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“A welcome addition to multivariate analysis. The discussion is lucid and very leisurely, excellently illustrated with applications drawn from a wide variety of fields. A good part of the book can be understood without very specialized statistical knowledge. It is a most welcome contribution to an interesting and lively subject.” -- Nature Originally published in 1974, this book is a reprint of a classic, still-valuable text.
The statistical analysis of discrete multivariate data has received a great deal of attention in the statistics literature over the past two decades. The develop ment ofappropriate models is the common theme of books such as Cox (1970), Haberman (1974, 1978, 1979), Bishop et al. (1975), Gokhale and Kullback (1978), Upton (1978), Fienberg (1980), Plackett (1981), Agresti (1984), Goodman (1984), and Freeman (1987). The objective of our book differs from those listed above. Rather than concentrating on model building, our intention is to describe and assess the goodness-of-fit statistics used in the model verification part of the inference process. Those books that emphasize model development tend to assume that the model can be tested with one of the traditional goodness-of-fit tests 2 2 (e.g., Pearson's X or the loglikelihood ratio G ) using a chi-squared critical value. However, it is well known that this can give a poor approximation in many circumstances. This book provides the reader with a unified analysis of the traditional goodness-of-fit tests, describing their behavior and relative merits as well as introducing some new test statistics. The power-divergence family of statistics (Cressie and Read, 1984) is used to link the traditional test statistics through a single real-valued parameter, and provides a way to consolidate and extend the current fragmented literature. As a by-product of our analysis, a new 2 2 statistic emerges "between" Pearson's X and the loglikelihood ratio G that has some valuable properties.
Discrete or count data arise in experiments where the outcome variables are the numbers of individuals classified into unique, non-overlapping categories. This revised edition describes the statistical models used in the analysis and summary of such data, and provides a sound introduction to the subject for graduate students and practitioners needing a review of the methodology. With many numerical examples throughout, it includes topics not covered in depth elsewhere, such as thenegative multinomial distribution; the many forms of the hypergeometric distribution; and coordinate free models. A detailed treatment of sample size estimation and power are given in terms of both exact inference and asymptotic, non-central chi-squared methods. A new section covering Poissonregression has also been included. An important feature of this book, missing elsewhere, is the integration of the software into the text.Many more exercises are provided (including 84% more applied exercises) than in the previous edition, helping consolidate the reader's understanding of all subjects covered, and making the book highly suitable for use in a classroom setting. Several new datasets, mostly from the health and medical sector, are discussed, including previously unpublished data from a study of Tourette's Syndrome in children.
An Applied Treatment of Modern Graphical Methods for Analyzing Categorical DataDiscrete Data Analysis with R: Visualization and Modeling Techniques for Categorical and Count Data presents an applied treatment of modern methods for the analysis of categorical data, both discrete response data and frequency data. It explains how to use graphical meth
This book is an introduction to the principles and methodology of modern multivariate statistical analysis. It is written for the user and potential user of multivariate techniques as well as for students coming to the subject for the first time. The author's emphasis is problem-orientated and he is at pains to stress geometrical intuition in preference to algebraic manipulation. Mathematical sections that are not essential for a practical understanding of the techniques are clearly indicated so that they may be skipped by the non-specialist. Discrete and mixed variable techniques are presented as well as continuous variable techniques to give a comprehensive coverage of the subject. This updated edition includes a new appendix which traces developments that have taken place in the years since the publication of the first edition and which clarifies some issues raised by readers of the original text. References to about 60 recent books and articles supplement the material in this appendix. Overall, this volume provides an up-to-date and readable practical account of the subject, both for students of statistics and for research workers in subjects as diverse as anthropology, education, industry, medicine and taxonomy. The new edition includes a survey of the most recent developments in the subject.
Studies in Econometrics, Time Series, and Multivariate Statistics covers the theoretical and practical aspects of econometrics, social sciences, time series, and multivariate statistics. This book is organized into three parts encompassing 28 chapters. Part I contains studies on logit model, normal discriminant analysis, maximum likelihood estimation, abnormal selection bias, and regression analysis with a categorized explanatory variable. This part also deals with prediction-based tests for misspecification in nonlinear simultaneous systems and the identification in models with autoregressive errors. Part II highlights studies in time series, including time series analysis of error-correction models, time series model identification, linear random fields, segmentation of time series, and some basic asymptotic theory for linear processes in time series analysis. Part III contains papers on optimality properties in discrete multivariate analysis, Anderson’s probability inequality, and asymptotic distributions of test statistics. This part also presents the comparison of measures, multivariate majorization, and of experiments for some multivariate normal situations. Studies on Bayes procedures for combining independent F tests and the limit theorems on high dimensional spheres and Stiefel manifolds are included. This book will prove useful to statisticians, mathematicians, and advance mathematics students.
The book is a collection of some of the research presented at the workshop of the same name held in May 2003 at Rutgers University. The workshop brought together researchers from two different communities: statisticians and specialists in computational geometry. The main idea unifying these two research areas turned out to be the notion of data depth, which is an important notion both in statistics and in the study of efficiency of algorithms used in computational geometry. Many of the articles in the book lay down the foundations for further collaboration and interdisciplinary research. Information for our distributors: Co-published with the Center for Discrete Mathematics and Theoretical Computer Science beginning with Volume 8. Volumes 1-7 were co-published with the Association for Computer Machinery (ACM).