Structural Equations with Latent Variables Book

Structural equation modeling (SEM) is a common tool for psychologists and social scientists. Many individuals know how to use software packages that produce results, but few understand the underlying mathematics involved in the analytic technique. Ken Bollen's book is the most rigorous treatment of structural equation modeling, even 19 years after it was written. Whereas other books may be more accessible, they do not illustrate the inner workings of the technique. Although some may argue that such understanding is not warranted, SEM techniques will produce numerous errors (e.g., under-identification, non-positive definite models, Heywood cases, etc.) that may sometimes be avoided by simply thinking about the mathematics involved. Jim Steiger, the former president of the Society for Multivariate Experimental Psychology (and an individual who has come up with statistics -- namely, the Root Mean Squared Error of Approximation, or RMSEA) has argued that one should not teach SEM until he or she has read and comprehended Bollen's book.

In addition to simply describing the technique especially well (as if that weren't enough), the book addresses issues in philosophy of science by way of statistical explanation. For example, classic definitions of causality have established three necessary but not sufficient conditions (1. cause precedes effect, 2. correlation, and 3. lack of potential alternative explanations). While (2) has long been taken for granted, Bollen explains mathematically why it is not necessary (although in all fairness, perhaps in the example he describes, (3) was not met). Still, I applaud the text writer for illuminating this point and changing the way I think about causality.

In terms of my earlier comment about accessibility, I used this text as suggested reading for a course on SEM. One of my brightest students who is now doing a Ph.D. in quantitative psychology and focusing on dynamic factor analysis (a particular usage of SEM) began the semester determined to read all suggested texts and articles. She quickly stated that she hated Bollen. However, after grasping SEM enough to use it for many purposes, the book seems more accessible. While there is almost nothing in the way of calculus in the book, there is a great deal of matrix algebra that occurs and, although there is a brief review/introduction to matrix algebra in the appendix, if the reader does not have such a background, the book may be hard going.

Furthermore, many recent developments in SEM are not covered. For example, the latent variable growth curve model is not discussed. Because the field has advanced, Bollen (and Patrick Curran, a colleague at UNC in psychology -- Bollen is in sociology) have also written a book on that very topic.

Additionally, I cannot suggest this text for the purpose of understanding the software packages for SEM per se; there are better texts (see Raykov & Marcoulides, for example) for this purpose. However, once the mathematics are understood, understanding the software is fairly easy.

I would suggest this book for use in a second course in SEM, or in a first course for someone who is very mathematically inclined. Furthermore, it is great for social scientists and statisticians who want to understand the elegance of this statistical technique. Perhaps in the future, Bollen will revise the text to address the minor issues of this wonderful book.