Model Selection and Multimodel Inference

chemists. Commenting on the new material in the second edition (2E), which was published in 1991, Blackwood (1994) noted the predominance of citations from the chemometrics literature and commented that “references from other statistical sources are sparse. ” Chemometrics had certainly arrived in a big way by 1991, and there had not been much impact from the statistical community. If the methodology has not developed greatly through the 1990s, then the applications certainly have blossomed. (See the Journal of Chemometrics or Chemometrics and Intelligent Laboratory Systems, which have a lot of papers that would work perfectly well in the pages of Technometrics.) Blackwood (1994) noted in his review of the 2E that “The mathematical and statistical theory behind factor analysis is generally well presented, but it is in the practice and application areas that the book does best” (p. 115). In the Preface, the author notes that “the introductory chapters, 1 through 5, remain unchanged” (p. ix). Why mess with a proven product? Blackwood (1994) did comment that “the book is not an easy read,” and “it requires a good deal of mathematical understanding to get through. ” See the review for a complete summary of the 2E. The remainder of the book has been revised considerably. Chapter 6, formerly “Spectral Methods of Factor Analysis,” has been reorganized and retitled as “Evolutionary Methods. ” It focuses on self-modeling methods and rank-annihilation factor analysis. This chapter is followed by additional material from the former Chapter 6 that has been expanded into two new chapters, “Multimode Analysis” and “Partial Least-Squares Regression. ” All statisticians are quite familiar with the latter methodology, if not with some of the advanced realizations in chemistry, such as multiblock PLS, serial PLS, and multilinear PLS, that are described in this chapter. The chapter on multimode analysis carries the factor analysis tools into the arena of multiway arrays. This chapter deals with three-dimensional rank-annihilation factor analysis, simultaneous analysis, three-mode factor analysis, and PARAFAC (parallel factor analysis). The four application chapters that conclude the book continue to bear the same titles as before, but they have all been updated to incorporate the latest advances in a wide variety of disciplines where various factor analysis methodologies have been applied. Three of the chapters are focused strictly within the realm of chemistry, whereas the  nal chapter broadens the spectrum to incorporate examples from related sciences, speci cally biomedical, fuels, environmental, and food science applications. Despite the vast computational complexity of many of the methods in the book, the author continues to make no attempt to integrate statistical software into the text. There is an appendix that discusses the Toolbox for Chemical Factor Analysis, a suite of Matlab which the author apparently wrote. However, no CD-ROM is included. These programs need to be purchased. Another appendix provides the actual Matlab code for three of the programs, which are like subroutines in FORTRAN in that they need to be strung together to create a factor analysis program. There is no reference to software packages from Umetrics or other companies whose software can carry out many of the analyses in the book.