth curve 158

4.4 An example of a linear latent growth curve 159

      4.4.1A latent growth curve model for BMI 160

      4.4.2 Graphic representation of individual trajectories(optional) 161

      4.4.3 Intraclass correlation (ICC) (optional) 165

      4.4.4Fitting a latent growth curve 167

      4.4.5Adding correlated adjacent error terms 180

      4.4.6 Adding a quadratic latent slope growth factor 181

      4.4.7 Adding a quadratic latent slope and correlating adjacent error terms 181

4.5 How can we add time-invariant covariates to our model? 188

      4.5.1 Interpreting a model with time-invariant covariates 192

4.6 Explaining the random effects—time-varying covariates 194

      4.6.1Fitting a model with time-invariant and time-varying covariates 195

      4.6.2 Interpreting a model with time-invariant and time-varying covariates 202

4.7 Constraining variances of error terms to be equal (optional) 203

4.8 Exercises 207

5 Group comparisons 209

5.1 Interaction as a traditional approach to multiple-group comparisons 209

5.2 The range of applications of Stata's multiple-group comparisons with sem 211

      5.2.1 A multiple indicators, multiple causes mode 211

      5.2.2 A measurement model 212

      5.2.3 A full structural equation model 212

5.3 A measurement model application 213

      5.3.1 Step 1: Testing for invariance comparing women and men 215

      5.3.2 Step 2: Testing for invariant loadings 219

      5.3.3 Step 3: Testing for an equal loadings and equal errorvariances model 224

      5.3.4Testing for equal intercepts 226

      5.3.5 Comparison of models 227

      5.3.6 Step 4: Comparison of means 230

      5.3.7 Step 5: Comparison of variances and covariance of latent variables 238

5.4 Multiple-group path analysis 240

      5.4.1What parameters are different? 245

      5.4.2 Fitting the model with the SEM Builder 250

      5.4.3 A standardized solution 251

      5.4.4 Constructing tables for publications 252

5.5 Multiple-group comparisons of structural equation models 254

5.6 Exercises 263

6 Epilogue-what now?

6.1What is next? 266

C1 A The graphical user interface 269

A.1 Introduction 269

A.2 Menus for Windows,Unix,and Mac 270

      A.2.1 The menus, explained 270

      A.2.2 The vertical drawing toolbar 271

A.3Designing a structural equation model 272

A.4Drawing anSEM model 276

A.5Fitting a structural equation model 281

A.6Post estimation commands 284

A.7Clearing preferences and restoring the defaults 285

B Entering data from summary statistics 287

References 297

Author index 299

Subject index 301

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