1st Edition

Logistic Regression Models

By Joseph M. Hilbe Copyright 2009
    656 Pages 25 B/W Illustrations
    by Chapman & Hall

    656 Pages 25 B/W Illustrations
    by Chapman & Hall

    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.

    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.


    Hilbe, Joseph M.

    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