Preface

In the past two decades structural equation modeling (SEM) has quickly pervaded various fields, such as psychiatry, psychology, sociology, economics, education, demography, political sciences, as well as biology and health studies. Compared with traditional statistical methods such as multiple regression, ANOVA, path analysis, and multilevel models, the advantages of SEM include, but are not limited to, the ability to take into account measurement errors; model multiple dependent variables simultaneously; test overall model fit; estimate direct, indirect and total effects; test complex and specific hypothesis; handle difficult data (time series with auto-correlated error, non-normal, censored, and categorical outcomes); test model parameter invariance across multiple populations/groups, and conduct mixture modeling to deal with population heterogeneity. However, SEM is still an under-utilized technique in social science studies and health studies. The intent of this book is to provide a resource for learning SEM, and a reference guide for some advanced SEM models.

The book emphasizes basic concepts, methods and applications of structural equation modeling. It covers the fundamentals of SEM, as well as some recently developed advanced SEM models. Written in non-mathematical terms, a variety of SEM models for studying both cross-section and longitudinal data are discussed. Examples of various SEM models are demonstrated using real-world research data. The internationally well-known computer program Mplus (Muthén & Muthén, 1998–2010) is used for model demonstrations, and Mplus program syntax is provided for each example model.

This book is divided into seven chapters. Chapter 1 gives an overview of SEM. The basic concepts of SEM, the methods and principles of SEM applications are discussed through five steps of model formulation, model identification, model estimation, model evaluation, and model modification.

Chapter 2 discusses confirmatory factor analysis (CFA) and its applications. Some advanced issues in CFA modeling, such as how to deal with violation of multivariate normality assumption, censored outcome measures, and categorical outcomes, are addressed in model demonstration. At the end of the chapter the first-order CFA model is extended to second-order CFA model.

Chapter 3 discusses SEM model and its applications, starting with the special case of SEM, called MIMIC (multiple indicators and multiple causes) model, different SEM models are discussed and demonstrated using real data. This chapter addresses some important practical issues that SEM practitioners often encounter, such as interactions between covariates, interactions involving latent variables, testing differential item functioning (DIF), testing indirect and total effects, and correcting for effect of measurement error in a single indicator variable.

Chapter 4 extends the application of SEM to longitudinal data analysis where subjects are followed up over time, with repeated measures of each variables of interest. A recently developed SEM model for longitudinal data analysis, called latent growth model (LGM), is discussed. Various LGM models such as linear LGM, non-linear LGM, multi-growth process LGM, two-part LGM, and LGM with categorical outcomes are demonstrated to assess features of outcome growth trajectories.

Chapter 5 extends the application of SEM from a single group to multiple groups to assess whether measuring instrument operates equivalently across different populations/groups (i.e., measurement invariance) or whether causal relationships are invariant across populations/groups. Model demonstrations in this chapter cover multi-group CFA models, including multi-group first-order and second-order CFA models, multi-group SEM, and multi-group LGM models.

In Chapter 6 we switch our topic to mixture models (or finite mixture models) that have increasingly gained in popularity as a framework of combination of variable-centered and person-centered analytic approach. Mixture modeling enables researchers to identify unknown a priori homogeneous groups/classes of individuals based on the measures of interest; examine the features of heterogeneity across the groups/classes; evaluate the effects of covariates on the group/class membership; assess the relationship between the group/class membership and other outcomes; and study transitions between the latent group/class memberships over time. Different mixture models including latent class analysis (LCA) model, latent transition analysis (LTA) model, growth mixture model (GMM) and factor mixture model (FMM) are discussed and demonstrated.

The last chapter discusses power analysis and sample size for structural equation modeling. After a brief review of the rule of thumbs, regarding appropriate sample size for SEM, different approaches to estimate the sample size needed for SEM are discussed. In terms of the ability to detect nonzero model parameters, both Satorra-Saris's method (1985) and Monte Carlo simulation are applied to conduct power analysis and sample size estimates for CFA and LGM models. And then we demonstrate how to use some newly developed methods of power analysis for SEM, such as the MacCallum, Browne, & Sugawara's method (1996) and the Kim's method (2005), to calculate statistical power given a sample size or to estimate an appropriate sample size to achieve a desired power (e.g., 0.80) based upon null hypothesis test about a model overall fit index.

Structural equation modeling is a generalized analytical framework that can deal with many sophisticated modeling situations. The recent development in structural equation modeling includes, but is not limited to, continuous time survival SEM (Larsen 2005; Asparouhov, Masyn & Muthen 2006), multilevel SEM (Muthèn 1994; Toland & De Ayala 2005), multilevel mixture SEM (Asparouhov & Muthèn 2008), and exploratory SEM (Asparouhov & Muthèn, 2009), as well as Bayesian structural equation modeling (BSEM) (Asparouhov & Muthèn 2010; Muthén & Asparouhov 2011b). These topics are beyond the scope of this book.

A wide variety of computer programs are now available for structural equation modeling. Most structural equation models can be set up and estimated with each of these programs. Which program should be used is often a matter of price, support, and personal preference. The computer program used in this book for model demonstration is Mplus (http://www.statmodel.com/) and is becoming increasingly popular in the field of structural equation modeling. This program allows researchers to conduct various advanced SEMs without much complexity of programming. The models demonstrated in this book are intended to show readers how to build SEM models in Mplus using both cross-sectional and longitudinal data. The Mplus syntax used for the example models are provided in the book. While data sets used for these example models in the book are drawn from public health studies. The methods and analytical techniques are applicable to all fields of quantitative social studies.

The target readership of the book is teachers, graduate students, and researchers in social sciences and health studies. This book can be used as a resource for learning SEM and a reference guide for conducting SEMs using Mplus. Readers are encouraged to contact the author at [email protected] in regard to feedback, suggestions and questions.