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The Statistical Analysis of Discrete Data

Author: Thomas J. Santner

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 381

ISBN-13: 1461210178

The Statistical Analysis of Discrete Data provides an introduction to cur rent statistical methods for analyzing discrete response data. The book can be used as a course text for graduate students and as a reference for researchers who analyze discrete data. The book's mathematical prereq uisites are linear algebra and elementary advanced calculus. It assumes a basic statistics course which includes some decision theory, and knowledge of classical linear model theory for continuous response data. Problems are provided at the end of each chapter to give the reader an opportunity to ap ply the methods in the text, to explore extensions of the material covered, and to analyze data with discrete responses. In the text examples, and in the problems, we have sought to include interesting data sets from a wide variety of fields including political science, medicine, nuclear engineering, sociology, ecology, cancer research, library science, and biology. Although there are several texts available on discrete data analysis, we felt there was a need for a book which incorporated some of the myriad recent research advances. Our motivation was to introduce the subject by emphasizing its ties to the well-known theories of linear models, experi mental design, and regression diagnostics, as well as to describe alterna tive methodologies (Bayesian, smoothing, etc. ); the latter are based on the premise that external information is available. These overriding goals, to gether with our own experiences and biases, have governed our choice of topics.

Discrete Data Analysis with R

Author: Michael Friendly

Publisher: CRC Press

Published: 2015-12-16

Total Pages: 700

ISBN-13: 1498725864

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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

Exact Analysis of Discrete Data

Author: Karim F. Hirji

Publisher: CRC Press

Published: 2005-11-18

Total Pages: 1066

ISBN-13: 142003619X

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Researchers in fields ranging from biology and medicine to the social sciences, law, and economics regularly encounter variables that are discrete or categorical in nature. While there is no dearth of books on the analysis and interpretation of such data, these generally focus on large sample methods. When sample sizes are not large or the data are

Statistical Analysis and Data Display

Author: Richard M. Heiberger

Publisher: Springer Science & Business Media

Published: 2013-06-29

Total Pages: 739

ISBN-13: 1475742843

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This presentation of statistical methods features extensive use of graphical displays for exploring data and for displaying the analysis. The authors demonstrate how to analyze data—showing code, graphics, and accompanying computer listings. They emphasize how to construct and interpret graphs, discuss principles of graphical design, and show how tabular results are used to confirm the visual impressions derived from the graphs. Many of the graphical formats are novel and appear here for the first time in print.

Goodness-of-Fit Statistics for Discrete Multivariate Data

Author: Timothy R.C. Read

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 221

ISBN-13: 1461245788

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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.

Structural Analysis of Discrete Data and Econometric Applications

Author:

Publisher:

Published: 2000

Total Pages:

ISBN-13:

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Contains TIF, PDF, and compressed PostScript files of scanned images from of all pages of Structural analysis of discrete data and econometric applications, by Charles F. Manski and Daniel L. McFadden, MIT Press, 1981. Users can download the entire book or portion of the book.

Models for Discreet Data

Author: Daniel Zelterman

Publisher: Oxford University Press, USA

Published: 1999-01-21

Total Pages: 297

ISBN-13: 0191523437

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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.

Modeling Discrete Time-to-Event Data

Author: Gerhard Tutz

Publisher: Springer

Published: 2016-06-14

Total Pages: 247

ISBN-13: 3319281585

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This book focuses on statistical methods for the analysis of discrete failure times. Failure time analysis is one of the most important fields in statistical research, with applications affecting a wide range of disciplines, in particular, demography, econometrics, epidemiology and clinical research. Although there are a large variety of statistical methods for failure time analysis, many techniques are designed for failure times that are measured on a continuous scale. In empirical studies, however, failure times are often discrete, either because they have been measured in intervals (e.g., quarterly or yearly) or because they have been rounded or grouped. The book covers well-established methods like life-table analysis and discrete hazard regression models, but also introduces state-of-the art techniques for model evaluation, nonparametric estimation and variable selection. Throughout, the methods are illustrated by real life applications, and relationships to survival analysis in continuous time are explained. Each section includes a set of exercises on the respective topics. Various functions and tools for the analysis of discrete survival data are collected in the R package discSurv that accompanies the book.

Applied Categorical and Count Data Analysis

Author: Wan Tang

Publisher: CRC Press

Published: 2023-04-06

Total Pages: 395

ISBN-13: 1000863972

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Developed from the authors’ graduate-level biostatistics course, Applied Categorical and Count Data Analysis, Second Edition explains how to perform the statistical analysis of discrete data, including categorical and count outcomes. The authors have been teaching categorical data analysis courses at the University of Rochester and Tulane University for more than a decade. This book embodies their decade-long experience and insight in teaching and applying statistical models for categorical and count data. The authors describe the basic ideas underlying each concept, model, and approach to give readers a good grasp of the fundamentals of the methodology without relying on rigorous mathematical arguments. The second edition covers classic concepts and popular topics, such as contingency tables, logistic regression models, and Poisson regression models, along with modern areas that include models for zero-modified count outcomes, parametric and semiparametric longitudinal data analysis, reliability analysis, and methods for dealing with missing values. As in the first edition, R, SAS, SPSS, and Stata programming codes are provided for all the examples, enabling readers to immediately experiment with the data in the examples and even adapt or extend the codes to fit data from their own studies. Designed for a one-semester course for graduate and senior undergraduate students in biostatistics, this self-contained text is also suitable as a self-learning guide for biomedical and psychosocial researchers. It will help readers analyze data with discrete variables in a wide range of biomedical and psychosocial research fields. Features: Describes the basic ideas underlying each concept and model Includes R, SAS, SPSS and Stata programming codes for all the examples Features significantly expanded Chapters 4, 5, and 8 (Chapters 4-6, and 9 in the second edition Expands discussion for subtle issues in longitudinal and clustered data analysis such as time varying covariates and comparison of generalized linear mixed-effect models with GEE

An Introduction to Categorical Data Analysis

Author: Alan Agresti

Publisher: John Wiley & Sons

Published: 2018-10-11

Total Pages: 400

ISBN-13: 1119405270

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A valuable new edition of a standard reference The use of statistical methods for categorical data has increased dramatically, particularly for applications in the biomedical and social sciences. An Introduction to Categorical Data Analysis, Third Edition summarizes these methods and shows readers how to use them using software. Readers will find a unified generalized linear models approach that connects logistic regression and loglinear models for discrete data with normal regression for continuous data. Adding to the value in the new edition is: • Illustrations of the use of R software to perform all the analyses in the book • A new chapter on alternative methods for categorical data, including smoothing and regularization methods (such as the lasso), classification methods such as linear discriminant analysis and classification trees, and cluster analysis • New sections in many chapters introducing the Bayesian approach for the methods of that chapter • More than 70 analyses of data sets to illustrate application of the methods, and about 200 exercises, many containing other data sets • An appendix showing how to use SAS, Stata, and SPSS, and an appendix with short solutions to most odd-numbered exercises Written in an applied, nontechnical style, this book illustrates the methods using a wide variety of real data, including medical clinical trials, environmental questions, drug use by teenagers, horseshoe crab mating, basketball shooting, correlates of happiness, and much more. An Introduction to Categorical Data Analysis, Third Edition is an invaluable tool for statisticians and biostatisticians as well as methodologists in the social and behavioral sciences, medicine and public health, marketing, education, and the biological and agricultural sciences.