Logistic Regression Models

Summary

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.

Many examples help explain the concepts and techniques of 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.

Features

• Examines the theoretical foundation of many logistic models, including binary, ordered, multinomial, panel, and exact
• Describes how each type of model is established, interpreted, and evaluated as to its goodness of fit
• Analyzes the models using Stata
• Offers R code at the end of most chapters to enable R users to duplicate the output displayed in the text
• Includes numerous exercises and real-world examples from the medical, ecological, physical, and social sciences
• Provides the example data sets online in Stata, R, Excel, SAS, SPSS, and Limdep formats

Solutions manual available upon qualifying course adoptions

Table of Contents

Preface
Introduction
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
Interactions
Introduction
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
Overdispersion
Introduction
The Nature and Scope of Overdispersion
Binomial Overdispersion
Binary Overdispersion
Real Overdispersion
Concluding Remarks
Ordered Logistic Regression
Introduction
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
Introduction
Continuation Ratio Models
Stereotype Logistic Model
Heterogeneous Choice Logistic Model
Adjacent Category Logistic Model
Proportional Slopes Models
Panel Models
Introduction
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
Conclusion
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
References
Author Index
Subject Index
Exercises and R Code appear at the end of most chapters.