Logit Models From Economics and Other Fields

We know of no other one book like this one. Statistical Models has the flavor (or we should spell that “flavour”) of Ross’s Probability Models (2000). Like Ross, Davison provides sound statistical tools to tackle applications in a concise, succinct tutelage, yet without abandoning mathematical sophistication or detail. But Davison’s topics are wide-ranging, nearing the level of exhaustive, covering usual subjects, such as Markov chains and regression methods, as well as more arcane topics, like graphical representations of probability expert systems. This, of course, partially explains the book’s long length. We hesitate to call this book a text. The author does so in his Preface, suggesting its use for a course up through a masters degree in statistics, where the students have had linear algebra and a theory of statistics and probability course. But senior undergraduates without the entire sequence of mathematical statistics will struggle with the latter sections of most chapters. Davison might disagree. He insists that readers seeking a more thorough mathematical treatment look elsewhere, but we believe this to be a self-effacing statement. Rarely does he use the words “beyond the scope of this book. ” We see on occasion a declaration such as (during a discussion of the binomial distribution in Chap. 3) “in order not to obscure the main points, the discussion above has been deliberately oversimplified” (p. 56). We suspect that little would look oversimplified to most students. A classroom text is expected to contain problems for students. Although exercises are included at the end of each section, most of which are of the showor-prove variety, we would have liked to see a short set of answers at the back of the book. Solutions would lend more credence to the claim that the book can be used as a text. Additionally, the “practicals” listed in Appendix A, which were to include data and S programs and be available on the internet were not yet complete (e-mail correspondence with the author on September 16, 2004) despite the publishing date of 2003. We are not surprised that these exercises were left as an afterthought, because the book is not a “cookbook” presentation enabling matching of real-world problems to examples therein. The examples in the book do illustrate techniques applied to real-world datasets (such as the Maize data, i.e., the Darwin plant heights) and are reworked with different modeling approaches, thus providing a feeling of continuity to the subject matter. As a text, this book would suit a class of exactly what the title implies—a statistical modeling course, one that would need to be created around the book. Instead, the Preface should have prepared us for a wonderfully rich treatise of cleverly attended-to examples and charming asides. Many of these interjections involve biographical sketches of famous mathematicians and statisticians—although Wald (see Wolfowitz 1952) was overlooked. And if the Preface had stated that seemingly every statistical technique available to the modern quantitative researcher would be considered, then we would have fully concurred that the author had met his goal. Some level of frustration may surface for the reader early in the book, if he or she left with the feeling that the choice of formulation was achieved through, perhaps, magic. An expansion on the following sentence from Chapter 4 (p. 150): “Model formulation involves judgement, experience, trial and error” inserted as an introductory section would help establish precepts underlying the role of modeling. Chapter 1 presents ample enticing data situations encountered, but a novice to the concept of modeling may need to be more intrepid than intrigued. Chapter 2 broadly discusses items usually seen in the theoretical statistics sequence, including order statistics, moments, and cumulants. Chapter 3 covers topics pertaining to confidence intervals, including pivots and simulations, which are also reexamined later in Chapter 7. Likelihood estimation and model selection are visited in Chapter 4. Davison’s analytical journey includes detailed and important discussions of building block statistical issues, such as describing the mechanics behind the normal distribution (Sec. 3.3) and explaining the workings of likelihood ratio statistics (Sec. 4.5) before moving into the core. We would describe the first four chapters (titled Introduction, Variation, Uncertainty, and Likelihood) as “mathematical statistics revisited,” yet the exploration sometimes features a different perspective on the topic that is more suited to a book of this style rather than to a plain mathematical statistics text. The book then launches into the meat of the material by describing classes of models in Chapters 5, 6, 8, and 9, including survival models, Markov processes, the general linear model and all of its variants (such as mixed models, with complications such as missing data), and then in Chapter 10 illustrates applications of nonlinear models. Chapter 11 covers the use of Bayesian statistics with accompanying computing techniques (e.g., Gibbs sampler). Altogether these chapters give the reader good grounding in the process of modeling. A synopsis of Chapter 12 could read as “warnings about relying on the old standby likelihood estimation. ” A map with plausibly linkable chapters for a feasible subset coverage of the book is offered in Chapter 1. This handy map of chapter dependencies could aid instructors in selecting alternative ways to teach from the book that may be more suitable for their particular classes. We love owning this book. It gets placed on our shelf among our favorite reference books like the old classic for engineers by Kreyszig (1972), which, incidentally, reviewers seem to either hate or love. We actually learned a lot and deepened our understanding of many topics (e.g., Fisher information, reversible chains, Slutsky’s lemma) while reading Davison’s explanations. Certainly, using a hypercritical eye, one could say that the bibliographies at the chapter ends are a bit skimpy. In our areas of major interest we could reveal holes in the references; for example, for censored data, recent work by Ren (2003) and Zhang, Liu, and Wu (2003) are important citations that are omitted. And a few topics must have been reserved for the second edition, namely circadian rhythm analysis (Qiu 2002). Even so, if asked to summarize Statistical Models in a single word, “complete” would serve as the only plausible answer.