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Logistic Regression Models

Author:
Joseph M. Hilbe
Publisher: Chapman & Hall/CRC
Copyright: 2009
ISBN-13: 978-1-4200-7575-5
Pages: 656; hardcover
Price: $74.50
Supplements:program files (LRM_ADO.ZIP)
datasets (LRM_DATA.ZIP)

Comment from the Stata technical group

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.


Table of contents

Preface
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
2.4.2.1 Prospective or Cohort Studies
2.4.2.2 Retrospective or Case–Control Studies
2.4.2.3 Comparisons
Exercises
R Code
Chapter 3 Estimation Methods
3.1 Derivation of the IRLS Algorithm
3.2 IRLS Estimation
3.3 Maximum Likelihood Estimation
Exercises
R Code
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
Exercises
R Code
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
Exercises
R Code
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
Exercises
R Code
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
7.3.3 LIMDEP AIC
7.3.4 SWARTZ AIC
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
7.4.1.1 Raw Residual
7.4.1.2 Pearson Residual
7.4.1.3 Deviance Residual
7.4.1.4 Standardized Pearson Residual
7.4.1.5 Standardized Deviance Residual
7.4.1.6 Likelihood Residuals
7.4.1.7 Anscombe Residuals
7.4.2 m-Asymptotic Residuals
7.4.2.1 Hat Matrix Diagonal Revisited
7.4.2.2 Other Influence Residuals
7.4.3 Conditional Effects Plot
7.5 Validation Models
Exercises
R Code
Chapter 8 Binomial Logistic Regression
Exercises
R Code
Chapter 9 Overdispersion
9.1 Introduction
9.2 The Nature and Scope of Overdispersion
9.3 Binomial Overdispersion
9.3.1 Apparent Overdispersion
9.3.1.1 Simulated Model Setup
9.3.1.2 Missing Predictor
9.3.1.3 Needed Interaction
9.3.1.4 Predictor Transformation
9.3.1.5 Misspecified Link Function
9.3.1.6 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
Exercises
R Code
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
Exercises
R Code
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
Exercises
R Code
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
Exercises
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
13.2.2.1 Independence Correlation Structure Schematic
13.2.2.2 Exchangeable Correlation Structure Schematic
13.2.2.3 Autoregressive Correlation Structure Schematic
13.2.2.4 Unstructured Correlation Structure Schematic
13.2.2.5 Stationary or m-Dependent Correlation Structure Schematic
13.2.2.6 Nonstationary Correlation Structure Schematic
13.2.3 GEE Binomial Logistic Models
13.2.4 GEE Fit Analysis—QIC
13.2.4.1 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
Exercises
R Code
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
Exercises
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
Exercises
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
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