## Discovering Structural Equation Modeling Using StataAlan C. AcockCopyright 2013 ISBN-13: 978-1-59718-133-4 Pages 304; paperback Price $48.00 | |

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See the back cover Table of contents Preface (pdf) Author index (pdf) Subject index (pdf) Download the datasets used in this book Obtain answers to the exercises |

*Discovering Structural Equation Modeling Using Stata*, by Alan Acock,
successfully introduces both the statistical principles involved in structural
equation modeling (SEM) and the use of Stata to fit these models. The book
uses an application-based approach to teaching SEM. Acock demonstrates how to
fit a wide variety of models that fall within the SEM framework and provides
datasets that enable the reader to follow along with each example. As each
type of model is discussed, concepts such as identification, handling of
missing data, model evaluation, and interpretation are covered in detail.

In Stata, structural equation models can be fit using the command language or
the graphical user interface (GUI) for SEM, known as the SEM Builder. The
book demonstrates both of these approaches. Throughout the text, the
examples use the **sem** command. Each chapter also includes brief
discussions on drawing the appropriate path diagram and performing estimation
from within the SEM Builder. A more in-depth coverage of the SEM Builder is
given in one of the book’s appendixes.

The first two chapters introduce the building blocks of SEM. Chapter 1 begins with overviews of Cronbach’s alpha as a measure of reliability and of exploratory factor analysis. Then, building on these concepts, Acock demonstrates how to perform confirmatory factor analysis, discusses a variety of statistics available for assessing the fit of the model, and shows a more general measurement of reliability that is based on confirmatory factor analysis. Chapter 2 focuses on using SEM to perform path analysis. It includes examples of mediation, moderation, cross-lagged panel models, and nonrecursive models.

Chapter 3 demonstrates how to combine the topics covered in the first two chapters to fit full structural equation models. The use of modification indices to guide model modification and computation of direct, indirect, and total effects for full structural equation models are also covered.

Chapter 4 details the application of SEM to growth curve modeling. After introducing the basic linear latent growth curve model, Acock extends this to more complex cases such as the inclusion of quadratic terms, time-varying covariates, and time-invariant covariates.

In chapter 5, Acock discusses testing for differences across groups in SEM.
He introduces the specialized **sem** syntax for multiple-group models and
discusses the intricacies of testing for group differences for the different
types of models presented in the preceding chapters.

*Discovering Structural Equation Modeling Using Stata* is an excellent
resource both for those who are new to SEM and for those who are familiar
with SEM but new to fitting these models in Stata. It is useful as a text
for courses covering SEM as well as for researchers performing SEM.

Dedication

List of tables

List of figures

Acknowledgments

1 Introduction to confirmatory factor analysis

1.1 Introduction

1.2 The "do not even think about it" approach

1.3 The principal component factor analysis approach

1.4 Alpha reliability for our nine-item scale

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

1.6 What can CFA add?

1.7 Fitting a CFA model

1.8 Interpreting and presenting CFA results

1.9 Assessing goodness of fit

1.12 Extensions and what is next

1.13 Exercises

1.A Using the SEM Builder to run a CFA

1.2 The "do not even think about it" approach

1.3 The principal component factor analysis approach

1.4 Alpha reliability for our nine-item scale

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

1.6 What can CFA add?

1.7 Fitting a CFA model

1.8 Interpreting and presenting CFA results

1.9 Assessing goodness of fit

1.9.1 Modification indices

1.9.2 Final model and estimating scale reliability

1.10 A two-factor model 1.9.2 Final model and estimating scale reliability

1.10.1 Evaluating the depression dimension

1.10.2 Estimating a two-factor model

1.11 Parceling 1.10.2 Estimating a two-factor model

1.12 Extensions and what is next

1.13 Exercises

1.A Using the SEM Builder to run a CFA

1.A.1 Drawing the model

1.A.2 Estimating the model

1.A.2 Estimating the model

2 Using structural equation modeling for path models

2.1 Introduction

2.2 Path model terminology

2.4 Estimating a model with correlated residuals

2.6 Testing equality of coefficients

2.7 A cross-lagged panel design

2.8 Moderation

2.9 Nonrecursive models

2.B Using the SEM Builder to run path models

2.2 Path model terminology

2.2.1 Exogenous predictor, endogenous outcome, and endogenous mediator variables

2.2.2 A hypothetical path model

2.3 A substantive example of a path model 2.2.2 A hypothetical path model

2.4 Estimating a model with correlated residuals

2.4.1 Estimating direct, indirect, and total effects

2.4.2 Strengthening our path model and adding covariates

2.5 Auxiliary variables 2.4.2 Strengthening our path model and adding covariates

2.6 Testing equality of coefficients

2.7 A cross-lagged panel design

2.8 Moderation

2.9 Nonrecursive models

2.9.1 Worked example of a nonrecursive model

2.9.2 Stability of a nonrecursive model

2.9.3 Model constraints

2.9.4 Equality constraints

2.10 Exercises 2.9.2 Stability of a nonrecursive model

2.9.3 Model constraints

2.9.4 Equality constraints

2.B Using the SEM Builder to run path models

3 Structural equation modeling

3.1 Introduction

3.2 The classic example of a structural equation model

3.4 Programming constraints

3.5 Structural model with formative indicators

3.2 The classic example of a structural equation model

3.2.1 Identification of a full structural equation model

3.2.2 Fitting a full structural equation model

3.2.3 Modifying our model

3.2.4 Indirect effects

3.3 Equality constraints 3.2.2 Fitting a full structural equation model

3.2.3 Modifying our model

3.2.4 Indirect effects

3.4 Programming constraints

3.5 Structural model with formative indicators

3.5.1 Identification and estimation of a composite latent variable

3.5.2 Multiple indicators, multiple causes model

3.6 Exercises 3.5.2 Multiple indicators, multiple causes model

4 Latent growth curves

4.1 Discovering growth curves

4.2 A simple growth curve model

4.3 Identifying a growth curve model

4.8 Exercises

4.2 A simple growth curve model

4.3 Identifying a growth curve model

4.3.1 An intuitive idea of identification

4.3.2 Identifying a quadratic growth curve

4.4 An example of a linear latent growth curve 4.3.2 Identifying a quadratic growth curve

4.4.1 A latent growth curve model for BMI

4.4.2 Graphic representation of individual trajectories (optional)

4.4.3 Intraclass correlation (ICC) (optional)

4.4.4 Fitting a latent growth curve

4.4.5 Adding correlated adjacent error terms

4.4.6 Adding a quadratic latent slope growth factor

4.4.7 Adding a quadratic latent slope and correlating adjacent error terms

4.5 How can we add time-invariant covariates to our model? 4.4.2 Graphic representation of individual trajectories (optional)

4.4.3 Intraclass correlation (ICC) (optional)

4.4.4 Fitting a latent growth curve

4.4.5 Adding correlated adjacent error terms

4.4.6 Adding a quadratic latent slope growth factor

4.4.7 Adding a quadratic latent slope and correlating adjacent error terms

4.5.1 Interpreting a model with time-invariant covariates

4.6 Explaining the random effects—time-varying covariates
4.6.1 Fitting a model with time-invariant and time-varying covariates

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

4.7 Constraining variances of error terms to be equal (optional) 4.6.2 Interpreting a model with time-invariant and time-varying covariates

4.8 Exercises

5 Group comparisons

5.1 Interaction as a traditional approach to multiple-group comparisons

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

5.6 Exercises

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

5.2.1 A multiple indicators, multiple causes model

5.2.2 A measurement model

5.2.3 A full structural equation model

5.3 A measurement model application 5.2.2 A measurement model

5.2.3 A full structural equation model

5.3.1 Step 1: Testing for invariance comparing women and men

5.3.2 Step 2: Testing for invariant loadings

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

5.3.4 Testing for equal intercepts

5.3.5 Comparison of models

5.3.6 Step 4: Comparison of means

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

5.4 Multiple-group path analysis 5.3.2 Step 2: Testing for invariant loadings

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

5.3.4 Testing for equal intercepts

5.3.5 Comparison of models

5.3.6 Step 4: Comparison of means

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

5.4.1 What parameters are different?

5.4.2 Fitting the model with the SEM Builder

5.4.3 A standardized solution

5.4.4 Constructing tables for publications

5.5 Multiple-group comparisons of structural equation models 5.4.2 Fitting the model with the SEM Builder

5.4.3 A standardized solution

5.4.4 Constructing tables for publications

5.6 Exercises

6 Epilogue—what now?

A The graphical user interface

A.1 Introduction

A.2 Menus for Windows, Unix, and Mac

A.4 Drawing an SEM model

A.5 Fitting a structural equation model

A.6 Postestimation commands

A.7 Clearing preferences and restoring the defaults

A.2 Menus for Windows, Unix, and Mac

A.2.1 The menus, explained

A.2.2 The vertical drawing toolbar

A.3 Designing a structural equation model A.2.2 The vertical drawing toolbar

A.4 Drawing an SEM model

A.5 Fitting a structural equation model

A.6 Postestimation commands

A.7 Clearing preferences and restoring the defaults

B Entering data from summary statistics

References