Credit where credit's due: Things in the book about which I didn't give adequate credit.
To avoid repetitiousness, please insert at the end of each entry below: "Sorry I was such a lazy jerk."
This page is organized by chapter in the book.
Chapter 1: Opinionated survey of MLM methods
Zero variance estimates (Section 1.4.1, p. 41). In this section I dinged other writers on mixed linear models for not talking about how often zero variance estimates occur. Given how huge the MLM literature is and the small fraction of it I'd actually read, I should've known better than to say "[A particular laudable book] is alone in forthrightly stating that zero variance estimates are common [etc.]". I should've said something like "Among the material I've read, [A particular laudable book] is alone [etc.]".
For example, Rob Weiss's book Modeling Longitudinal Data (2005 Springer) discusses zero variance estimates in its Section 6.5, using the nice analogy of seeking a mountain top in a dense fog, without knowing that there are tall cliffs nearby with the ocean crashing at the bottom. His section 6.1.1 also talks about how this problem affects likelihood ratio tests. Box and Tiao's Bayesian Inference in Statistical Analysis (1973) also discusses zero (frequentist) variance estimates in Sections 5.1 and 5.2 -- more below (see Chapter 18).
I will gladly add a plug here for anybody else who has written about this problem.
Chapter 18: Zero variance estimates
Balanced one-way random effect model (Section 18.1.1). The material in this section is very similar to Section 3B of Bruce Hill's 1965 JASA paper on the one-way random effects model. Sorry about that, Bruce.
Box and Tiao's Bayesian Inference in Statistical Analysis (1973) gives a briefer treatment of this material in Section 5.2; in particular, page 255 (Section 5.2.4) gives a necessary and sufficient condition for a zero (frequentist) estimate of the between-groups variance. Sorry about that, Georges.
Thanks to Rob Weiss for telling me about these two earlier publications.
Posterior modes on the boundary of the parameter space. 28 Oct 2014: I just read Christian Robert's JASA review of the 3rd edition of Bayesian Data Analysis, by Andrew Gelman et al, which notes that their Section 13.2 discusses posterior modes on the boundary of the parameter space. I didn't know this and haven't read this section of their book, so I can't comment beyond saying I'm delighted these heavyweights had something to say on this matter. Sorry about that, Andrew, John, Hal, David, Aki, and Don.