Preface

It was a pleasant surprise when we were asked by our original publisher to come up with a revised second edition within three years of publication of the first edition. The first edition was warmly received by the intended audiences. However, over the last three years we ourselves had critically examined the book and had come to realize that in view of certain newer approaches to the analyses (such as the mixed models approach), a revision could make the book even more useful. It is our pleasure to present to our audiences a second revised edition, which is now copublished by SAS Institute Inc. and John Wiley & Sons.

Applied multivariate techniques are routinely used in a variety of disciplines such as agriculture, anthropology, applied statistics, biological sciences, business, chemistry, econometrics, education, engineering, marketing, medicine, psychology, quality control, and sociology. With such a diverse readership, we thought it essential to present multivariate techniques in a general context while at the same time keeping the mathematical and statistical requirements to a bare minimum. We have sincerely attempted to achieve this objective.

Audience

The book is written both as a handy reference for researchers and practitioners as well as a supplementary college text. Researchers and practitioners can also adapt the material for a self-taught tutorial. Students and their instructors in senior undergraduate or beginning graduate classes in applied statistics will find the book useful as an accompanying computational supplement to a more advanced book on applied multivariate statistics. The book can also be adapted for a statistics service course for graduate students from the nonstatistical disciplines.

Approach

Primary emphasis is on statistical methodology as applied to various scientific disciplines. SAS software is used as the crucial computational aid to carry out various intensive calculations which so naturally occur in any typical multivariate analysis application. Discussion in this volume is limited to only the normal theory-based multivariate analysis.

We believe that those who use multivariate methods should not only understand appropriate statistical techniques useful in their particular situation but should also be able to discern the appropriate approach and distinguish it from an approach that seems correct but is completely inappropriate in a particular context. Quite often, these differences are subtle, and there are scenarios where the presumably best approach may be completely invalid due to one reason or the other. The problem is further compounded by the understandable temptation to take the shortest route by choosing the analysis that can be readily performed using a particular software package or a canned computer program, regardless of its appropriateness, over a more appropriate analysis not so readily available. This book attempts to demonstrate this process of discernment, problem definition, selection of an appropriate analysis or a combination of many, while providing both the needed SAS code to achieve these goals and the subsequent interpretation of the SAS output.

This approach largely eliminates the need for two books, one for learning multivariate techniques and another for mastering the software usage. Instead of taking various multivariate procedures in SAS one at a time and demonstrating their potential to solve a large number of different problems, we have chosen to discuss various multivariate situations one by one and then identify the most appropriate SAS analyses for them. Many of these analyses may occasionally result from the combined applications of two or more SAS procedures. All multivariate methods are illustrated by appropriate examples. In most cases, the data sets considered are real and are adapted from the published literature from a variety of disciplines.

Prerequisites

A course in applied statistics dealing with the essentials of the (univariate) experimental designs and regression theory and some familiarity with matrix algebra (just enough to interpret the notationally presented statistical models and linear hypotheses) provide an adequate preparation to read this book. Some familiarity with SAS programming (the DATA step and the basic rules of the SAS language) will also be helpful. See the References for a list of SAS documentation.

Overview of Chapters

Chapter 1 provides a summary of important multivariate results. In Chapter 2, various graphical methods for the exploratory multivariate analysis are presented. In Chapter 3, a brief review of the theory of multivariate regression models is provided, which is followed by a number of applications. Chapter 4 deals with the analysis of experimental data. Since the underlying theory, though a bit more complex, is essentially parallel to that presented in Chapter 3, we have largely confined our discussion here to modeling and applications in a variety of experimental designs.

Chapter 5, "Analysis of Repeated Measures Data" and Chapter 6, "Analysis of Repeated Measures Using Mixed Models," occupy a relatively larger space than other chapters in the book. This emphasis requires some further explanation. The repeated measures data are multivariate in nature but are often analyzed using some of the univariate techniques. Both the univariate and multivariate approaches have their own advantages and shortcomings and both are important in their own rights. Both of these approaches are discussed in these chapters. Complexity of models is inherent in the repeated measures data; variety in terms of models is plentiful, and many of these models are commonly used in different disciplines. As a result, we have decided to provide a careful systematic discussion of some of the most commonly used models with an appropriate explanation of the analyses performed by various SAS procedures. However, our coverage, though extensive, is still by no means exhaustive.

The book also contains two appendices. The first of these contains some of the commonly needed and useful multivariate matrix manipulation statements from the SAS IML procedure. It is included so that researchers who wish to perform some further nonstandard analyses of the data should be able to do so with minimal effort using PROC IML. Of course, no attempt is made to be exhaustive, and we readily admit that our selection of items here is purely due to our personal preference and our own exposure and experience with similar analyses. The second appendix contains all the data sets used in the book but not included as part of the corresponding SAS codes due to their large sizes.

Several errors of the first edition have been fixed in the second edition. However, in a work of this size, integrating various aspects of statistical methods and data analysis, there are bound to be some errors and gaps which we may have unintentionally introduced while adding the new material. We will greatly appreciate any comments, suggestions or criticisms which will help us improve this work further.

Acknowledgments

A number of people have contributed to this project in a number of ways. Our sincere thanks are due to outside peer reviewers and internal reviewers at SAS Institute who worked on either of the two editions and to Mr. Jim Ashton (SAS Institute Inc.), Professor Naveen Bansal (Marquette University), Professor Robert Ling (Clemson University) Professor Kenneth Portier (University of Florida), Professor David Scott (Rice University) for critically reading the manuscript for the second edition and for their helpful suggestions. Whole or parts of the manuscript were initially read by Professors A. M. Kshirsagar (University of Michigan), T. K. Nayak (George Washington University), S. D. Peddada (University of Virginia), and N. H. Timm (University of Pittsburgh). We greatly acknowledge their interest in this project. Special thanks are due to Professor Kshirsagar for a number of discussion sessions at various occasions. We thank Professor Robert Kushler (Oakland University) for many helpful criticisms while revising the book and Professor Hans-Peter Piepho (Universitaet Kassel) and Professor Choudary Hanumara (University of Rhode Island) for pointing out certain errors. We also thank Professor N. R. Chaganty (Old Dominion University) for many helpful discussions. Our students Ms. Shobha Prabhala and Ms. Karen Meldrum read parts of an earlier draft of the manuscript. Ms. Raja Vishnubhotla, a local SAS expert at Oakland University, answered our numerous inquiries about SAS. Parts of the book were typed by Ms. Kathy Jegla, Ms. Barbara Jeffrey, and Ms. Sujatha Naik. We kindly thank them for their assistance.

People at SAS Institute, especially Mr. David Baggett, Ms. Caroline Brickley, Ms. Julie Platt, and Ms. Judy Whatley, were most helpful and generous with their suggestions and time. We very much appreciate their understanding and their willingness to extend many of the deadlines.

We would also like to acknowledge the Oakland University Research Foundation for partially supporting some of the travel of R.Khattree and the Old Dominion University for approving the sabbatical of D.N.Naik during Fall 1994 while working on the first edition. We also thank our two departments in the respective universities for playing the host during our numerous visits to each other's institutions.

Last, but not least, our sincere thanks go to our wives, Nidhi and Sujatha, and our little ones Vaidehee and Navin for allowing us to work during late, odd hours and over the weekends. We thank them for their understanding that this book could not have been completed just by working during regular hours.

R. KHATTREE

Rochester, Michigan

D. N. NAIK

Norfolk, Virginia