Contents
List of Figures page xi
List of Tables xii
Preface xv
1 Introduction 1
1.1 Poisson Distribution 3
1.2 Poisson Regression 8
1.3 Examples 10
1.4 Overview of Major Issues 15
1.5 Bibliographic Notes 17
2 Model Specification and Estimation 19
2.1 Introduction 19
2.2 Example and Definitions 20
2.3 Likelihood-Based Models 22
2.4 Generalized Linear Models 27
2.5 Moment-Based Models 37
2.6 Testing 44
2.7 Derivations 50
2.8 Bibliographic Notes 57
2.9 Exercises 57
3 Basic Count Regression 59
3.1 Introduction 59
3.2 Poisson MLE, PMLE, and GLM 61
3.3 Negative binomial MLE and QGPMLE 70
3.4 Overdispersion Tests 77
3.5 Use of Regression Results 79
3.6 Ordered and Other Discrete-Choice Models 85
3.7 Other Models 88
3.8 Iteratively Reweighted Least Squares 93
3.9 Bibliographic Notes 94
3.10 Exercises 95
viii Contents
4 Generalized Count Regression 96
4.1 Introduction 96
4.2 Mixture Models for Unobserved Heterogeneity 97
4.3 Models Based on Waiting-Time Distributions 106
4.4 Katz, Double-Poisson, and Generalized Poisson 112
4.5 Truncated Counts 117
4.6 Censored Counts 121
4.7 Hurdle and Zero-Inflated Models 123
4.8 Finite Mixtures and Latent Class Analysis 128
4.9 Estimation by Simulation 134
4.10 Derivations 135
4.11 Bibliographic Notes 136
4.12 Exercises 137
5 Model Evaluation and Testing 139
5.1 Introduction 139
5.2 Residual Analysis 140
5.3 Goodness of Fit 151
5.4 Hypothesis Tests 158
5.5 Inference with Finite Sample Corrections 163
5.6 Conditional Moment Specification Tests 168
5.7 Discriminating among Nonnested Models 182
5.8 Derivations 185
5.9 Bibliographic Notes 187
5.10 Exercises 188
6 Empirical Illustrations 189
6.1 Introduction 189
6.2 Background 190
6.3 Analysis of Demand for Health Services 192
6.4 Analysis of Recreational Trips 206
6.5 LR Test: A Digression 216
6.6 Concluding Remarks 218
6.7 Bibliographic Notes 219
6.8 Exercises 220
7 Time Series Data 221
7.1 Introduction 221
7.2 Models for Time Series Data 222
7.3 Static Regression 226
7.4 Integer-Valued ARMA Models 234
7.5 Autoregressive Models 238
7.6 Serially Correlated Error Models 240
7.7 State-Space Models 242
7.8 Hidden Markov Models 244
7.9 Discrete ARMA Models 245
7.10 Application 246
Contents ix
7.11 Derivations: Tests of Serial Correlation 248
7.12 Bibliographic Notes 250
7.13 Exercises 250
8 Multivariate Data 251
8.1 Introduction 251
8.2 Characterizing Dependence 252
8.3 Parametric Models 256
8.4 Moment-Based Estimation 260
8.5 Orthogonal Polynomial Series Expansions 263
8.6 Mixed Multivariate Models 269
8.7 Derivations 272
8.8 Bibliographic Notes 273
9 Longitudinal Data 275
9.1 Introduction 275
9.2 Models for Longitudinal Data 276
9.3 Fixed Effects Models 280
9.4 RandomEffects Models 287
9.5 Discussion 290
9.6 Specification Tests 293
9.7 Dynamic and Transition Models 294
9.8 Derivations 299
9.9 Bibliographic Notes 300
9.10 Exercises 300
10 Measurement Errors 301
10.1 Introduction 301
10.2 Measurement Errors in Exposure 302
10.3 Measurement Errors in Regressors 307
10.4 Measurement Errors in Counts 309
10.5 Underreported Counts 313
10.6 Derivations 323
10.7 Bibliographic Notes 324
10.8 Exercises 325
11 NonrandomSamples and Simultaneity 326
11.1 Introduction 326
11.2 Alternative Sampling Frames 326
11.3 Simultaneity 331
11.4 Sample Selection 336
11.5 Bibliographic Notes 343
12 Flexible Methods for Counts 344
12.1 Introduction 344
12.2 Efficient Moment-Based Estimation 345
12.3 Flexible Distributions Using Series Expansions 350
12.4 Flexible Models of Conditional Mean 356
x Contents
12.5 Flexible Models of Conditional Variance 358
12.6 Example and Model Comparison 364
12.7 Derivations 367
12.8 Count Models: Retrospect and Prospect 367
12.9 Bibliographic Notes 369
Appendices:
A Notation and Acronyms 371
B Functions, Distributions, and Moments 374
B.1 Gamma Function 374
B.2 Some Distributions 375
B.3 Moments of Truncated Poisson 376
C Software 378
References 379
Author Index 399
Subject Index 404