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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 |
R^{2} and Pseudo-R^{2} 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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