Combining simultaneous equations with latent variables and measurement models results in general latent variable SEMs, the subject of Chapter 6. It covers model specifications, implied moments, identification, estimation, outliers and influential cases, model fit, and respecification in such models. Furthermore, Chapter 6 also explores higher order factor analysis, longitudinal models, and Bayesian estimation.

Chapter 7 covers models with categorical endogenous variables. It examines the consequences of treating such variables as continuous and how to modify SEMs to take account of categorical variables. It begins with single equation regression-like models for binary, ordinal, and count variables and builds to multiequation models. It includes a polychoric correlation approach, models with exogenous observed variables, the treatment of missing values, and alternative modeling approaches for categorical variables.

This chapter introduces structural equation models (SEMs). It defines SEMs and outlines their history. It also presents several widespread misunderstandings about SEMs and presents their strengths and weaknesses. Finally, the chapter provides an outline of the remaining book chapters.

Chapter 2 focuses on background information that is essential to understanding SEMs. This includes providing the general structural equation model that appears throughout the book along with definitions of the notation and the assumptions of the model. The chapter introduces path diagram symbols and their relation to the equation form of the model. It also describes differences between endogenous and exogenous variables and observed and latent variables for both continuous and categorical variables. In addition, the chapter introduces the problems of missing data, outliers and influential cases, and multiple significance testing, issues that are common in all types of models. Finally, basic rules of expected values, variances, and covariances are part of the chapter.

Models with multiple equations rather than a single equation are the subject of Chapter 4. It covers model specification, implied moments, model identification, model estimation, and model interpretation, fit, and diagnostics in the context of such models. The consequences of measurement error and the treatment of mediation effects are part of the chapter. Finally, the chapter compares simultaneous equation models and Directed Acyclic Graphs (DAGs).

Measurement models are the focus of Chapter 5. It treats the nature of concepts, theoretical definitions, and latent variables. Chapter 5 explains model specification, implied moments, model identification, model estimation, and model interpretation, fit, and diagnostics in confirmatory factor analysis (CFA) models. Factor score prediction and respecification of models are two other topics it covers.

Chapter 3 concentrates on single equation regression models but presents them from the perspective of structural equations models. It introduces and applies the major steps of structural equation modeling: model specification, implied moments, model identification, model estimation, and model interpretation and fit. It also includes diagnostics and testing for regression and a discussion of the consequences of using multiple regression with variables measured with errors.

In the Preface, I wrote that the primary purpose of the book was to provide readers with a solid foundation in structural equation models (SEMs). I had several audiences in mind. One was those who desired to be more informed users of SEMs. These readers aspire to an understanding that goes beyond the input commands and output of SEM programs. I also hoped to reach quantitative methodologists who sought to master and to create new tools for SEMs. Finally, I aimed to compose a resource for statisticians, biostatisticians, and data scientists who wished to learn about latent variable modeling with multiple indicators and systems of equations. For those who have made it this far, I hope that your knowledge of SEMs is much deeper than before.

It is often desired to extract more information from a test score than is available in a single number. The almost universal response to such desires is to divide the overall test score into subcomponents/subscores (e.g., math and verbal scores, reading fluency and reading comprehension, etc.). We summarize the rules governing the legitimate use of subscores and report on the frequency, in modern practice, that it is done correctly. In short, dividing up a test into subscores reduces its reliability, and subsequently, its validity. Using the military’s ASVAB test as an example, we show that the overall score is the only good predictor of later performance and the nine subtests are not effective in differentiating types of skills and knowledge.

Zombie ideas are awful ideas that ought to be dead, but which keep getting revivified and so are still walking among us. Three prominent zombies which we discuss are:

1. 1. coaching for admissions tests gives a large unfair advantage;

2. 2. admitting strivers (kids from lower SES who score higher than expected) makes things fairer;

3. 3. making tests optional makes things fairer.