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Ordinal Data Modeling
Journal of Statistical Planning and Inference 100 (2002) 87–88
www.elsevier.com/locate/jspi
Book review Ordinal Data Modeling Valen E. Johnson and James H. Albert; Springer, New York, 1999, 258pp., ISBN 0-387-98718-5 This book presents a wide variety of methods for analyzing binary and ordinal response data, including methods for regression modeling, assessing interrater agreement and item response modeling. The emphasis is on Bayesian methods, although frequentist methods are described as well. In the course of laying out the background material, the authors present the most lucid introduction to Bayesian methods and computation I have ever read. It is an excellent book, providing clear descriptions of a number of speci7c methods while presenting enough general theory to allow readers to extend the methods to other applications. The preface indicates that prerequisites for the book are a course in elementary statistics and familiarity with multiple regression. The reader also needs a good background in calculus to grasp the discussion of integrals in the book, particularly in Chapter 2 and a good knowledge of linear algebra, particularly in Chapter 5. As stated in the preface, this book in intended for “graduate students and researchers in statistics and the social sciences.” This is a diverse audience, but, in my opinion, the authors are very successful in accomplishing a di;cult aim, “... to bridge the gap between recent theoretical developments in statistics and the application of these methods in the social sciences.” A key to the authors’ success emerges early in the book. In Section 1:1, before introducing maximum likelihood and Bayesian methods for estimating a binomial proportion, the authors motivate the statistical problem with real-data examples. This technique is maintained throughout the book; each general discussion of methodology is illustrated with examples. The book also makes excellent use of graphics to illustrate the statistical concepts and the results from the application of the statistical methods to the examples. Chapters 1 and 2 lay out the background material necessary for the speci7c methods in Chapters 3 – 6 and the case study in Chapter 7. Chapter 1 gives an overview of Bayesian and frequentist inference. The estimation of a binomial proportion and a normal mean is used to illustrate the general concepts of point and interval estimation, prediction, and the use of conjugate and nonconjugate priors. Chapter 2 describes a number of methods for Bayesian computaion, including “non-simulation-based algorithms” such as multivariate normal approximations to the posterior distribution and Gauss–Hermite quadrature. Simulation-based methods, including Metropolis–Hastings algorithms and Gibbs sampling are also presented clearly.
PII: S 0 3 7 8 - 3 7 5 8 ( 0 1 ) 0 0 1 0 5 - 7
88
Book review / Journal of Statistical Planning and Inference 100 (2002) 87–88
Chapter 3 focuses on binary regression models. A strength of this chapter is the discussion of model criticism and selection, both from a Bayesian and frequentist perspective. The analysis of ordinal data begins with Chapter 4. The remaining chapters present methods for analyzing data from several raters, ROC analysis and item-response modeling. A case study of grades is presented in Chapter 7. All of these methods are illustrated with good examples. An appendix give a description of the MATLAB functions used for most of the computations in the book, as well as a reference for a Web site where these functions can be obtained. An important topic that is not addressed speci7cally in the text is the common problem of longitudinal ordinal responses. This point is debatable since there is enough detail about the general theory and methods of computation to allow a reader to apply Bayesian methods to the problem of longitudinal ordinal data. In summary, this is an excellent book. It is a careful and lucid presentation of methods for analyzing ordinal data but it is also valuable for the more general discussion of Bayesian methods of inference and computation presented in the 7rst two chapters. Mark R. Conaway Division of Biostatistics and Epidemiology, Department of Health Evaluation Sciences, The University of Virginia, Charlottesville, VA 22908, USA
www.elsevier.com/locate/jspi
Book review Ordinal Data Modeling Valen E. Johnson and James H. Albert; Springer, New York, 1999, 258pp., ISBN 0-387-98718-5 This book presents a wide variety of methods for analyzing binary and ordinal response data, including methods for regression modeling, assessing interrater agreement and item response modeling. The emphasis is on Bayesian methods, although frequentist methods are described as well. In the course of laying out the background material, the authors present the most lucid introduction to Bayesian methods and computation I have ever read. It is an excellent book, providing clear descriptions of a number of speci7c methods while presenting enough general theory to allow readers to extend the methods to other applications. The preface indicates that prerequisites for the book are a course in elementary statistics and familiarity with multiple regression. The reader also needs a good background in calculus to grasp the discussion of integrals in the book, particularly in Chapter 2 and a good knowledge of linear algebra, particularly in Chapter 5. As stated in the preface, this book in intended for “graduate students and researchers in statistics and the social sciences.” This is a diverse audience, but, in my opinion, the authors are very successful in accomplishing a di;cult aim, “... to bridge the gap between recent theoretical developments in statistics and the application of these methods in the social sciences.” A key to the authors’ success emerges early in the book. In Section 1:1, before introducing maximum likelihood and Bayesian methods for estimating a binomial proportion, the authors motivate the statistical problem with real-data examples. This technique is maintained throughout the book; each general discussion of methodology is illustrated with examples. The book also makes excellent use of graphics to illustrate the statistical concepts and the results from the application of the statistical methods to the examples. Chapters 1 and 2 lay out the background material necessary for the speci7c methods in Chapters 3 – 6 and the case study in Chapter 7. Chapter 1 gives an overview of Bayesian and frequentist inference. The estimation of a binomial proportion and a normal mean is used to illustrate the general concepts of point and interval estimation, prediction, and the use of conjugate and nonconjugate priors. Chapter 2 describes a number of methods for Bayesian computaion, including “non-simulation-based algorithms” such as multivariate normal approximations to the posterior distribution and Gauss–Hermite quadrature. Simulation-based methods, including Metropolis–Hastings algorithms and Gibbs sampling are also presented clearly.
PII: S 0 3 7 8 - 3 7 5 8 ( 0 1 ) 0 0 1 0 5 - 7
88
Book review / Journal of Statistical Planning and Inference 100 (2002) 87–88
Chapter 3 focuses on binary regression models. A strength of this chapter is the discussion of model criticism and selection, both from a Bayesian and frequentist perspective. The analysis of ordinal data begins with Chapter 4. The remaining chapters present methods for analyzing data from several raters, ROC analysis and item-response modeling. A case study of grades is presented in Chapter 7. All of these methods are illustrated with good examples. An appendix give a description of the MATLAB functions used for most of the computations in the book, as well as a reference for a Web site where these functions can be obtained. An important topic that is not addressed speci7cally in the text is the common problem of longitudinal ordinal responses. This point is debatable since there is enough detail about the general theory and methods of computation to allow a reader to apply Bayesian methods to the problem of longitudinal ordinal data. In summary, this is an excellent book. It is a careful and lucid presentation of methods for analyzing ordinal data but it is also valuable for the more general discussion of Bayesian methods of inference and computation presented in the 7rst two chapters. Mark R. Conaway Division of Biostatistics and Epidemiology, Department of Health Evaluation Sciences, The University of Virginia, Charlottesville, VA 22908, USA