Logistic Regression Models

Logistic Regression Models, by Joseph Hilbe, arose from Hilbe’s course in logistic regression at statistics.com. The book includes many Stata examples using both official and user-written commands and includes Stata output and graphs.


Hilbe begins with simple contingency tables and covers fitting algorithms, parameter interpretation, and diagnostics. The later chapters include models for overdispersion, complex response variables, longitudinal data, and survey data. The final chapter describes exact logistic regression, available in Stata 10 with the new exlogistic command. Hilbe does not oversimplify controversial issues, like interactions and standardized coefficients.


The prerequisite for most of the book is a working knowledge of multiple regression, but some sections use multivariate calculus and matrix algebra.


Hilbe is coauthor (with James Hardin) of the popular Stata Press book Generalized Linear Models and Extensions. He also wrote the first versions of Stata’s logistic and glm commands.


The fourth printing has been revised: examples in the book now use Stata version 11 code in place of earlier version code, where applicable.



Chapter 1 Introduction
1.1 The Normal Model
1.2 Foundation of the Binomial Model
1.3 Historical and Software Considerations
1.4 Chapter Profiles


Chapter 2 Concepts Related to the Logistic Model
2.1 2 × 2 Table Logistic Model
2.2 2 × k Table Logistic Model
2.3 Modeling a Quantitative Predictor
2.4 Logistic Modeling Designs

2.4.1 Experimental Studies
2.4.2 Observational Studies Prospective or Cohort Studies Retrospective or Case–Control Studies Comparisons

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Chapter 3 Estimation Methods
3.1 Derivation of the IRLS Algorithm
3.2 IRLS Estimation
3.3 Maximum Likelihood Estimation
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Chapter 4 Derivation of the Binary Logistic Algorithm
4.1 Terms of the Algorithm
4.2 Logistic GLM and ML Algorithms
4.3 Other Bernoulli Models
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Chapter 5 Model Development

5.1 Building a Logistic Model

5.1.1 Interpretations
5.1.2 Full Model
5.1.3 Reduced Model

5.2 Assessing Model Fit: Link Specification

5.2.1 Box–Tidwell Test
5.2.2 Tukey–Pregibon Link Test
5.2.3 Test by Partial Residuals
5.2.4 Linearity of Slopes Test
5.2.5 Generalized Additive Models
5.2.6 Fractional Polynomials

5.3 Standardized Coefficients
5.4 Standard Errors

5.4.1 Calculating Standard Errors
5.4.2 The z-Statistic
5.4.3 p-Values
5.4.4 Confidence Intervals
5.4.5 Confidence Intervals of Odds Ratios

5.5 Odds Ratios as Approximations of Risk Ratios

5.5.1 Epidemiological Terms and Studies
5.5.2 Odds Ratios, Risk Ratios, and Risk Models
5.5.3 Calculating Standard Errors and Confidence Intervals
5.5.4 Risk Difference and Attributable Risk
5.5.5 Other Resources on Odds Ratios and Risk Ratios

5.6 Scaling of Standard Errors
5.7 Robust Variance Estimators
5.8 Bootstrapped and Jackknifed Standard Errors
5.9 Stepwise Methods
5.10 Handling Missing Values
5.11 Modeling an Uncertain Response
5.12 Constraining Coefficients
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Chapter 6 Interactions
6.1 Introduction
6.2 Binary × Binary Interactions

6.2.1 Interpretation—as Odds Ratio
6.2.2 Standard Errors and Confidence Intervals
6.2.3 Graphical Analysis

6.3 Binary × Categorical Interactions
6.4 Binary × Continuous Interactions

6.4.1 Notes on Centering
6.4.2 Constructing and Interpreting the Interaction
6.4.3 Interpretation
6.4.4 Standard Errors and Confidence Intervals
6.4.5 Significance of Interaction
6.4.6 Graphical Analysis

6.5 Categorical × Continuous Interactions

6.5.1 Interpretation
6.5.2 Standard Errors and Confidence Intervals
6.5.3 Graphical Representation

6.6 Thoughts about Interactions

6.6.1 Binary × Binary
6.6.2 Continuous × Binary
6.6.3 Continuous × Continuous

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Chapter 7 Analysis of Model Fit

7.1 Traditional Fit Tests for Logistic Regression

7.1.1 R2 and Pseudo-R2 Statistics
7.1.2 Deviance Statistic
7.1.3 Likelihood Ratio Test

7.2 Hosmer–Lemeshow GOF Test

7.2.1 Hosmer–Lemeshow GOF Test
7.2.2 Classification Matrix
7.2.3 ROC Analysis

7.3 Information Criteria Tests

7.3.1 Akaike Information Criterion—AIC
7.3.2 Finite Sample AIC Statistic
7.3.5 Bayesian Information Criterion (BIC)
7.3.6 HQIC Goodness-of-Fit Statistic
7.3.7 A Unified AIC Fit Statistic

7.4 Residual Analysis

7.4.1 GLM-Based Residuals Raw Residual Pearson Residual Deviance Residual Standardized Pearson Residual Standardized Deviance Residual Likelihood Residuals Anscombe Residuals

7.4.2 m-Asymptotic Residuals Hat Matrix Diagonal Revisited Other Influence Residuals

7.4.3 Conditional Effects Plot

7.5 Validation Models
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Chapter 8 Binomial Logistic Regression
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Chapter 9 Overdispersion
9.1 Introduction
9.2 The Nature and Scope of Overdispersion
9.3 Binomial Overdispersion

9.3.1 Apparent Overdispersion Simulated Model Setup Missing Predictor Needed Interaction Predictor Transformation Misspecified Link Function Existing Outlier(s)

9.3.2 Relationship: Binomial and Poisson

9.4 Binary Overdispersion

9.4.1 The Meaning of Binary Model Overdispersion
9.4.2 Implicit Overdispersion

9.5 Real Overdispersion

9.5.1 Methods of Handling Real Overdispersion
9.5.2 Williams’ Procedure
9.5.3 Generalized Binomial Regression

9.6 Concluding Remarks
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Chapter 10 Ordered Logistic Regression
10.1 Introduction
10.2 The Proportional Odds Model
10.3 Generalized Ordinal Logistic Regression
10.4 Partial Proportional Odds
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Chapter 11 Multinomial Logistic Regression

11.1 Unordered Logistic Regression

11.1.1 The Multinomial Distribution
11.1.2 Interpretation of the Multinomial Model

11.2 Independence of Irrelevant Alternatives
11.3 Comparison to Multinomial Probit
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Chapter 12 Alternative Categorical Response Models
12.1 Introduction
12.2 Continuation Ratio Models
12.3 Stereotype Logistic Model
12.4 Heterogeneous Choice Logistic Model
12.5 Adjacent Category Logistic Model
12.6 Proportional Slopes Models

12.6.1 Proportional Slopes Comparative Algorithms
12.6.2 Modeling Synthetic Data
12.6.3 Tests of Proportionality



Chapter 13 Panel Models
13.1 Introduction
13.2 Generalized Estimating Equations

13.2.1 GEE: Overview of GEE Theory
13.2.2 GEE Correlation Structures Independence Correlation Structure Schematic Exchangeable Correlation Structure Schematic Autoregressive Correlation Structure Schematic Unstructured Correlation Structure Schematic Stationary or m-Dependent Correlation Structure Schematic Nonstationary Correlation Structure Schematic

13.2.3 GEE Binomial Logistic Models
13.2.4 GEE Fit Analysis—QIC QIC/QICu Summary–Binary Logistic Regression

13.2.5 Alternating Logistic Regression
13.2.6 Quasi-Least Squares Regression
13.2.7 Feasibility
13.2.8 Final Comments on GEE

13.3 Unconditional Fixed Effects Logistic Model
13.4 Conditional Logistic Models

13.4.1 Conditional Fixed Effects Logistic Models
13.4.2 Matched Case–Control Logistic Model
13.4.3 Rank-Ordered Logistic Regression

13.5 Random Effects and Mixed Models Logistic Regression

13.5.1 Random Effects and Mixed Models: Binary Response
13.5.2 Alternative AIC-Type Statistics for Panel Data
13.5.3 Random-Intercept Proportional Odds

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Chapter 14 Other Types of Logistic-Based Models

14.1 Survey Logistic Models

14.1.1 Interpretation

14.2 Scobit-Skewed Logistic Regression
14.3 Discriminant Analysis

14.3.1 Dichotomous Discriminant Analysis
14.3.2 Canonical Linear Discriminant Analysis
14.3.3 Linear Logistic Discriminant Analysis



Chapter 15 Exact Logistic Regression
15.1 Exact Methods
15.2 Alternative Modeling Methods

15.2.1 Monte Carlo Sampling Methods
15.2.2 Median Unbiased Estimation
15.2.3 Penalized Logistic Regression





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
Author: Joseph M. Hilbe
ISBN-13: 978-1-4200-7575-5
©Copyright: 2009 Chapman & Hall/CRC

Logistic Regression Models, by Joseph Hilbe, arose from Hilbe’s course in logistic regression at statistics.com. The book includes many Stata examples using both official and user-written commands and includes Stata output and graphs.