Logistic regression models:
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| Main Author: | |
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| Format: | Book |
| Language: | English |
| Published: |
Boca Raton ; London ; New York
CRC Press
2017
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| Series: | Texts in statistical science
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | xviii, 637 Seiten Illustrationen |
| ISBN: | 9781138106710 |
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Record in the Search Index
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| adam_text | Contents
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 2x2 Table Logistic Model.......................................16
2.2 2xk 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..................276
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.........................................................289
R Code............................................................291
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................................341
9.5 Real Over dispersion..........................................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
RCode..............................................................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
|
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| isbn | 9781138106710 |
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| spelling | Hilbe, Joseph M. 1944-2017 Verfasser (DE-588)128751851 aut Logistic regression models Joseph M. Hilbe Boca Raton ; London ; New York CRC Press 2017 xviii, 637 Seiten Illustrationen txt rdacontent n rdamedia nc rdacarrier Texts in statistical science Datenverarbeitung Logistic regression analysis Data processing Regressionsanalyse (DE-588)4129903-6 gnd rswk-swf Logistische Verteilung (DE-588)4299453-6 gnd rswk-swf Regressionsmodell (DE-588)4127980-3 gnd rswk-swf Regressionsanalyse (DE-588)4129903-6 s Logistische Verteilung (DE-588)4299453-6 s DE-604 Regressionsmodell (DE-588)4127980-3 s Äquivalent Druck-Ausgabe, Hardcover 978-1-4200-7575-5 Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029863441&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Hilbe, Joseph M. 1944-2017 Logistic regression models Datenverarbeitung Logistic regression analysis Data processing Regressionsanalyse (DE-588)4129903-6 gnd Logistische Verteilung (DE-588)4299453-6 gnd Regressionsmodell (DE-588)4127980-3 gnd |
| subject_GND | (DE-588)4129903-6 (DE-588)4299453-6 (DE-588)4127980-3 |
| title | Logistic regression models |
| title_auth | Logistic regression models |
| title_exact_search | Logistic regression models |
| title_full | Logistic regression models Joseph M. Hilbe |
| title_fullStr | Logistic regression models Joseph M. Hilbe |
| title_full_unstemmed | Logistic regression models Joseph M. Hilbe |
| title_short | Logistic regression models |
| title_sort | logistic regression models |
| topic | Datenverarbeitung Logistic regression analysis Data processing Regressionsanalyse (DE-588)4129903-6 gnd Logistische Verteilung (DE-588)4299453-6 gnd Regressionsmodell (DE-588)4127980-3 gnd |
| topic_facet | Datenverarbeitung Logistic regression analysis Data processing Regressionsanalyse Logistische Verteilung Regressionsmodell |
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