Logistic Regression Using SAS

Theory and Application, Second Edition

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Author: Paul D. Allison

Publisher: SAS Institute

ISBN: 1607649950

Category: Mathematics

Page: 348

View: 452

If you are a researcher or student with experience in multiple linear regression and want to learn about logistic regression, Paul Allison's Logistic Regression Using SAS: Theory and Application, Second Edition, is for you! Informal and nontechnical, this book both explains the theory behind logistic regression, and looks at all the practical details involved in its implementation using SAS. Several real-world examples are included in full detail. This book also explains the differences and similarities among the many generalizations of the logistic regression model. The following topics are covered: binary logistic regression, logit analysis of contingency tables, multinomial logit analysis, ordered logit analysis, discrete-choice analysis, and Poisson regression. Other highlights include discussions on how to use the GENMOD procedure to do loglinear analysis and GEE estimation for longitudinal binary data. Only basic knowledge of the SAS DATA step is assumed. The second edition describes many new features of PROC LOGISTIC, including conditional logistic regression, exact logistic regression, generalized logit models, ROC curves, the ODDSRATIO statement (for analyzing interactions), and the EFFECTPLOT statement (for graphing nonlinear effects). Also new is coverage of PROC SURVEYLOGISTIC (for complex samples), PROC GLIMMIX (for generalized linear mixed models), PROC QLIM (for selection models and heterogeneous logit models), and PROC MDC (for advanced discrete choice models). This book is part of the SAS Press program.

Categorical Data Analysis Using SAS, Third Edition

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Author: Maura E. Stokes,Charles S. Davis,Gary G. Koch

Publisher: SAS Institute

ISBN: 1612900909

Category: Mathematics

Page: 590

View: 8850

Statisticians and researchers will find Categorical Data Analysis Using SAS, Third Edition, by Maura Stokes, Charles Davis, and Gary Koch, to be a useful discussion of categorical data analysis techniques as well as an invaluable aid in applying these methods with SAS. Practical examples from a broad range of applications illustrate the use of the FREQ, LOGISTIC, GENMOD, NPAR1WAY, and CATMOD procedures in a variety of analyses. Topics discussed include assessing association in contingency tables and sets of tables, logistic regression and conditional logistic regression, weighted least squares modeling, repeated measurements analyses, loglinear models, generalized estimating equations, and bioassay analysis. The third edition updates the use of SAS/STAT software to SAS/STAT 12.1 and incorporates ODS Graphics. Many additional SAS statements and options are employed, and graphs such as effect plots, odds ratio plots, regression diagnostic plots, and agreement plots are discussed. The material has also been revised and reorganized to reflect the evolution of categorical data analysis strategies. Additional techniques include such topics as exact Poisson regression, partial proportional odds models, Newcombe confidence intervals, incidence density ratios, and so on. This book is part of the SAS Press program.

Survival Analysis Using SAS

A Practical Guide, Second Edition

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Author: Paul D. Allison

Publisher: SAS Institute

ISBN: 9781599948843

Category: Mathematics

Page: 336

View: 8871

Easy to read and comprehensive, Survival Analysis Using SAS: A Practical Guide, Second Edition, by Paul D. Allison, is an accessible, data-based introduction to methods of survival analysis. Researchers who want to analyze survival data with SAS will find just what they need with this fully updated new edition that incorporates the many enhancements in SAS procedures for survival analysis in SAS 9. Although the book assumes only a minimal knowledge of SAS, more experienced users will learn new techniques of data input and manipulation. Numerous examples of SAS code and output make this an eminently practical book, ensuring that even the uninitiated become sophisticated users of survival analysis. The main topics presented include censoring, survival curves, Kaplan-Meier estimation, accelerated failure time models, Cox regression models, and discrete-time analysis. Also included are topics not usually covered in survival analysis books, such as time-dependent covariates, competing risks, and repeated events. Survival Analysis Using SAS: A Practical Guide, Second Edition, has been thoroughly updated for SAS 9, and all figures are presented using ODS Graphics. This new edition also documents major enhancements to the STRATA statement in the LIFETEST procedure; includes a section on the PROBPLOT command, which offers graphical methods to evaluate the fit of each parametric regression model; introduces the new BAYES statement for both parametric and Cox models, which allows the user to do a Bayesian analysis using MCMC methods; demonstrates the use of the counting process syntax as an alternative method for handling time-dependent covariates; contains a section on cumulative incidence functions; and describes the use of the new GLIMMIX procedure to estimate random-effects models for discrete-time data. This book is part of the SAS Press program.

Predictive Modeling with SAS Enterprise Miner

Practical Solutions for Business Applications, Second Edition

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Author: Kattamuri S. Sarma, PhD

Publisher: SAS Institute

ISBN: 1607648180

Category: Mathematics

Page: 500

View: 5419

Learn the theory behind and methods for predictive modeling using SAS Enterprise Miner. Learn how to produce predictive models and prepare presentation-quality graphics in record time with Predictive Modeling with SAS Enterprise Miner: Practical Solutions for Business Applications, Second Edition. If you are a graduate student, researcher, or statistician interested in predictive modeling; a data mining expert who wants to learn SAS Enterprise Miner; or a business analyst looking for an introduction to predictive modeling using SAS Enterprise Miner, you'll be able to develop predictive models quickly and effectively using the theory and examples presented in this book. Author Kattamuri Sarma offers the theory behind, programming steps for, and examples of predictive modeling with SAS Enterprise Miner, along with exercises at the end of each chapter. You'll gain a comprehensive awareness of how to find solutions for your business needs. This second edition features expanded coverage of the SAS Enterprise Miner nodes, now including File Import, Time Series, Variable Clustering, Cluster, Interactive Binning, Principal Components, AutoNeural, DMNeural, Dmine Regression, Gradient Boosting, Ensemble, and Text Mining. Develop predictive models quickly, learn how to test numerous models and compare the results, gain an in-depth understanding of predictive models and multivariate methods, and discover how to do in-depth analysis. Do it all with Predictive Modeling with SAS Enterprise Miner. This book is part of the SAS Press program.

Fixed Effects Regression Methods for Longitudinal Data Using SAS

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Author: Paul D. Allison

Publisher: SAS Institute

ISBN: 9781590477786

Category: Mathematics

Page: 160

View: 7505

Fixed Effects Regression Methods for Longitudinal Data Using SAS, written by Paul Allison, is an invaluable resource for all researchers interested in adding fixed effects regression methods to their tool kit of statistical techniques. First introduced by economists, fixed effects methods are gaining widespread use throughout the social sciences. Designed to eliminate major biases from regression models with multiple observations (usually longitudinal) for each subject (usually a person), fixed effects methods essentially offer control for all stable characteristics of the subjects, even characteristics that are difficult or impossible to measure. This straightforward and thorough text shows you how to estimate fixed effects models with several SAS procedures that are appropriate for different kinds of outcome variables. The theoretical background of each model is explained, and the models are then illustrated with detailed examples using real data. The book contains thorough discussions of the following uses of SAS procedures: PROC GLM for estimating fixed effects linear models for quantitative outcomes, PROC LOGISTIC for estimating fixed effects logistic regression models, PROC PHREG for estimating fixed effects Cox regression models for repeated event data, PROC GENMOD for estimating fixed effects Poisson regression models for count data, and PROC CALIS for estimating fixed effects structural equation models. To gain the most benefit from this book, readers should be familiar with multiple linear regression, have practical experience using multiple regression on real data, and be comfortable interpreting the output from a regression analysis. An understanding of logistic regression and Poisson regression is a plus. Some experience with SAS is helpful, but not required. This book is part of the SAS Press program.

Segmentation and Lifetime Value Models Using SAS

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Author: Edward C. Malthouse

Publisher: SAS Institute

ISBN: 1612907067

Category: Mathematics

Page: 182

View: 3709

Help your organization determine the value of its customer relationships with Segmentation and Lifetime Value Models Using SAS. This book contains a wealth of information that will help you perform analyses to identify your customers and make informed marketing investments. It answers core questions on customer relationship management (CRM), provides an overall framework for thinking about CRM, and offers real-world examples across a variety of industries. Edward C. Malthouse introduces you to a number of useful models, ranging from simple to more complicated examples, and discusses their applications. You'll learn about segmentation models for identifying groups of customers and about lifetime value models for estimating the future value of the segments. You'll learn how to prepare data and estimate models using Base SAS, SAS/STAT, SAS/IML, and SQL. Marketing analysts, CRM analysts, database managers, and anyone looking to address the challenges of allocating marketing resources to different customer groups will benefit from the concepts and exercises in this book. Analysts will learn how to approach unique business problems. Managers will gain a sense of what's possible and what to ask of their analytics departments. This book is part of the SAS Press program.

Practical Time Series Analysis Using SAS

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Author: Anders Milhoj

Publisher: SAS Institute

ISBN: 1612901700

Category: Computers

Page: 204

View: 7996

Anders Milhøj's Practical Time Series Analysis Using SAS explains and demonstrates through examples how you can use SAS for time series analysis. It offers modern procedures for forecasting, seasonal adjustments, and decomposition of time series that can be used without involved statistical reasoning. The book teaches, with numerous examples, how to apply these procedures with very simple coding. In addition, it also gives the statistical background for interested readers. Beginning with an introductory chapter that covers the practical handling of time series data in SAS using the TIMESERIES and EXPAND procedures, it goes on to explain forecasting, which is found in the ESM procedure; seasonal adjustment, including trading-day correction using PROC X12; and unobserved component models using the UCM procedure.SAS Products and Releases: Base SAS: 9.3 SAS/STAT: 9.3 Operating Systems: Windows

Regression Analysis by Example

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Author: Samprit Chatterjee,Ali S. Hadi

Publisher: John Wiley & Sons

ISBN: 0470055456

Category: Mathematics

Page: 416

View: 6922

The essentials of regression analysis through practical applications Regression analysis is a conceptually simple method for investigating relationships among variables. Carrying out a successful application of regression analysis, however, requires a balance of theoretical results, empirical rules, and subjective judgement. Regression Analysis by Example, Fourth Edition has been expanded and thoroughly updated to reflect recent advances in the field. The emphasis continues to be on exploratory data analysis rather than statistical theory. The book offers in-depth treatment of regression diagnostics, transformation, multicollinearity, logistic regression, and robust regression. This new edition features the following enhancements: Chapter 12, Logistic Regression, is expanded to reflect the increased use of the logit models in statistical analysis A new chapter entitled Further Topics discusses advanced areas of regression analysis Reorganized, expanded, and upgraded exercises appear at the end of each chapter A fully integrated Web page provides data sets Numerous graphical displays highlight the significance of visual appeal Regression Analysis by Example, Fourth Edition is suitable for anyone with an understanding of elementary statistics. Methods of regression analysis are clearly demonstrated, and examples containing the types of irregularities commonly encountered in the real world are provided. Each example isolates one or two techniques and features detailed discussions of the techniques themselves, the required assumptions, and the evaluated success of each technique. The methods described throughout the book can be carried out with most of the currently available statistical software packages, such as the software package R. An Instructor's Manual presenting detailed solutions to all the problems in the book is available from the Wiley editorial department.

Categorical Data Analysis Using the SAS System

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Author: Maura E. Stokes,Charles S. Davis,Gary G. Koch

Publisher: Wiley-SAS

ISBN: 9780471224242

Category: Mathematics

Page: 648

View: 6376

Along with providing a useful discussion of categorical data analysis techniques, this book shows how to apply these methods with the SAS System. The authors include practical examples from a broad range of applications to illustrate the use of the FREQ, LOGISTIC, GENMOD, and CATMOD procedures in a variety of analyses. They also discuss other procedures such as PHREG and NPAR1WAY.

Analyzing Receiver Operating Characteristic Curves with SAS

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Author: Mithat Gonen

Publisher: SAS Institute

ISBN: 1629597961

Category: Mathematics

Page: 148

View: 1090

As a diagnostic decision-making tool, receiver operating characteristic (ROC) curves provide a comprehensive and visually attractive way to summarize the accuracy of predictions. They are used extensively in medical diagnosis and increasingly in fields such as data mining, credit scoring, weather forecasting, and psychometry. In Analyzing Receiver Operating Characteristic Curves with SAS, author Mithat Gonen illustrates the many existing SAS procedures that can be tailored to produce ROC curves and expands upon further analyses using other SAS procedures and macros. Both parametric and nonparametric methods for analyzing ROC curves are covered in detail. Topics addressed include: Appropriate methods for binary, ordinal, and continuous measures Computations using PROC FREQ, PROC LOGISTIC, PROC NLMIXED, and macros Comparing the ROC curves of several markers and adjusting them for covariates ROC curves with censored data Using the ROC curve for evaluating multivariable prediction models via bootstrap and cross-validation ROC curves in SAS Enterprise Miner And more! Written for any statistician interested in learning more about ROC curve methodology, the book assumes readers have a basic understanding of regression procedures and moderate familiarity with Base SAS and SAS/STAT. Some familiarity with SAS/GRAPH is helpful but not essential. This book is part of the SAS Press program.

The Economic Organization of the Household

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Author: W. Keith Bryant,Cathleen D. Zick

Publisher: Cambridge University Press

ISBN: 9781139447355

Category: Business & Economics

Page: N.A

View: 1503

Surveying the field of the economics of the household, the second edition of this text reviews the theory of the consumer at the intermediate undergraduate level. It then applies and extends it to consumer demand and expenditures, consumption and saving, time allocation among market work, home work, and leisure, human capital emphasizing investment in education, children and health, fertility, marriage, and divorce. Influenced by Gary Becker and his associates, the models developed are used to help explain modern U.S. trends in family behavior. Topics are discussed with the aid of geometry and a little algebra. For those with calculus, mathematical endnotes provide the models on which the text discussions are based and interesting applications beyond the scope of the text.

Business Survival Analysis Using SAS

An Introduction to Lifetime Probabilities

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Author: Jorge Ribeiro

Publisher: SAS Institute

ISBN: 1629605190

Category: Computers

Page: 236

View: 5823

Solve business problems involving time-to-event and resulting probabilities by following the modeling tutorials in Business Survival Analysis Using SAS®: An Introduction to Lifetime Probabilities, the first book to be published in the field of business survival analysis! Survival analysis is a challenge. Books applying to health sciences exist, but nothing about survival applications for business has been available until now. Written for analysts, forecasters, econometricians, and modelers who work in marketing or credit risk and have little SAS modeling experience, Business Survival Analysis Using SAS® builds on a foundation of SAS code that works in any survival model and features numerous annotated graphs, coefficients, and statistics linked to real business situations and data sets. This guide also helps recent graduates who know the statistics but do not necessarily know how to apply them get up and running in their jobs. By example, it teaches the techniques while avoiding advanced theoretical underpinnings so that busy professionals can rapidly deliver a survival model to meet common business needs. From first principles, this book teaches survival analysis by highlighting its relevance to business cases. A pragmatic introduction to survival analysis models, it leads you through business examples that contextualize and motivate the statistical methods and SAS coding. Specifically, it illustrates how to build a time-to-next-purchase survival model in SAS® Enterprise Miner, and it relates each step to the underlying statistics and to Base SAS® and SAS/STAT® software. Following the many examples—from data preparation to validation to scoring new customers—you will learn to develop and apply survival analysis techniques to scenarios faced by companies in the financial services, insurance, telecommunication, and marketing industries, including the following scenarios: Time-to-next-purchase for marketing Employer turnover for human resources Small business portfolio macroeconometric stress tests for banks International Financial Reporting Standard (IFRS 9) lifetime probability of default for banks and building societies "Churn," or attrition, models for the telecommunications and insurance industries

SAS Statistics by Example

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Author: Ron Cody, EdD

Publisher: SAS Institute

ISBN: 1612900127

Category: Computers

Page: 274

View: 9806

In SAS Statistics by Example, Ron Cody offers up a cookbook approach for doing statistics with SAS. Structured specifically around the most commonly used statistical tasks or techniques--for example, comparing two means, ANOVA, and regression--this book provides an easy-to-follow, how-to approach to statistical analysis not found in other books. For each statistical task, Cody includes heavily annotated examples using ODS Statistical Graphics procedures such as SGPLOT, SGSCATTER, and SGPANEL that show how SAS can produce the required statistics. Also, you will learn how to test the assumptions for all relevant statistical tests. Major topics featured include descriptive statistics, one- and two-sample tests, ANOVA, correlation, linear and multiple regression, analysis of categorical data, logistic regression, nonparametric techniques, and power and sample size. This is not a book that teaches statistics. Rather, SAS Statistics by Example is perfect for intermediate to advanced statistical programmers who know their statistics and want to use SAS to do their analyses. This book is part of the SAS Press program.

SAS for Mixed Models, Second Edition

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Author: Ramon C. Littell, Ph.D.,Walter W. Stroup, Ph.D.,George A. Milliken, Ph.D.,Russell D. Wolfinger, Ph.D.,Oliver Schabenberger, Ph.D.

Publisher: SAS Institute

ISBN: 9781599940786

Category: Mathematics

Page: 828

View: 4376

The indispensable, up-to-date guide to mixed models using SAS. Discover the latest capabilities available for a variety of applications featuring the MIXED, GLIMMIX, and NLMIXED procedures in SAS for Mixed Models, Second Edition, the comprehensive mixed models guide for data analysis, completely revised and updated for SAS 9 by authors Ramon Littell, George Milliken, Walter Stroup, Russell Wolfinger, and Oliver Schabenberger. The theory underlying the models, the forms of the models for various applications, and a wealth of examples from different fields of study are integrated in the discussions of these models: random effect only and random coefficients models; split-plot, multilocation, and repeated measures models; hierarchical models with nested random effects; analysis of covariance models; spatial correlation models; generalized linear mixed models; and nonlinear mixed models. Professionals and students with a background in two-way ANOVA and regression and a basic knowledge of linear models and matrix algebra will benefit from the topics covered. This book is part of the SAS Press program.

Statistical Graphics Procedures by Example

Effective Graphs Using SAS

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Author: Sanjay Matange,Dan Heath

Publisher: SAS Institute

ISBN: 1607648873

Category: MATHEMATICS

Page: 370

View: 5627

Sanjay Matange and Dan Heath's "Statistical Graphics Procedures by Example: Effective Graphs Using SAS" shows the innumerable capabilities of SAS Statistical Graphics (SG) procedures. The authors begin with a general discussion of the principles of effective graphics, ODS Graphics, and the SG procedures. They then move on to show examples of the procedures' many features. The book is designed so that you can easily flip through it, find the graph you need, and view the code right next to the example. Among the topics included are how to combine plot statements to create custom graphs; customizing graph axes, legends, and insets; advanced features, such as annotation and attribute maps; tips and tricks for creating the optimal graph for the intended usage; real-world examples from the health and life sciences domain; and ODS styles. The procedures in "Statistical Graphics Procedures by Example" are specifically designed for the creation of analytical graphs. That makes this book a must-read for analysts and statisticians in the health care, clinical trials, financial, and insurance industries. However, you will find that the examples here apply to all fields.

Fundamentals of Predictive Analytics with JMP, Second Edition

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Author: Ron Klimberg,B. D. McCullough

Publisher: SAS Institute

ISBN: 1629608017

Category: Computers

Page: 406

View: 6722

Written for students in undergraduate and graduate statistics courses, as well as for the practitioner who wants to make better decisions from data and models, this updated and expanded second edition of Fundamentals of Predictive Analytics with JMP(R) bridges the gap between courses on basic statistics, which focus on univariate and bivariate analysis, and courses on data mining and predictive analytics. Going beyond the theoretical foundation, this book gives you the technical knowledge and problem-solving skills that you need to perform real-world multivariate data analysis. First, this book teaches you to recognize when it is appropriate to use a tool, what variables and data are required, and what the results might be. Second, it teaches you how to interpret the results and then, step-by-step, how and where to perform and evaluate the analysis in JMP . Using JMP 13 and JMP 13 Pro, this book offers the following new and enhanced features in an example-driven format: an add-in for Microsoft Excel Graph Builder dirty data visualization regression ANOVA logistic regression principal component analysis LASSO elastic net cluster analysis decision trees k-nearest neighbors neural networks bootstrap forests boosted trees text mining association rules model comparison With today’s emphasis on business intelligence, business analytics, and predictive analytics, this second edition is invaluable to anyone who needs to expand his or her knowledge of statistics and to apply real-world, problem-solving analysis. This book is part of the SAS Press program.

Text Mining and Analysis

Practical Methods, Examples, and Case Studies Using SAS

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Author: Dr. Goutam Chakraborty,Murali Pagolu,Satish Garla

Publisher: SAS Institute

ISBN: 1612907873

Category: Mathematics

Page: 340

View: 7097

Big data: It's unstructured, it's coming at you fast, and there's lots of it. In fact, the majority of big data is text-oriented, thanks to the proliferation of online sources such as blogs, emails, and social media. However, having big data means little if you can't leverage it with analytics. Now you can explore the large volumes of unstructured text data that your organization has collected with Text Mining and Analysis: Practical Methods, Examples, and Case Studies Using SAS. This hands-on guide to text analytics using SAS provides detailed, step-by-step instructions and explanations on how to mine your text data for valuable insight. Through its comprehensive approach, you'll learn not just how to analyze your data, but how to collect, cleanse, organize, categorize, explore, and interpret it as well. Text Mining and Analysis also features an extensive set of case studies, so you can see examples of how the applications work with real-world data from a variety of industries. Text analytics enables you to gain insights about your customers' behaviors and sentiments. Leverage your organization's text data, and use those insights for making better business decisions with Text Mining and Analysis. This book is part of the SAS Press program.

SAS and R

Data Management, Statistical Analysis, and Graphics, Second Edition

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Author: Ken Kleinman,Nicholas J. Horton

Publisher: CRC Press

ISBN: 1466584491

Category: Mathematics

Page: 468

View: 8735

An Up-to-Date, All-in-One Resource for Using SAS and R to Perform Frequent Tasks The first edition of this popular guide provided a path between SAS and R using an easy-to-understand, dictionary-like approach. Retaining the same accessible format, SAS and R: Data Management, Statistical Analysis, and Graphics, Second Edition explains how to easily perform an analytical task in both SAS and R, without having to navigate through the extensive, idiosyncratic, and sometimes unwieldy software documentation. The book covers many common tasks, such as data management, descriptive summaries, inferential procedures, regression analysis, and graphics, along with more complex applications. New to the Second Edition This edition now covers RStudio, a powerful and easy-to-use interface for R. It incorporates a number of additional topics, including using application program interfaces (APIs), accessing data through database management systems, using reproducible analysis tools, and statistical analysis with Markov chain Monte Carlo (MCMC) methods and finite mixture models. It also includes extended examples of simulations and many new examples. Enables Easy Mobility between the Two Systems Through the extensive indexing and cross-referencing, users can directly find and implement the material they need. SAS users can look up tasks in the SAS index and then find the associated R code while R users can benefit from the R index in a similar manner. Numerous example analyses demonstrate the code in action and facilitate further exploration. The datasets and code are available for download on the book’s website.

Regression Modeling Strategies

With Applications to Linear Models, Logistic and Ordinal Regression, and Survival Analysis

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Author: Frank Harrell

Publisher: Springer

ISBN: 3319194259

Category: Mathematics

Page: 582

View: 6642

This highly anticipated second edition features new chapters and sections, 225 new references, and comprehensive R software. In keeping with the previous edition, this book is about the art and science of data analysis and predictive modeling, which entails choosing and using multiple tools. Instead of presenting isolated techniques, this text emphasizes problem solving strategies that address the many issues arising when developing multivariable models using real data and not standard textbook examples. It includes imputation methods for dealing with missing data effectively, methods for fitting nonlinear relationships and for making the estimation of transformations a formal part of the modeling process, methods for dealing with "too many variables to analyze and not enough observations," and powerful model validation techniques based on the bootstrap. The reader will gain a keen understanding of predictive accuracy and the harm of categorizing continuous predictors or outcomes. This text realistically deals with model uncertainty and its effects on inference, to achieve "safe data mining." It also presents many graphical methods for communicating complex regression models to non-statisticians. Regression Modeling Strategies presents full-scale case studies of non-trivial datasets instead of over-simplified illustrations of each method. These case studies use freely available R functions that make the multiple imputation, model building, validation and interpretation tasks described in the book relatively easy to do. Most of the methods in this text apply to all regression models, but special emphasis is given to multiple regression using generalized least squares for longitudinal data, the binary logistic model, models for ordinal responses, parametric survival regression models and the Cox semi parametric survival model. A new emphasis is given to the robust analysis of continuous dependent variables using ordinal regression. As in the first edition, this text is intended for Masters' or Ph.D. level graduate students who have had a general introductory probability and statistics course and who are well versed in ordinary multiple regression and intermediate algebra. The book will also serve as a reference for data analysts and statistical methodologists, as it contains an up-to-date survey and bibliography of modern statistical modeling techniques. Examples used in the text mostly come from biomedical research, but the methods are applicable anywhere predictive models ("analytics") are useful, including economics, epidemiology, sociology, psychology, engineering and marketing.