Holdings: Logistic regression models

Logistic regression models:

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Bibliographic Details
Main Author:	Hilbe, Joseph M. 1944-2017 (Author)
Format:	Book
Language:	English
Published:	Boca Raton [u.a.] CRC Press 2009
Series:	Texts in statistical science A Chapman & Hall book
Subjects:	Datenverarbeitung Logistic regression analysis > Data processing Regressionsmodell Logistische Verteilung Regressionsanalyse
Online Access:	Inhaltsverzeichnis
Physical Description:	XVIII, 637 S. graph. Darst.
ISBN:	9781420075755

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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 2 X 2 TABLE LOGISTIC MODEL..........................................................................16 2.2 2X1 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 VII VIII CONTENTS 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 RCODE..................................................................................................................171 CHAPTER 6 INTERACTIONS......................................................................................189 6.1 INTRODUCTION................................................................................................189 6.2 BINARY X BINARY INTERACTIONS....................................................................191 6.2.1 INTERPRETATIONAS 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 CONTENTS IX 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 R 2 AND PSEUDO-R 2 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 CRITERIONAIC...........................................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 X CONTENTS 9 EXERCISES...............................................................................................................289 R CODE..................................................................................................................291 CHAPTER 8 BINOMIAL LOGISTIC REGRESSION......................................................297 EXERCISES...............................................................................................................313 RCODE..................................................................................................................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 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 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 CONTENTS XI 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 CONTENTS XII 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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spelling	Hilbe, Joseph M. 1944-2017 Verfasser (DE-588)128751851 aut Logistic regression models Joseph M. Hilbe Boca Raton [u.a.] CRC Press 2009 XVIII, 637 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Texts in statistical science A Chapman & Hall book Datenverarbeitung Logistic regression analysis Data processing Regressionsmodell (DE-588)4127980-3 gnd rswk-swf Logistische Verteilung (DE-588)4299453-6 gnd rswk-swf Regressionsanalyse (DE-588)4129903-6 gnd rswk-swf Regressionsanalyse (DE-588)4129903-6 s Logistische Verteilung (DE-588)4299453-6 s DE-604 Regressionsmodell (DE-588)4127980-3 s HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017736503&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 Regressionsmodell (DE-588)4127980-3 gnd Logistische Verteilung (DE-588)4299453-6 gnd Regressionsanalyse (DE-588)4129903-6 gnd
subject_GND	(DE-588)4127980-3 (DE-588)4299453-6 (DE-588)4129903-6
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 Regressionsmodell (DE-588)4127980-3 gnd Logistische Verteilung (DE-588)4299453-6 gnd Regressionsanalyse (DE-588)4129903-6 gnd
topic_facet	Datenverarbeitung Logistic regression analysis Data processing Regressionsmodell Logistische Verteilung Regressionsanalyse
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017736503&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
work_keys_str_mv	AT hilbejosephm logisticregressionmodels

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