Request: Logistic Regression Models for Ordinal Response Variables

Ann A. O'Connell

Description: Logistic Regression Models for Ordinal Response Variables provides applied researchers in the social, educational, and behavioral sciences with an accessible and comprehensive coverage of analyses for ordinal outcomes. The content builds on a review of logistic regression, and extends to details of the cumulative (proportional) odds, continuation ratio, and adjacent category models for ordinal data. Description and examples of partial proportional odds models are also provided. This book is highly readable, with lots of examples and in-depth explanations and interpretations of model characteristics. SPSS and SAS are used for all examples; data and syntax are available from the author's website. The examples are drawn from an educational context, but applications to other fields of inquiry are noted, such as HIV prevention, behavior change, counseling psychology, social psychology, etc.). The level of the book is set for applied researchers who need to quickly understand the use and application of these kinds of ordinal regression models.

Annette J. Dobson University

• Provides an accessible but thorough introduction to the most up-to-date, commonly used statistical methods
• Emphasizes graphical methods for exploratory data analysis, visualizing numerical optimization, and plotting residuals
• Assumes a working knowledge of basic statistical concepts and methods and an acquaintance with calculus and matrix algebra
• Includes numerous examples from a wider range of application areas, including business, medicine, agriculture, biology, engineering, and the social sciences

Generalized linear models provide a unified theoretical and conceptual framework for many of the most commonly used statistical methods. In the ten years since publication of the first edition of this bestselling text, great strides have been made in the development of new methods and in software for generalized linear models and other closely related models.

Thoroughly revised and updated, An Introduction to Generalized Linear Models, Second Edition continues to initiate intermediate students of statistics, and the many other disciplines that use statistics, in the practical use of these models and methods. The new edition incorporates many of the important developments of the last decade, including survival analysis, nominal and ordinal logistic regression, generalized estimating equations, and multi-level models. It also includes modern methods for checking model adequacy and examples from an even wider range of application.

Statistics can appear to the uninitiated as a collection of unrelated tools. An Introduction to Generalized Linear Models, Second Edition illustrates how these apparently disparate methods are examples or special cases of a conceptually simple structure based on the exponential family of distribution, maximum likelihood estimation, and the principles of statistical modelling.

Contents

• Background
• Scope
• Notation
• Distributions Related to the Normal Distribution
• Quadratic Forms
• Estimation
• Exercises

• Introduction
• Examples
• Some Principles of Statistical Modelling
• Notation and Coding for Explanatory Variables
• Exercises

• Introduction
• Exponential Family of Distributions
• Properties of Distributions in the Exponential Family
• Generalized Linear Models
• Examples
• Exercises

• Introduction
• Example: Failure Times for Pressure Vessels
• Maximum Likelihood Estimation
• Poisson Regression Example
• Exercises

• Introduction
• Sampling Distribution for Score Statistics
• Taylor Series Approximations
• Sampling Distribution for Maximum Likelihood Estimators
• Log-Likelihood Ratio Statistic
• Sampling Distribution for the Deviance
• Hypothesis Testing
• Exercises

• Introduction
• Basic Results
• Multiple Linear Regression
• Analysis of Variance
• Analysis of Covariance
• General Linear Models
• Exercises

• Probability Distributions
• Generalized Linear Models
• Dose Response Models
• General Logistic Regression Model
• Goodness of Fit Statistics
• Residuals
• Other Diagnostics
• Example: Senility and WAIS
• Exercises

• Introduction
• Multinominal Distribution
• Nominal Logistic Regression
• Ordinal Logistic Regression
• General Comments
• Exercises

• Introduction
• Poisson Regression
• Examples of Contingency Tables
• Probability Models for Contingency Tables
• Log-Linear Models
• Inference for Log-Linear Models
• Numerical Examples
• Remarks
• Exercises

• Introduction
• Survivor Functions and Hazard Functions
• Empirical Survivor Function
• Estimation
• Inference
• Model checking
• Example: Remission Times
• Exercises

• Introduction
• Example: Recovery from Stroke
• Repeated Measures Models for Normal Data
• Repeated Measures Models for NON-NORMAL DATA
• Multilevel Models
• Stroke Example Continued
• Comments
• Exercises

David G. Kleinbaum Emory University Mitchel Klein Emory University

This is the second edition of this text on logistic regression methods. As in the first edition, each chapter contains a presentation of its topic in "lecture-book" format together with objectives, an outline, key formulae, practice exercises, and a test. The "lecture-book" has a sequence of illustrations and formulae in the left column of each page and a script (i.e., text) in the right column. This format allows you to read the script in conjunction with the illustrations and formulae that highlight the main points, formulae, or examples being presented.

This second edition includes five new chapters and an appendix. The new chapters are:

Chapters 9 and 10 extend logistic regression to response variables that have more than two categories. Chapters 11-13 extend logistic regression to generalized estimating equations (GEE) and other methods for analyzing correlated response data.

The appendix "Computer Programs for Logistic Regression" provides descriptions and examples of computer programs for carrying out the variety of logistic regression procedures described in the main text. The software packages considered are SAS Version 8.0, SPSS Version 10.0 and STATA Version 7.0.

Written for: Graduate students, researchers

Contents

• Introduction to Logistic Regression
• Important Special Cases of the Logistical Model
• Computing the Odds Ration in Logistic Regression
• Maximum Likelihood Techniques: An Overview
• Statistical Inference Using Maximum Likelihood Techniques
• Modeling Strategy Guidelines
• Modeling Strategy for Assessing Interaction and Confounding
• Analysis of Matched Data Using Logistic Regression
• Polytomous Logistic Regression
• Ordinal Logistic Regression
• Logistic Regression for Correlated Data
• GEE Examples
• Other Approaches for Analysis of Correlated Data

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