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E-raamat: Logistic Regression Models

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(California Institute of Technology, Pasadena, and Arizona State University, Tempe, USA)
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Logistic Regression Models presents an overview of the full range of logistic models, including binary, proportional, ordered, partially ordered, and unordered categorical response regression procedures. Other topics discussed include panel, survey, skewed, penalized, and exact logistic models. The text illustrates how to apply the various models to health, environmental, physical, and social science data.

Examples illustrate successful modeling The text first provides basic terminology and concepts, before explaining the foremost methods of estimation (maximum likelihood and IRLS) appropriate for logistic models. It then presents an in-depth discussion of related terminology and examines logistic regression model development and interpretation of the results. After focusing on the construction and interpretation of various interactions, the author evaluates assumptions and goodness-of-fit tests that can be used for model assessment. He also covers binomial logistic regression, varieties of overdispersion, and a number of extensions to the basic binary and binomial logistic model. Both real and simulated data are used to explain and test the concepts involved. The appendices give an overview of marginal effects and discrete change as well as a 30-page tutorial on using Stata commands related to the examples used in the text. Stata is used for most examples while R is provided at the end of the chapters to replicate examples in the text.

Apply the models to your own data Data files for examples and questions used in the text as well as code for user-authored commands are provided on the books website, formatted in Stata, R, Excel, SAS, SPSS, and Limdep.

See Professor Hilbe discuss the book.

Arvustused

This book really does cover everything you ever wanted to know about logistic regression with updates available on the authors website. Hilbe, a former national athletics champion, philosopher, and expert in astronomy, is a master at explaining statistical concepts and methods. Readers familiar with his other expository work will know what to expectgreat clarity. The book provides considerable detail about all facets of logistic regression. No step of an argument is omitted so that the book will meet the needs of the reader who likes to see everything spelt out, while a person familiar with some of the topics has the option to skip "obvious" sections. The material has been thoroughly road-tested through classroom and web-based teaching. The focus is on helping the reader to learn and understand logistic regression. The audience is not just students meeting the topic for the first time, but also experienced users. I believe the book really does meet the authors goal . Annette J. Dobson, Biometrics, June 2012

Overall this is a comprehensive book, which will provide a very useful resource and handbook for anyone whose work involves modelling binary data. David J. Hand, International Statistical Review (2011), 79

useful as a textbook in a course on logistic regression. Andreas Rosenblad, Technometrics, May 2011

Preface xiii
Chapter 1 Introduction 1
1.1 The Normal Model
1
1.2 Foundation of the Binomial Model
1
1.3 Historical and Software Considerations
3
1.4
Chapter Profiles
10
Chapter 2 Concepts Related to the Logistic Model 15
2.1 2 x 2 Table Logistic Model
16
2.2 2 x k Table Logistic Model
25
2.3 Modeling a Quantitative Predictor
38
2.4 Logistic Modeling Designs
42
2.4.1 Experimental Studies
43
2.4.2 Observational Studies
43
2.4.2.1 Prospective or Cohort Studies
43
2.4.2.2 Retrospective or Case-Control Studies
44
2.4.2.3 Comparisons
44
Exercises
45
R Code
47
Chapter 3 Estimation Methods 51
3.1 Derivation of the IRLS Algorithm
51
3.2 IRLS Estimation
56
3.3 Maximum Likelihood Estimation
58
Exercises
61
R Code
62
Chapter 4 Derivation of the Binary Logistic Algorithm 63
4.1 Terms of the Algorithm
63
4.2 Logistic GLM and ML Algorithms
67
4.3 Other Bernoulli Models
68
Exercises
70
R Code
71
Chapter 5 Model Development 73
5.1 Building a Logistic Model
73
5.1.1 Interpretations
76
5.1.2 Full Model
79
5.1.3 Reduced Model
81
5.2 Assessing Model Fit: Link Specification
82
5.2.1 Box-Tidwell Test
83
5.2.2 Tukey-Pregibon Link Test
84
5.2.3 Test by Partial Residuals
85
5.2.4 Linearity of Slopes Test
87
5.2.5 Generalized Additive Models
90
5.2.6 Fractional Polynomials
95
5.3 Standardized Coefficients
99
5.4 Standard Errors
102
5.4.1 Calculating Standard Errors
102
5.4.2 The z-Statistic
103
5.4.3 p-Values
104
5.4.4 Confidence Intervals
104
5.4.5 Confidence Intervals of Odds Ratios
106
5.5 Odds Ratios as Approximations of Risk Ratios
106
5.5.1 Epidemiological Terms and Studies
106
5.5.2 Odds Ratios, Risk Ratios, and Risk Models
109
5.5.3 Calculating Standard Errors and Confidence Intervals
121
5.5.4 Risk Difference and Attributable Risk
127
5.5.5 Other Resources on Odds Ratios and Risk Ratios
131
5.6 Scaling of Standard Errors
132
5.7 Robust Variance Estimators
136
5.8 Bootstrapped and Jackknifed Standard Errors
139
5.9 Stepwise Methods
143
5.10 Handling Missing Values
148
5.11 Modeling an Uncertain Response
158
5.12 Constraining Coefficients
161
Exercises
165
R Code
171
Chapter 6 Interactions 189
6.1 Introduction
189
6.2 Binary x Binary Interactions
191
6.2.1 Interpretation—as Odds Ratio
194
6.2.2 Standard Errors and Confidence Intervals
197
6.2.3 Graphical Analysis
198
6.3 Binary x Categorical Interactions
201
6.4 Binary x Continuous Interactions
206
6.4.1 Notes on Centering
206
6.4.2 Constructing and Interpreting the Interaction
209
6.4.3 Interpretation
213
6.4.4 Standard Errors and Confidence Intervals
215
6.4.5 Significance of Interaction
217
6.4.6 Graphical Analysis
217
6.5 Categorical x Continuous Interactions
221
6.5.1 Interpretation
223
6.5.2 Standard Errors and Confidence Intervals
225
6.5.3 Graphical Representation
225
6.6 Thoughts about Interactions
228
6.6.1 Binary x Binary
230
6.6.2 Continuous x Binary
230
6.6.3 Continuous x Continuous
230
Exercises
233
R Code
235
Chapter 7 Analysis of Model Fit 243
7.1 Traditional Fit Tests for Logistic Regression
243
7.1.1 R2 and Pseudo-R2 Statistics
243
7.1.2 Deviance Statistic
246
7.1.3 Likelihood Ratio Test
248
7.2 Hosmer-Lemeshow GOF Test
249
7.2.1 Hosmer-Lemeshow GOF Test
250
7.2.2 Classification Matrix
254
7.2.3 ROC Analysis
258
7.3 Information Criteria Tests
259
7.3.1 Akaike Information Criterion—AIC
259
7.3.2 Finite Sample AIC Statistic
262
7.3.3 LIMDEP AIC
263
7.3.4 SWARTZ AIC
263
7.3.5 Bayesian Information Criterion (BIC)
263
7.3.6 HQIC Goodness-of-Fit Statistic
267
7.3.7 A Unified AIC Fit Statistic
267
7.4 Residual Analysis
268
7.4.1 GLM-Based Residuals
269
7.4.1.1 Raw Residual
270
7.4.1.2 Pearson Residual
271
7.4.1.3 Deviance Residual
272
7.4.1.4 Standardized Pearson Residual
274
7.4.1.5 Standardized Deviance Residual
277
7.4.1.6 Likelihood Residuals
279
7.4.1.7 Anscombe Residuals
279
7.4.2 m-Asymptotic Residuals
280
7.4.2.1 Hat Matrix Diagonal Revisited
281
7.4.2.2 Other Influence Residuals
281
7.4.3 Conditional Effects Plot
284
7.5 Validation Models
286
Exercises
290
R Code
292
Chapter 8 Binomial Logistic Regression 297
Exercises
313
R Code
316
Chapter 9 Overdispersion 319
9.1 Introduction
319
9.2 The Nature and Scope of Overdispersion
319
9.3 Binomial Overdispersion
320
9.3.1 Apparent Overdispersion
321
9.3.1.1 Simulated Model Setup
322
9.3.1.2 Missing Predictor
323
9.3.1.3 Needed Interaction
324
9.3.1.4 Predictor Transformation
326
9.3.1.5 Misspecified Link Function
327
9.3.1.6 Existing Outlier(s)
329
9.3.2 Relationship: Binomial and Poisson
334
9.4 Binary Overdispersion
338
9.4.1 The Meaning of Binary Model Overdispersion
338
9.4.2 Implicit Overdispersion
340
9.5 Real Overdispersion
341
9.5.1 Methods of Handling Real Overdispersion
341
9.5.2 Williams' Procedure
342
9.5.3 Generalized Binomial Regression
345
9.6 Concluding Remarks
346
Exercises
346
R Code
348
Chapter 10 Ordered Logistic Regression 353
10.1 Introduction
353
10.2 The Proportional Odds Model
355
10.3 Generalized Ordinal Logistic Regression
375
10.4 Partial Proportional Odds
376
Exercises
378
R Code
381
Chapter 11 Multinomial Logistic Regression 385
11.1 Unordered Logistic Regression
385
11.1.1 The Multinomial Distribution
385
11.1.2 Interpretation of the Multinomial Model
387
11.2 Independence of Irrelevant Alternatives
396
11.3 Comparison to Multinomial Probit
399
Exercises
405
R Code
407
Chapter 12 Alternative Categorical Response Models 411
12.1 Introduction
411
12.2 Continuation Ratio Models
412
12.3 Stereotype Logistic Model
419
12.4 Heterogeneous Choice Logistic Model
422
12.5 Adjacent Category Logistic Model
427
12.6 Proportional Slopes Models
429
12.6.1 Proportional Slopes Comparative Algorithms
430
12.6.2 Modeling Synthetic Data
432
12.6.3 Tests of Proportionality
435
Exercises
438
Chapter 13 Panel Models 441
13.1 Introduction
441
13.2 Generalized Estimating Equations
442
13.2.1 GEE: Overview of GEE Theory
444
13.2.2 GEE Correlation Structures
446
13.2.2.1 Independence Correlation Structure Schematic
448
13.2.2.2 Exchangeable Correlation Structure Schematic
450
13.2.2.3 Autoregressive Correlation Structure Schematic
451
13.2.2.4 Unstructured Correlation Structure Schematic
453
13.2.2.5 Stationary or m-Dependent Correlation Structure Schematic
455
13.2.2.6 Nonstationary Correlation Structure Schematic
456
13.2.3 GEE Binomial Logistic Models
458
13.2.4 GEE Fit Analysis—QIC
460
13.2.4.1 QIC/QICu Summary-Binary Logistic Regression
464
13.2.5 Alternating Logistic Regression
466
13.2.6 Quasi-Least Squares Regression
470
13.2.7 Feasibility
474
13.2.8 Final Comments on GEE
479
13.3 Unconditional Fixed Effects Logistic Model
481
13.4 Conditional Logistic Models
483
13.4.1 Conditional Fixed Effects Logistic Models
483
13.4.2 Matched Case-Control Logistic Model
487
13.4.3 Rank-Ordered Logistic Regression
490
13.5 Random Effects and Mixed Models Logistic Regression
496
13.5.1 Random Effects and Mixed Models: Binary Response
496
13.5.2 Alternative AIC-Type Statistics for Panel Data
504
13.5.3 Random-Intercept Proportional Odds
505
Exercises
510
R Code
514
Chapter 14 Other Types of Logistic-Based Models 519
14.1 Survey Logistic Models
519
14.1.1 Interpretation
524
14.2 Scobit-Skewed Logistic Regression
528
14.3 Discriminant Analysis
531
14.3.1 Dichotomous Discriminant Analysis
532
14.3.2 Canonical Linear Discriminant Analysis
536
14.3.3 Linear Logistic Discriminant Analysis
539
Exercises
540
Chapter 15 Exact Logistic Regression 543
15.1 Exact Methods
543
15.2 Alternative Modeling Methods
550
15.2.1 Monte Carlo Sampling Methods
550
15.2.2 Median Unbiased Estimation
552
15.2.3 Penalized Logistic Regression
554
Exercises
558
Conclusion 559
Appendix A: Brief Guide to Using Stata Commands 561
Appendix B: Stata and R Logistic Models 589
Appendix C: Greek Letters and Major Functions 591
Appendix D: Stata Binary Logistic Command 593
Appendix E: Derivation of the Beta Binomial 597
Appendix F: Likelihood Function of the Adaptive Gauss–Hermite Quadrature Method of Estimation 599
Appendix G: Data Sets 601
Appendix H: Marginal Effects and Discrete Change 605
References 613
Author Index 625
Subject Index 629
Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA and Arizona State University, Tempe, AZ
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