Logistic Regression Models: 1st Edition (Paperback) book cover

Logistic Regression Models

1st Edition

By Joseph M. Hilbe

Chapman and Hall/CRC

656 pages | 25 B/W Illus.

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Logistic Regression Models presents an overview of the full range of logistic models, including binary, proportional, ordered, partially ordered, and unordered categorical response regression procedures. Other topics discussed include panel, survey, skewed, penalized, and exact logistic models. The text illustrates how to apply the various models to health, environmental, physical, and social science data.

Examples illustrate successful modeling

The text first provides basic terminology and concepts, before explaining the foremost methods of estimation (maximum likelihood and IRLS) appropriate for logistic models. It then presents an in-depth discussion of related terminology and examines logistic regression model development and interpretation of the results. After focusing on the construction and interpretation of various interactions, the author evaluates assumptions and goodness-of-fit tests that can be used for model assessment. He also covers binomial logistic regression, varieties of overdispersion, and a number of extensions to the basic binary and binomial logistic model. Both real and simulated data are used to explain and test the concepts involved. The appendices give an overview of marginal effects and discrete change as well as a 30-page tutorial on using Stata commands related to the examples used in the text. Stata is used for most examples while R is provided at the end of the chapters to replicate examples in the text.

Apply the models to your own data

Data files for examples and questions used in the text as well as code for user-authored commands are provided on the book’s website, formatted in Stata, R, Excel, SAS, SPSS, and Limdep.

See Professor Hilbe discuss the book.


This book really does cover everything you ever wanted to know about logistic regression … with updates available on the author’s website. Hilbe, a former national athletics champion, philosopher, and expert in astronomy, is a master at explaining statistical concepts and methods. Readers familiar with his other expository work will know what to expect—great clarity.

The book provides considerable detail about all facets of logistic regression. No step of an argument is omitted so that the book will meet the needs of the reader who likes to see everything spelt out, while a person familiar with some of the topics has the option to skip "obvious" sections. The material has been thoroughly road-tested through classroom and web-based teaching. …

The focus is on helping the reader to learn and understand logistic regression. The audience is not just students meeting the topic for the first time, but also experienced users. I believe the book really does meet the author’s goal … .

—Annette J. Dobson, Biometrics, June 2012

Overall this is a comprehensive book, which will provide a very useful resource and handbook for anyone whose work involves modelling binary data.

—David J. Hand, International Statistical Review (2011), 79

… useful as a textbook in a course on logistic regression.

—Andreas Rosenblad, Technometrics, May 2011

Table of Contents



The Normal Model

Foundation of the Binomial Model

Historical and Software Considerations

Chapter Profiles

Concepts Related to the Logistic Model

2 × 2 Table Logistic Model

2 × k Table Logistic Model

Modeling a Quantitative Predictor

Logistic Modeling Designs

Estimation Methods

Derivation of the IRLS Algorithm

IRLS Estimation

Maximum Likelihood Estimation

Derivation of the Binary Logistic Algorithm

Terms of the Algorithm

Logistic GLM and ML Algorithms

Other Bernoulli Models

Model Development

Building a Logistic Model

Assessing Model Fit: Link Specification

Standardized Coefficients

Standard Errors

Odds Ratios as Approximations of Risk Ratios

Scaling of Standard Errors

Robust Variance Estimators

Bootstrapped and Jackknifed Standard Errors

Stepwise Methods

Handling Missing Values

Modeling an Uncertain Response

Constraining Coefficients



Binary X Binary Interactions

Binary X Categorical Interactions

Binary X Continuous Interactions

Categorical X Continuous Interaction

Thoughts about Interactions

Analysis of Model Fit

Traditional Fit Tests for Logistic Regression

Hosmer–Lemeshow GOF Test

Information Criteria Tests

Residual Analysis

Validation Models

Binomial Logistic Regression



The Nature and Scope of Overdispersion

Binomial Overdispersion

Binary Overdispersion

Real Overdispersion

Concluding Remarks

Ordered Logistic Regression


The Proportional Odds Model

Generalized Ordinal Logistic Regression

Partial Proportional Odds

Multinomial Logistic Regression

Unordered Logistic Regression

Independence of Irrelevant Alternatives

Comparison to Multinomial Probit

Alternative Categorical Response Models


Continuation Ratio Models

Stereotype Logistic Model

Heterogeneous Choice Logistic Model

Adjacent Category Logistic Model

Proportional Slopes Models

Panel Models


Generalized Estimating Equations

Unconditional Fixed Effects Logistic Model

Conditional Logistic Models

Random Effects and Mixed Models Logistic Regression

Other Types of Logistic-Based Models

Survey Logistic Models

Scobit-Skewed Logistic Regression

Discriminant Analysis

Exact Logistic Regression

Exact Methods

Alternative Modeling Methods


Appendix A: Brief Guide to Using Stata Commands

Appendix B: Stata and R Logistic Models

Appendix C: Greek Letters and Major Functions

Appendix D: Stata Binary Logistic Command

Appendix E: Derivation of the Beta-Binomial

Appendix F: Likelihood Function of the Adaptive Gauss–Hermite Quadrature Method of Estimation

Appendix G: Data Sets

Appendix H: Marginal Effects and Discrete Change


Author Index

Subject Index

Exercises and R Code appear at the end of most chapters.

About the Series

Chapman & Hall/CRC Texts in Statistical Science

Learn more…

Subject Categories

BISAC Subject Codes/Headings:
MATHEMATICS / Probability & Statistics / General