The Statistical Analysis of Discrete Data

The Statistical Analysis of Discrete Data
Author: Thomas J. Santner
Publisher: Springer Science & Business Media
Total Pages: 381
Release: 2012-12-06
Genre: Business & Economics
ISBN: 1461210178

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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

Discrete Data Analysis with R
Author: Michael Friendly
Publisher: CRC Press
Total Pages: 700
Release: 2015-12-16
Genre: Mathematics
ISBN: 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

Exact Analysis of Discrete Data
Author: Karim F. Hirji
Publisher: CRC Press
Total Pages: 1066
Release: 2005-11-18
Genre: Mathematics
ISBN: 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

Goodness-of-Fit Statistics for Discrete Multivariate Data

Goodness-of-Fit Statistics for Discrete Multivariate Data
Author: Timothy R.C. Read
Publisher: Springer Science & Business Media
Total Pages: 221
Release: 2012-12-06
Genre: Mathematics
ISBN: 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.

Statistical Analysis and Data Display

Statistical Analysis and Data Display
Author: Richard M. Heiberger
Publisher: Springer Science & Business Media
Total Pages: 739
Release: 2013-06-29
Genre: Mathematics
ISBN: 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.

Structural Analysis of Discrete Data with Econometric Applications

Structural Analysis of Discrete Data with Econometric Applications
Author: Charles F. Manski
Publisher: MIT Press (MA)
Total Pages: 512
Release: 1981
Genre: Business & Economics
ISBN:

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The thirteen papers in "Structural Analysis of Discrete Data" are previously unpublished major research contributions solicited by the editors. They have been specifically prepared to fulfill the two-fold purpose of the volume, first to provide the econometrics student with an overview of the present extent of the subject and to delineate the boundaries of current research, both in terms of methodology and applications. "Coordinated publication of important findings" should, as the editors state, "lower the cost of entry into the field and speed dissemination of recent research into the graduate econometrics classroom."A second purpose of the volume is to communicate results largely reported in the econometrics literature to a wider community of researchers to whom they are directly relevant, including applied econometricians, statisticians in the area of discrete multivariate analysis, specialists in biometrics, psychometrics, and sociometrics, and analysts in various applied fields such as finance, marketing, and transportation.The papers are grouped into four sections: "Statistical Analysis of Discrete Probability Models, " with papers by the editors and by Steven Cosslett; "Dynamic Discrete Probability Models, " consisting of two contributions by James Heckman; "Structural Discrete Probability Models Derived from Theories of Choice, " with papers by Daniel McFadden, Gregory Fischer and Daniel Nagin, Steven Lerman and Charles Manski, and Moshe Ben-Akiva and Thawat Watanatada; and "Simultaneous Systems Models with Discrete Endogenous Variables, " with contributions by Lung-Fei Lee, Jerry Hausman and David Wise, Dale Poirier, Peter Schmidt, and Robert Avery.Among the applications treated are income maintenance experiments, physician behavior, consumer credit, and intra-urban location and transportation.

Models for Discrete Data

Models for Discrete Data
Author: Daniel Zelterman
Publisher: Oxford University Press
Total Pages: 233
Release: 1999
Genre: Art
ISBN: 9780198524366

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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 book describes the statistical models used in the analysis and summary of such data, and provides an introduction to the subject for graduate students and practitioners needing a review of the methodology. It includes topics not covered in depth elsewhere, such as the negative multinomial distribution; the many forms of the hypergeometric distribution; and coordinate free models.

Modeling Discrete Time-to-Event Data

Modeling Discrete Time-to-Event Data
Author: Gerhard Tutz
Publisher: Springer
Total Pages: 252
Release: 2016-06-14
Genre: Mathematics
ISBN: 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.

An Introduction to Categorical Data Analysis

An Introduction to Categorical Data Analysis
Author: Alan Agresti
Publisher: John Wiley & Sons
Total Pages: 400
Release: 2018-10-11
Genre: Mathematics
ISBN: 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.

Confidence Intervals for Discrete Data in Clinical Research

Confidence Intervals for Discrete Data in Clinical Research
Author: Vivek Pradhan
Publisher: CRC Press
Total Pages: 240
Release: 2021-11-15
Genre: Mathematics
ISBN: 1351690175

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Confidence Intervals for Discrete Data in Clinical Research is designed as a toolbox for biomedical researchers. Analysis of discrete data is one of the most used yet vexing areas in clinical research. The array of methodologies available in the literature to address the inferential questions for binomial and multinomial data can be a double-edged sword. On the one hand, these methods open a rich avenue of exploration of data; on the other, the wide-ranging and competing methodologies potentially lead to conflicting inferences, adding to researchers' confusion and frustration and also leading to reporting bias. This book addresses the problems that many practitioners experience in choosing and implementing fit for purpose data analysis methods to answer critical inferential questions for binomial and count data. The book is an outgrowth of the authors' collective experience in biomedical research and provides an excellent overview of inferential questions of interest for binomial proportions and rates based on count data, and reviews various solutions to these problems available in the literature. Each chapter discusses the strengths and weaknesses of the methods and suggests practical recommendations. The book's primary focus is on applications in clinical research, and the goal is to provide direct benefit to the users involved in the biomedical field.