Longitudinal Structural Equation Modeling, Todd D. Little, Guilford Press 2013.
Let me start by saying that this is one of the best textbooks I’ve ever read. It was written as if the author was our mentor, and I really get the feeling that he’s sharing his wisdom with us rather than trying to be pedagogically correct. The book is full of insights on how he thinks about building and applying SEMs, and the lessons he’s learned the hard way.
It’s a little risky to endorse a highly-targeted book like this: it’s dedicated to longitudinal SEMs that don’t include categorical variables. But the discussion and advice that it has is so valuable that I’d recommend it to anyone who is interested in SEMs.
For example, his discussion on scale setting — you have to nail down something regarding a latent variable (“construct”) in order to provide a defined scale — and in addition to the way that most SEM software does it (fixing one of the loading factors to 1), there are two other ways to do it, both of which provide several important advantages. (The book’s website provides example Lisrel, Mplus, and R lavaan code illustrating select chapters, including the one that illustrates scaling.)
As another example, he talks about phantom constructs (latent variables), which is an expert’s trick for modifying your model to change coefficients into more interpretable forms. As one example, you can convert the SEM’s native covariance between latent variables into correlations, post-estimation, by simple algebra. But you couldn’t take two of these correlations (from different times in a longitudinal study, say) and use the model to do a chi-squared test of the significance of the difference between them. Using phantom constructs, with certain constraints, the model can yield correlations directly, so you could properly test their significance.
I could go on, but the bottom line is the book is well-written, entertaining, enlightening, well-illustrated, insightful, and it covers many areas of basic SEM as well as the specifics of the more complicated longitudinal SEM. It’s $60 for a 380-page hardback, and worth every penny.