Logistic Regression Models

by Hilbe; Joseph M.

• ISBN13: 9781420075755
• ISBN10: 1420075756
• Edition: 1st
• Format: Hardcover
• Copyright: 2009-05-11
• Publisher: Chapman & Hall/

Summary

This text presents an overview of the full range of logistic models, including binary, proportional, ordered, and categorical response regression procedures. It illustrates how to apply the models to medical, health, environmental/ecological, physical, and social science data. Stata is used to develop, evaluate, and display most models while R code is given at the end of most chapters. The author examines the theoretical foundation of the models and describes how each type of model is established, interpreted, and evaluated as to its goodness of fit. Example data sets are available online in various formats and a solutions manual is available for qualifying instructors.

Author Biography

Joseph M. Hilbe is a Solar System Ambassador with NASA's Jet Propulsion Laboratory at the California Institute of Technology, an Emeritus Professor at the University of Hawaii, and an adjunct professor of statistics at Arizona State University. Professor Hilbe is an elected fellow of both the American Statistical Association and the Royal Statistical Society and an elected member of the International Statistical Institute. He has authored several popular books, including Negative Binomial Regression (Cambridge University Press), as well as Generalized Estimating Equations (Chapman Hall/CRC) and Generalized Linear Models and Extensions (Stata Press) with J. Hardin.

Table of Contents

Preface	p. xiii
Introduction	p. 1
The Normal Model	p. 1
Foundation of the Binomial Model	p. 1
Historical and Software Considerations	p. 3
Chapter Profiles	p. 10
Concepts Related to the Logistic Model	p. 15
2 × 2 Table Logistic Model	p. 16
2 × k Table Logistic Model	p. 25
Modeling a Quantitative Predictor	p. 38
Logistic Modeling Designs	p. 42
Experimental Studies	p. 43
Observational Studies	p. 43
Prospective or Cohort Studies	p. 43
Retrospective or Case-Control Studies	p. 44
Comparisons	p. 44
Exercises	p. 45
R Code	p. 47
Estimation Methods	p. 51
Derivation of the IRLS Algorithm	p. 51
IRLS Estimation	p. 56
Maximum Likelihood Estimation	p. 58
Exercises	p. 61
R Code	p. 62
Derivation of the Binary Logistic Algorithm	p. 63
Terms of the Algorithm	p. 63
Logistic GLM and ML Algorithms	p. 67
Other Bernoulli Models	p. 68
Exercises	p. 70
R Code	p. 71
Model Development	p. 73
Building a Logistic Model	p. 73
Interpretations	p. 76
Full Model	p. 79
Reduced Model	p. 81
Assessing Model Fit: Link Specification	p. 82
Box-Tidwell Test	p. 83
Tukey-Pregibon Link Test	p. 84
Test by Partial Residuals	p. 85
Linearity of Slopes Test	p. 87
Generalized Additive Models	p. 90
Fractional Polynomials	p. 95
Standardized Coefficients	p. 99
Standard Errors	p. 102
Calculating Standard Errors	p. 102
The z-Statistic	p. 103
p-Values	p. 104
Confidence Intervals	p. 104
Confidence Intervals of Odds Ratios	p. 106
Odds Ratios as Approximations of Risk Ratios	p. 106
Epidemiological Terms and Studies	p. 106
Odds Ratios, Risk Ratios, and Risk Models	p. 109
Calculating Standard Errors and Confidence Intervals	p. 121
Risk Difference and Attributable Risk	p. 127
Other Resources on Odds Ratios and Risk Ratios	p. 131
Scaling of Standard Errors	p. 132
Robust Variance Estimators	p. 136
Bootstrapped and Jackknifed Standard Errors	p. 139
Stepwise Methods	p. 143
Handling Missing Values	p. 148
Modeling an Uncertain Response	p. 158
Constraining Coefficients	p. 161
Exercises	p. 165
R Code	p. 171
Interactions	p. 189
Introduction	p. 189
Binary × Binary Interactions	p. 191
Interpretation-as Odds Ratio	p. 194
Standard Errors and Confidence Intervals	p. 197
Graphical Analysis	p. 198
Binary × Categorical Interactions	p. 201
Binary × Continuous Interactions	p. 206
Notes on Centering	p. 206
Constructing and Interpreting the Interaction	p. 209
Interpretation	p. 213
Standard Errors and Confidence Intervals	p. 215
Significance of Interaction	p. 217
Graphical Analysis	p. 217
Categorical × Continuous Interactions	p. 221
Interpretation	p. 223
Standard Errors and Confidence Intervals	p. 225
Graphical Representation	p. 225
Thoughts about Interactions	p. 228
Binary × Binary	p. 230
Continuous × Binary	p. 230
Continuous × Continuous	p. 230
Exercises	p. 233
R Code	p. 235
Analysis of Model Fit	p. 243
Traditional Fit Tests for Logistic Regression	p. 243
R2 and Pseudo-R2 Statistics	p. 243
Deviance Statistic	p. 246
Likelihood Ratio Test	p. 248
Hosmer-Lemeshow GOF Test	p. 249
Hosmer-Lemeshow GOF Test	p. 250
Classification Matrix	p. 254
ROC Analysis	p. 258
Information Criteria Tests	p. 259
Akaike Information Criterion-AIC	p. 259
Finite Sample AIC Statistic	p. 262
LIMDEP AIC	p. 263
SWARTZ AIC	p. 263
Bayesian Information Criterion (BIC)	p. 263
HQIC Goodness-of-Fit Statistic	p. 267
A Unified AIC Fit Statistic	p. 267
Residual Analysis	p. 268
GLM-Based Residuals	p. 269
7.4.1.1	p. 270
7.4.1.2	p. 271
7.4.1.3	p. 272
7.4.1.4	p. 274
7.4.1.5	p. 277
7.4.1.6	p. 279
7.4.1.7	p. 279
m-Asymptotic Residuals	p. 280
7.4.2.1	p. 281
7.4.2.2	p. 281
Conditional Effects Plot	p. 284
Validation Models	p. 286
Exercises	p. 290
R Code	p. 292
Binomial Logistic Regression	p. 297
Exercises	p. 313
R Code	p. 316
Overdispersion	p. 319
Introduction	p. 319
The Nature and Scope of Overdispersion	p. 319
Binomial Overdispersion	p. 320
Apparent Overdispersion	p. 321
Simulated Model Setup	p. 322
Missing Predictor	p. 323
Needed Interaction	p. 324
Predictor Transformation	p. 326
Misspecified Link Function	p. 327
Existing Outlier(s)	p. 329
Relationship: Binomial and Poisson	p. 334
Binary Overdispersion	p. 338
The Meaning of Binary Model Overdispersion	p. 338
Implicit Overdispersion	p. 340
Real Overdispersion	p. 341
Methods of Handling Real Overdispersion	p. 341
Williams' Procedure	p. 342
Generalized Binomial Regression	p. 345
Concluding Remarks	p. 346
Exercises	p. 346
R Code	p. 348
Ordered Logistic Regression	p. 353
Introduction	p. 353
The Proportional Odds Model	p. 355
Generalized Ordinal Logistic Regression	p. 375
Partial Proportional Odds	p. 376
Exercises	p. 378
R Code	p. 381
Multinomial Logistic Regression	p. 385
Unordered Logistic Regression	p. 385
The Multinomial Distribution	p. 385
Interpretation of the Multinomial Model	p. 387
Independence of Irrelevant Alternatives	p. 396
Comparison to Multinomial Probit	p. 399
Exercises	p. 405
R Code	p. 407
Alternative Categorical Response Models	p. 411
Introduction	p. 411
Continuation Ratio Models	p. 412
Stereotype Logistic Model	p. 419
Heterogeneous Choice Logistic Model	p. 422
Adjacent Category Logistic Model	p. 427
Proportional Slopes Models	p. 429
Proportional Slopes Comparative Algorithms	p. 430
Modeling Synthetic Data	p. 432
Tests of Proportionality	p. 435
Exercises	p. 438
Panel Models	p. 441
Introduction	p. 441
Generalized Estimating Equations	p. 442
GEE: Overview of GEE Theory	p. 444
GEE Correlation Structures	p. 446
Independence Correlation Structure Schematic	p. 448
Exchangeable Correlation Structure Schematic	p. 450
Autoregressive Correlation Structure Schematic	p. 451
Unstructured Correlation Structure Schematic	p. 453
Stationary or m-Dependent Correlation Structure Schematic	p. 455
Nonstationary Correlation Structure Schematic	p. 456
GEE Binomial Logistic Models	p. 458
GEE Fit Analysis-QIC	p. 460
QIC/QICu Summary-Binary Logistic Regression	p. 464
Alternating Logistic Regression	p. 466
Quasi-Least Squares Regression	p. 470
Feasibility	p. 474
Final Comments on GEE	p. 479
Unconditional Fixed Effects Logistic Model	p. 481
Conditional Logistic Models	p. 483
Conditional Fixed Effects Logistic Models	p. 483
Matched Case-Control Logistic Model	p. 487
Rank-Ordered Logistic Regression	p. 490
Random Effects and Mixed Models Logistic Regression	p. 496
Random Effects and Mixed Models: Binary Response	p. 496
Alternative AIC-Type Statistics for Panel Data	p. 504
Random-Intercept Proportional Odds	p. 505
Exercises	p. 510
R Code	p. 514
Other Types of Logistic-Based Models	p. 519
Survey Logistic Models	p. 519
Interpretation	p. 524
Scobit-Skewed Logistic Regression	p. 528
Discriminant Analysis	p. 531
Dichotomous Discriminant Analysis	p. 532
Canonical Linear Discriminant Analysis	p. 536
Linear Logistic Discriminant Analysis	p. 539
Exercises	p. 540
Exact Logistic Regression	p. 543
Exact Methods	p. 543
Alternative Modeling Methods	p. 550
Monte Carlo Sampling Methods	p. 550
Median Unbiased Estimation	p. 552
Penalized Logistic Regression	p. 554
Exercises	p. 558
Conclusion	p. 559
Brief Guide to Using Stata Commands	p. 561
Stata and R Logistic Models	p. 589
Greek Letters and Major Functions	p. 591
Stata Binary Logistic Command	p. 593
Derivation of the Beta Binomial	p. 597
Likelihood Function of the Adaptive Gauss-Hermite Quadrature Method of Estimation	p. 599
Data Sets	p. 601
Marginal Effects and Discrete Change	p. 605
References	p. 613
Author Index	p. 625
Subject Index	p. 629
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