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

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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 *R*^{2} and Pseudo-*R*^{2} 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

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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

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

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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

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

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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

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