Logistic Regression Models

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

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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

Prefacep. xiii
Introductionp. 1
The Normal Modelp. 1
Foundation of the Binomial Modelp. 1
Historical and Software Considerationsp. 3
Chapter Profilesp. 10
Concepts Related to the Logistic Modelp. 15
2 2 Table Logistic Modelp. 16
2 k Table Logistic Modelp. 25
Modeling a Quantitative Predictorp. 38
Logistic Modeling Designsp. 42
Experimental Studiesp. 43
Observational Studiesp. 43
Prospective or Cohort Studiesp. 43
Retrospective or Case-Control Studiesp. 44
Comparisonsp. 44
Exercisesp. 45
R Codep. 47
Estimation Methodsp. 51
Derivation of the IRLS Algorithmp. 51
IRLS Estimationp. 56
Maximum Likelihood Estimationp. 58
Exercisesp. 61
R Codep. 62
Derivation of the Binary Logistic Algorithmp. 63
Terms of the Algorithmp. 63
Logistic GLM and ML Algorithmsp. 67
Other Bernoulli Modelsp. 68
Exercisesp. 70
R Codep. 71
Model Developmentp. 73
Building a Logistic Modelp. 73
Interpretationsp. 76
Full Modelp. 79
Reduced Modelp. 81
Assessing Model Fit: Link Specificationp. 82
Box-Tidwell Testp. 83
Tukey-Pregibon Link Testp. 84
Test by Partial Residualsp. 85
Linearity of Slopes Testp. 87
Generalized Additive Modelsp. 90
Fractional Polynomialsp. 95
Standardized Coefficientsp. 99
Standard Errorsp. 102
Calculating Standard Errorsp. 102
The z-Statisticp. 103
p-Valuesp. 104
Confidence Intervalsp. 104
Confidence Intervals of Odds Ratiosp. 106
Odds Ratios as Approximations of Risk Ratiosp. 106
Epidemiological Terms and Studiesp. 106
Odds Ratios, Risk Ratios, and Risk Modelsp. 109
Calculating Standard Errors and Confidence Intervalsp. 121
Risk Difference and Attributable Riskp. 127
Other Resources on Odds Ratios and Risk Ratiosp. 131
Scaling of Standard Errorsp. 132
Robust Variance Estimatorsp. 136
Bootstrapped and Jackknifed Standard Errorsp. 139
Stepwise Methodsp. 143
Handling Missing Valuesp. 148
Modeling an Uncertain Responsep. 158
Constraining Coefficientsp. 161
Exercisesp. 165
R Codep. 171
Interactionsp. 189
Introductionp. 189
Binary Binary Interactionsp. 191
Interpretation-as Odds Ratiop. 194
Standard Errors and Confidence Intervalsp. 197
Graphical Analysisp. 198
Binary Categorical Interactionsp. 201
Binary Continuous Interactionsp. 206
Notes on Centeringp. 206
Constructing and Interpreting the Interactionp. 209
Interpretationp. 213
Standard Errors and Confidence Intervalsp. 215
Significance of Interactionp. 217
Graphical Analysisp. 217
Categorical Continuous Interactionsp. 221
Interpretationp. 223
Standard Errors and Confidence Intervalsp. 225
Graphical Representationp. 225
Thoughts about Interactionsp. 228
Binary Binaryp. 230
Continuous Binaryp. 230
Continuous Continuousp. 230
Exercisesp. 233
R Codep. 235
Analysis of Model Fitp. 243
Traditional Fit Tests for Logistic Regressionp. 243
R2 and Pseudo-R2 Statisticsp. 243
Deviance Statisticp. 246
Likelihood Ratio Testp. 248
Hosmer-Lemeshow GOF Testp. 249
Hosmer-Lemeshow GOF Testp. 250
Classification Matrixp. 254
ROC Analysisp. 258
Information Criteria Testsp. 259
Akaike Information Criterion-AICp. 259
Finite Sample AIC Statisticp. 262
Bayesian Information Criterion (BIC)p. 263
HQIC Goodness-of-Fit Statisticp. 267
A Unified AIC Fit Statisticp. 267
Residual Analysisp. 268
GLM-Based Residualsp. 269 270 271 272 274 277 279 279
m-Asymptotic Residualsp. 280 281 281
Conditional Effects Plotp. 284
Validation Modelsp. 286
Exercisesp. 290
R Codep. 292
Binomial Logistic Regressionp. 297
Exercisesp. 313
R Codep. 316
Overdispersionp. 319
Introductionp. 319
The Nature and Scope of Overdispersionp. 319
Binomial Overdispersionp. 320
Apparent Overdispersionp. 321
Simulated Model Setupp. 322
Missing Predictorp. 323
Needed Interactionp. 324
Predictor Transformationp. 326
Misspecified Link Functionp. 327
Existing Outlier(s)p. 329
Relationship: Binomial and Poissonp. 334
Binary Overdispersionp. 338
The Meaning of Binary Model Overdispersionp. 338
Implicit Overdispersionp. 340
Real Overdispersionp. 341
Methods of Handling Real Overdispersionp. 341
Williams' Procedurep. 342
Generalized Binomial Regressionp. 345
Concluding Remarksp. 346
Exercisesp. 346
R Codep. 348
Ordered Logistic Regressionp. 353
Introductionp. 353
The Proportional Odds Modelp. 355
Generalized Ordinal Logistic Regressionp. 375
Partial Proportional Oddsp. 376
Exercisesp. 378
R Codep. 381
Multinomial Logistic Regressionp. 385
Unordered Logistic Regressionp. 385
The Multinomial Distributionp. 385
Interpretation of the Multinomial Modelp. 387
Independence of Irrelevant Alternativesp. 396
Comparison to Multinomial Probitp. 399
Exercisesp. 405
R Codep. 407
Alternative Categorical Response Modelsp. 411
Introductionp. 411
Continuation Ratio Modelsp. 412
Stereotype Logistic Modelp. 419
Heterogeneous Choice Logistic Modelp. 422
Adjacent Category Logistic Modelp. 427
Proportional Slopes Modelsp. 429
Proportional Slopes Comparative Algorithmsp. 430
Modeling Synthetic Datap. 432
Tests of Proportionalityp. 435
Exercisesp. 438
Panel Modelsp. 441
Introductionp. 441
Generalized Estimating Equationsp. 442
GEE: Overview of GEE Theoryp. 444
GEE Correlation Structuresp. 446
Independence Correlation Structure Schematicp. 448
Exchangeable Correlation Structure Schematicp. 450
Autoregressive Correlation Structure Schematicp. 451
Unstructured Correlation Structure Schematicp. 453
Stationary or m-Dependent Correlation Structure Schematicp. 455
Nonstationary Correlation Structure Schematicp. 456
GEE Binomial Logistic Modelsp. 458
GEE Fit Analysis-QICp. 460
QIC/QICu Summary-Binary Logistic Regressionp. 464
Alternating Logistic Regressionp. 466
Quasi-Least Squares Regressionp. 470
Feasibilityp. 474
Final Comments on GEEp. 479
Unconditional Fixed Effects Logistic Modelp. 481
Conditional Logistic Modelsp. 483
Conditional Fixed Effects Logistic Modelsp. 483
Matched Case-Control Logistic Modelp. 487
Rank-Ordered Logistic Regressionp. 490
Random Effects and Mixed Models Logistic Regressionp. 496
Random Effects and Mixed Models: Binary Responsep. 496
Alternative AIC-Type Statistics for Panel Datap. 504
Random-Intercept Proportional Oddsp. 505
Exercisesp. 510
R Codep. 514
Other Types of Logistic-Based Modelsp. 519
Survey Logistic Modelsp. 519
Interpretationp. 524
Scobit-Skewed Logistic Regressionp. 528
Discriminant Analysisp. 531
Dichotomous Discriminant Analysisp. 532
Canonical Linear Discriminant Analysisp. 536
Linear Logistic Discriminant Analysisp. 539
Exercisesp. 540
Exact Logistic Regressionp. 543
Exact Methodsp. 543
Alternative Modeling Methodsp. 550
Monte Carlo Sampling Methodsp. 550
Median Unbiased Estimationp. 552
Penalized Logistic Regressionp. 554
Exercisesp. 558
Conclusionp. 559
Brief Guide to Using Stata Commandsp. 561
Stata and R Logistic Modelsp. 589
Greek Letters and Major Functionsp. 591
Stata Binary Logistic Commandp. 593
Derivation of the Beta Binomialp. 597
Likelihood Function of the Adaptive Gauss-Hermite Quadrature Method of Estimationp. 599
Data Setsp. 601
Marginal Effects and Discrete Changep. 605
Referencesp. 613
Author Indexp. 625
Subject Indexp. 629
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