Regression for Categorical Data

Description

Contents......Page 3 Preface......Page 7 Categorical Data: Examples and Basic Concepts......Page 9 Organization of This Book......Page 13 Basic Components of Structured Regression......Page 14 Classical Linear Regression......Page 23 Exercises......Page 35 Distribution Models for Binary Responses and Basic Concepts......Page 37 Linking Response and Explanatory Variables......Page 41 The Logit Model......Page 45 The Origins of the Logistic Function and the Logit Model......Page 56 Exercises......Page 57 Basic Structure......Page 59 Generalized Linear Models for Continuous Responses......Page 61 GLMs for Discrete Responses......Page 64 Further Concepts......Page 68 Modeling of Grouped Data......Page 70 Maximum Likelihood Estimation......Page 71 Inference......Page 75 Goodness-of-Fit for Grouped Observations......Page 80 Computation of Maximum Likelihood Estimates......Page 83 Hat Matrix for Generalized Linear Models......Page 84 Quasi-Likelihood Modeling......Page 86 Exercises......Page 87 4 Modeling of Binary Data......Page 89 Maximum Likelihood Estimation......Page 90 Discrepancy between Data and Fit......Page 95 Diagnostic Checks......Page 101 Structuring the Linear Predictor......Page 109 Comparing Non-Nested Models......Page 121 Explanatory Value of Covariates......Page 122 Further Reading......Page 127 Exercises......Page 128 Alternative Links in Binary Regression......Page 130 The Missing Link......Page 137 Overdispersion......Page 139 Conditional Likelihood......Page 145 Exercises......Page 147 6 Regularization & Variable Selection for Parametric Models......Page 149 Classical Subset Selection......Page 150 Regularization by Penalization......Page 151 Boosting Methods......Page 169 Simultaneous Selection of Link Function and Predictors......Page 176 Categorical Predictors......Page 179 Bayesian Approach......Page 184 Exercises......Page 185 7 Regression Analysis of Count Data......Page 187 The Poisson Distribution......Page 188 Poisson Regression Model......Page 191 Inference for the Poisson Regression Model......Page 192 Poisson Regression with an Offset......Page 196 Poisson Regression with Overdispersion......Page 198 Negative Binomial Model and Alternatives......Page 200 Zero-Inflated Counts......Page 204 Hurdle Models......Page 206 Further Reading......Page 209 Exercises......Page 210 8 Multinomial Response Models......Page 212 The Multinomial Distribution......Page 214 The Multinomial Logit Model......Page 215 Structuring the Predictor......Page 220 Logit Model as Multivariate Generalized Linear Model......Page 222 Inference for Multicategorical Response Models......Page 223 Multinomial Models with Hierarchically Structured Response......Page 228 Discrete Choice Models......Page 231 Nested Logit Model......Page 236 Regularization for the Multinomial Model......Page 238 Further Reading......Page 243 Exercises......Page 244 9 Ordinal Response Models......Page 246 Cumulative Models......Page 248 Sequential Models......Page 257 Further Properties and Comparison of Models......Page 260 Alternative Models......Page 262 Inference for Ordinal Models......Page 266 Exercises......Page 270 Univariate Generalized Non-Parametric Regression......Page 273 Non-Parametric Regression with Multiple Covariates......Page 289 Structured Additive Regression......Page 293 Functional Data and Signal Regression......Page 311 Further Reading......Page 317 Exercises......Page 318 Regression and Classification Trees......Page 320 Multivariate Adaptive Regression Splines......Page 331 Exercises......Page 332 12 Analysis of Contingency Tables - Log-Linear & Graphical Models......Page 334 Types of Contingency Tables......Page 335 Log-Linear Models for Two-Way Tables......Page 338 Log-Linear Models for Three-Way Tables......Page 341 Specific Log-Linear Models......Page 344 Log-Linear and Graphical Models for Higher Dimensions......Page 348 Collapsibility......Page 351 Log-Linear Models and the Logit Model......Page 352 Inference for Log-Linear Models......Page 353 Model Selection and Regularization......Page 357 Mosaic Plots......Page 360 Further Reading......Page 361 Exercises......Page 362 13 Multivariate Response Models......Page 365 Conditional Modeling......Page 367 Marginal Parametrization and Generalized Log-Linear Models......Page 372 General Marginal Models: Association as Nuisance and GEEs......Page 373 Marginal Homogeneity......Page 387 Further Reading......Page 394 Exercises......Page 395 14 Random Effects Models & Finite Mixtures......Page 397 Linear Random Effects Models for Gaussian Data......Page 398 Generalized Linear Mixed Models......Page 404 Estimation Methods for Generalized Mixed Models......Page 409 Multicategorical Response Models......Page 418 The Marginalized Random Effects Model......Page 421 Semiparametric Mixed Models......Page 422 Finite Mixture Models......Page 424 Further Reading......Page 428 Exercises......Page 429 15 Prediction & Classification......Page 430 Basic Concepts of Prediction......Page 431 Methods for Optimal Classification......Page 439 Basics of Estimated Classification Rules......Page 446 Parametric Classification Methods......Page 452 Non-Parametric Methods......Page 458 Neural Networks......Page 469 Examples......Page 472 Variable Selection in Classification......Page 474 Prediction of Ordinal Outcomes......Page 475 Model-Based Prediction......Page 481 Further Reading......Page 482 Exercises......Page 483 A.1 Discrete Distributions......Page 486 A.2 Continuous Distributions......Page 488 B.1 Linear Algebra......Page 491 B.2 Taylor Approximation......Page 492 B.3 Conditional Expectation, Distribution......Page 494 B.4 EM Algorithm......Page 495 C.1 Simplification of Penalties......Page 497 C.2 Linear Constraints......Page 499 C.3 Fisher Scoring with Penalty Term......Page 500 D.1 Kullback-Leibler Distance......Page 501 E.1 Laplace Approximation......Page 505 E.2 Gauss-Hermite Integration......Page 506 E.3 Inversion of Pseudo-Fisher Matrix......Page 508 Examples......Page 509 Biblo......Page 512 Index......Page 544