Abstract
The Topic and Major Aim of the Textbook
There are a number of textbooks that give an introduction to structural equation modeling (SEM) in general. As a counterpoint, Timothy A. Brown’s textbook provides an introduction solely dedicated to “Confirmatory Factor Analysis (CFA) for Applied Research.” Given that CFA is a broad and complex topic, most SEM textbooks do not focus on the issues associated with CFA measurement models. Many applied research questions are related to CFA as the primary analysis technique, and a large amount of time is devoted to analyzing measurement models. Furthermore, introductory textbooks on SEM typically do not focus on advanced topics like categorical indicators, multilevel data analysis, or scale reliability evaluation, and so on, which are all needed in applied research. The second edition of Timothy Brown’s introductory textbook attempts to fill this gap and succeeds in being a user-friendly guide to CFA.
Outline of the Book
The book can be divided into two parts: The first part includes five chapters on the fundamentals of CFA. An overview is presented that introduces all of the aspects necessary for conducting a CFA, understanding its results, and modifying the measurement model.
The second part of the book contains six further chapters on several topics within the CFA framework, including missing values, categorical data, multitrait–multimethod models, and Bayesian CFA. Because each of these chapters provides short introductions to specific CFA issues, they can be read in any order.
As the author emphasizes in the preface, five key strategies are used successfully throughout the textbook to organize each chapter: (1) Each concept is introduced using an applied data set (along with software syntax and an output of typical commercial software packages for latent variable modeling). (2) Very helpful tables are used to summarize each step of a method or procedure (e.g., information on how to report on a CFA study; see p. 129). (3) Figures and path diagrams are used to illustrate the various model types or statistical concepts (e.g., factor rotation and parameter distributions in Bayesian CFA). (4) Several chapters have appendices with additional didactical material for interested users (e.g., data generation in Monte Carlo simulation studies). (5) An external website (http://www.guilford.com/brown3-materials) offers syntax and data sets for most chapters as well as additional useful material (e.g., links to other resources).
Specific Contents
In Chapter 1, the basic concepts of and motivations for conducting a CFA are explained. This includes an introduction to measurement models, indicators, factors, and factor loadings. The readers gain an understanding of the importance of conducting a construct validation, examining method effects, and evaluating measurement invariance. Furthermore, Chapter 1 provides an overview of the following sections.
Chapter 2 introduces the common factor model and the exploratory factor analysis (EFA) using figures and the example of depression. For the EFA, factor extraction, factor selection, factor rotation, and factor score estimation are presented. As a didactic tool, a table is used to summarize fundamental steps and procedural recommendations for conducting an EFA.
Chapter 3 is the heart of the textbook. It is a beautiful introduction to CFA. It begins with a description of the similarities and differences between EFA and CFA and goes on to introduce the readers to the purpose of a CFA, subsequently focusing on parameters, notation(s), and fundamental equations, and properties of a CFA model. Furthermore, model identification and maximum likelihood (ML) estimation as well as an evaluation of model fit are presented. Throughout the chapter, multiple figures and tables are used in order to illustrate the differences not only between various models but also between different notation(s). Technically necessary equations and matrices are reduced to a minimum without omitting important concepts or failing to generate a depth of understanding. Helpful guidelines for model identification and for interpreting goodness-of-fit measures are provided as well.
Chapter 4 demonstrates the specification and interpretation of CFA models in statistical software packages. It uses an empirical example from personality research to demonstrate how to apply the concepts of a CFA presented in the previous chapter in order to evaluate measurement models. Four commercial latent variable software packages are applied (LISREL, Mplus, EQS, and SAS). Their input and output files (including the results) are discussed extensively. The code is instructive and useful for applied researchers and graduate students. The interpretation of parameter estimates of the CFA model is explained in detail, and valuable recommendations are given as to which information should be reported in a CFA study. As a simple but brilliant didactic tool, the chapter concludes with an example report on a CFA model (as an appendix). However, it would have been beneficial if a noncommercial software had been presented as well (both in this chapter and throughout the rest of the book). For example, the lavaan package (Rosseel, 2012), which is freely available for the R-project environment for statistical computing, has gained much attention in recent years.
Chapter 5 focuses on model revision and comparison. Poor-fitting models are often encountered by substantive researchers and the chapter helps to deal with several problems that arise as a result. It gives advice on how to respecify models and discusses the sources of poor-fitting or improper solutions as well as their remedy. New techniques, such as exploratory SEM, are introduced as intermediate steps between EFA and CFA that offer more realistic measurement models.
Chapter 6 is the first chapter on specific issues in the CFA framework. It provides an introduction to the CFA of Multitrait–Multimethod (MTMM) Matrices by using an example from clinical psychology. Convergent and discriminant validity as well as the concept of method effects are presented. The chapter discusses in detail two MTMM CFA models (correlated trait-correlated method (CTCM) and correlated trait-uncorrelated method (CTUM) models), including their parameterization, extensions, as well as advantages and disadvantages. Syntax for several software packages is made available as well. Furthermore, Brown addresses the negative consequences that can occur when methods variance and measurement error are not accounted for, which serves as a valuable didactic tool. However, the fact that the chapter only focuses on two specific MTMM CFA models could be considered to be a minor shortcoming. For example, (traditional) multiplicative (nonlinear) MTMM CFA models are not mentioned at all. Furthermore, in recent years, numerous important theoretical contributions have been made leading to a differentiation of the method effect concept (e.g., Eid et al., 2008). As a result, MTMM CFA models have been developed that are important for applied researchers as well (e.g., multilevel MTMM CFA models).
Chapter 7 presents the CFA with equality parameter constraints within single groups, multiple groups, and mean structures. The procedures offer a variety of possibilities for examining the measurement invariance and population heterogeneity. Again, extensive substantive examples and software syntax are presented in detail (including several tables). Again, it would have been helpful if the freely available R packages lavaan and semTools (semTools Contributors, 2014) had been presented as well, for they offer very user-friendly possibilities for examining the measurement invariance (with sparse syntax). Furthermore, it would have been useful if the issue of population heterogeneity had been discussed in a separate chapter. Mixture/nonlinear latent variable modeling offers a variety of ways to detect and understand unobserved/observed population heterogeneity (for an overview, see Kelava & Brandt, 2014).
In Chapter 8, additional applications (other types of CFA models) are shown: higher order factor models and bifactor models, CFA evaluation of scale reliability, and models with formative indicators. The higher order factor models and bifactor models are introduced using substantive research examples and intuitive figures and tables. The complexity of the equations for (point and interval) estimation of scale reliability is reduced to a minimum so that they are easier to understand. Models with formative indicators are illustrated with numerous substantive research examples and path diagrams.
Chapter 9 addresses special data issues in CFA, including missing, nonnormal, and categorical data. The parallels between CFA and item response theory are illustrated, which allows for a more general view of statistical modeling of measurement models in both frameworks.
Chapter 10 presents strategies for determining the sample size required to achieve sufficient statistical power in a CFA. The Satorra-Saris method and the Monte Carlo approach are presented. A demystifying example, which shows that even complex methods can be made accessible to a broad readership, is provided as an appendix to illustrate the Monte Carlo simulation of data in depth.
Finally, Chapter 11 gives an overview of some recent developments involving CFA models, with a particular focus on Bayesian CFA and multilevel factor models. The underlying Bayesian concepts are explained in a very clear and straightforward way by means of helpful figures (illustrations of posterior, prior, and likelihood distributions). An applied example of political attitudes is used to illustrate the concepts.
The Significance of the Book
Timothy A. Brown’s textbook is written for applied researchers and graduate students. With this audience in mind, the second edition maintains the accessible nature and applied focus of the first edition, while being updated to include recent advancements of CFA modeling and software developments. In addition, the author managed to arrange the chapters in a very clear and coherent manner, despite the depth and overall scope of the book. Summaries at the beginning and end of each chapter, an extensive number of substantive examples, figures and tables, appendices, software input and output files, as well as a sophisticated structure (e.g., order of chapters, headings, etc.) make each chapter very easy to follow. With the greatest discipline, the book focuses on the needs of applied researchers who are confronted with many real problems during the analysis of empirical data (outside the ideal world of typical psychometric assumptions). It emphasizes that there is not just one single way to analyze data with a CFA but a multitude of competing models that need to be evaluated from both a statistical and a conceptual (substantive) point of view. Despite some minor shortcomings, it still provides readers with clear recommendations and guidelines of how to deal with problems as well as a comprehensive overview of the most important aspects of CFA that an applied researcher should know. Given these outstanding qualities, I strongly believe that Timothy A. Brown’s textbook on Confirmatory Factor Analysis for Applied Research will continue to have a strong impact on applied researchers (including the Journal of Educational and Behavioral Statistics readership) and graduate students. The first edition has become a benchmark textbook in the field of introductory psychometrics, and the carefully revised second edition will widen its readership and make an impact very soon.