Six Sigma Quality Improvement with MINITAB

adjustments proposed by Kenward and Roger (1997). Comparisons between the MIXED and GLM procedures are not stressed to the extent that they were in the first edition. The second edition covers the same topics presented in the first edition as well as three additional topics: “Mixed Model Diagnostics” (Chapter 10), “Power Calculations for Mixed Models” (Chapter 12), and “Some Bayesian Approaches to Mixed Models” (Chapter 13). Chapter 10 begins with a discussion of residual diagnostics for linear models and extensions for the linear mixed model using marginal and conditional residuals calculated with the MIXED procedure. Studentized versions of these residuals can now be calculated in MIXED using the RESIDUAL option in the MODEL statement or by the GLIMMIX procedure. This chapter presents examples to illustrate these procedures and options. In addition, there are discussion and example sections pertaining to influence diagnostics available with the INFLUENCE option in the MODEL statement for the MIXED procedure. Chapter 12 describes power calculations based upon a current dataset with the idea that the current data set represents a pilot study for experiments yet to be conducted. Examples are given to demonstrate the use of the MIXED procedure for performing these power calculations, for constructing power curves, for comparing designs, and for simulating power. Chapter 13 provides a brief description of the mixed model from a Bayesian perspective. This description includes criticisms of p values and alternatives, such as approximate values for Bayes factors. This chapter also shows how to simulate a random sample from the posterior distribution for a variance-component model using the PRIOR statement in the MIXED procedure. In their example, the default Jeffrey’s prior is used for the variance-components. For the fixed effects, a flat prior is used, which is the only available prior. While it is often the case that a new edition of a book differs only slightly from its previous edition, this is not true for this particular text. In addition to the new material discussed previously, the second edition makes some revisions to every chapter. These revisions are too numerous to list individually, but some of the revisions are substantial. For instance, the chapters on “Generalized Linear Mixed Models” (Chapter 14) and “Nonlinear Mixed Models” (Chapter 15) have been altered since version 9.1 accommodates the GLIMMIX and NLMIXED procedures. These chapters have new sections describing these procedures and corresponding applications have also been modified. In fact, Chapter 15 contains three new applications. These chapters also point out that the GLIMMIX procedure is an enhancement of the GLIMMIX macro while the NLMIXED procedure does not completely replace the NLINMIX macro. Chapter 15 contains a nice example and discussion section comparing NLMIXED and NLINMIX. With the addition of these new procedures, MIXED is no longer the only available procedure for analyzing mixed models. The “Introduction” (Chapter 1) now contains examples and discussion to aid the reader in determining the appropriate SAS procedure to use in particular applications. The extent of changes regarding the remaining chapters depends upon the topic. The chapter entitled “Common Mixed Models” (Chapter 2 in 1st ed.) has been replaced by a nice chapter on “Multi-factor Treatment Designs with Multiple Error Terms” (Chapter 4). This chapter essentially has six new sections and is better organized than the previous edition. However, such changes will be an adjustment for statisticians and students who have found Chapter 2 in the first edition to be so helpful. Chapters geared toward applications have been modified with sections containing new or thoroughly revised examples. These include Chapter 5 “Analysis of Repeated Measures Data” (two sections), Chapter 6 “Best Linear Unbiased Prediction” (two sections), Chapter 7 “Analysis of Covariance” (one section), Chapter 8 “Random Coefficient Models” (one section), Chapter 9 “Heterogeneous Variance Models” (three sections), Chapter 11 “Spatial Variability” (two sections), and Chapter 16 “Case Studies” (three sections). Other chapters on “Randomized Complete Block Designs” (Chapter 2) and “Random Effects Models” (Chapter 3) have not been altered as much. Still, there are subsections in all chapters which have been carefully revised and rewritten. It is also interesting that this text uses the GLIMMIX procedure in Chapters 2, 4, 5, 7, and 16 for the normal linear mixed model where the MIXED procedure would have previously been used. This is done to illustrate available graphical displays (see pp. 33–35, 189–190), obtain estimates and simultaneous tests involving specified fixed effect terms using the LSMESTIMATE statement (see pp. 128–130, 315–316), and to obtain estimates and tests involving simple effects using the SLICEDIFF options in the LSMEANS statement (see pp. 192–194, 316). As with its predecessor, SAS for Mixed Models (2nd edition) will be an invaluable reference for anyone who works with mixed models, especially for those who use the SAS system. For those of us who have nearly worn through the first edition, this is a good opportunity to purchase an updated copy. First of all, this is because the second edition contains numerous changes which lead to substantial improvements in the overall presentation. Secondly, this edition is updated for SAS version 9.1 and includes examples demonstrating the use of the GLIMMIX and NLMIXED procedures as well as the use of ODS statements. Finally, this edition will be vital to those specifically interested in using residual diagnostics, power calculations, and Bayesian approaches. The SAS documentation and GLIMMIX documentation (SAS Institute 2003, 2006) are also good sources containing helpful details and examples. Overall, this text will be a valuable reference for a broad range of applications that demonstrate the implementation of mixed model methodology. The authors have provided a great service to those who use mixed models by providing this updated version.