List of Figures
List of Tables
Preface
Preface to the First Edition
1 Introduction
1.1 Poisson Distribution and Its Characterizations
1.2 Poisson Regression
1.3 Examples
1.4 Overview of Major Issues
1.5 Bibliographic Notes
2 Model Specification and Estimation
2.1 Introduction
2.2 Example and Definitions
2.3 Likelihood-Based Models
2.4 Generalized Linear Models
2.5 Moment-Based Models
2.6 Testing
2.7 Robust Inference
2.8 Derivation of Results
2.9 Bibliographic Notes
2.10 Exercises
3 Basic Count Regression
3.1 Introduction
3.2 Poisson MLE, QLME, and GLM
3.3 Negative Binomial MLE and QGPMLE
3.4 Overdispersion Tests
3.5 Use of Regression Results
3.6 Ordered and Other Discrete-Outcome Models
3.7 Other Models
3.8 Iteratively Reweighted Least Squares
3.9 Bibliographic Notes
3.10 Exercises
4 Generalized Count Regression
4.1 Introduction
4.2 Mixture Models
4.3 Truncated Counts
4.4 Censored Counts
4.5 Hurdle Models
4.6 Zero-Inflated Count Models
4.7 Hierarchical Models
4.8 Finite Mixtures and Latent Class Analysis
4.9 Count Models with Cross-Sectional Dependence
4.10 Models Based on Waiting Time Distributions
4.11 Katz, Double Poisson, and Generalized Poisson
4.12 Derivations
4.13 Bibliographic Notes
4.14 Exercises
5 Model Evaluation and Testing
5.1 Introduction
5.2 Residual Analysis
5.3 Goodness of Fit
5.4 Discriminating among Nonnested Models
5.5 Tests for Overdispersion
5.6 Conditional Moment Specification Tests
5.7 Derivations
5.8 Bibliographic Notes
5.9 Exercises
6 Empirical Illustrations
6.1 Introduction
6.2 Background
6.3 Analysis of Demand for Health Care
6.4 Analysis of Recreational Trips
6.5 Analysis of Fertility Data
6.6 Model Selection Criteria: A Digression
6.7 Concluding Remarks
6.8 Bibliographic Notes
6.9 Exercises
7 Time Series Data
7.1 Introduction
7.2 Models for Time Series Data
7.3 Static Count Regression
7.4 Serially Correlated Heterogeneity Models
7.5 Autoregressive Models
7.6 Integer-Valued ARMA Models
7.7 State Space Models
7.8 Hidden Markov Models
7.9 Dynamic Ordered Probit Model
7.10 Discrete ARMA Models
7.11 Applications
7.12 Derivations
7.13 Bibliographic Notes
7.14 Exercises
8 Multivariate Data
8.1 Introduction
8.2 Characterizing and Generating Dependence
8.3 Sources of Dependence
8.4 Multivariate Count Models
8.5 Copula-Based Models
8.6 Moment-Based Estimation
8.7 Testing for Dependence
8.8 Mixed Multivariate Models
8.9 Empirical Example
8.10 Derivations
8.11 Bibliographic Notes
9 Longitudinal Data
9.1 Introduction
9.2 Models for Longitudinal Data
9.3 Population Averaged Models
9.4 Fixed Effects Models
9.5 Random Effects Models
9.6 Discussion
9.7 Specification Tests
9.8 Dynamic Longitudinal Models
9.9 Endogenous Regressors
9.10 More Flexible Functional Forms for Longitudinal Data
9.11 Derivations
9.12 Bibliographic Notes
9.13 Exercises
10 Endogenous Regressors and Selection
10.1 Introduction
10.2 Endogeneity in Recursive Models
10.3 Selection Models for Counts
10.4 Moment-Based Methods for Endogenous Regressors
10.5 Example: Doctor Visits and Health Insurance
10.6 Selection and Endogeneity in Two-Part Models
10.7 Alternative Sampling Frames
10.8 Bibliographic Notes
11 Flexible Methods for Counts
11.1 Introduction
11.2 Flexible Distributions Using Series Expansions
11.3 Flexible Models of the Conditional Mean
11.4 Flexible Models of the Conditional Variance
11.5 Quantile Regression for Counts
11.6 Nonparametric Methods
11.7 Efficient Moment-Based Estimation
11.8 Analysis of Patent Counts
11.9 Derivations
11.10 Bibliographic Notes
12 Bayesian Methods for Counts
12.1 Introduction
12.2 Bayesian Approach
12.3 Poisson Regression
12.4 Markov Chain Monte Carlo Methods
12.5 Count Models
12.6 Roy Model for Counts
12.7 Bibliographic Notes
13 Measurement Errors
13.1 Introduction
13.2 Measurement Errors in Regressors
13.3 Measurement Errors in Exposure
13.4 Measurement Errors in Counts
13.5 Underreported Counts
13.6 Underreported and Overreported Counts
13.7 Simulation Example: Poisson with Mismeasured Regressor
13.8 Derivations
13.9 Bibliographic Notes
13.10 Exercises
A Notation and Acronyms
B Functions, Distributions, and Moments
B.1 Gamma Function
B.2 Some Distributions
B.3 Moments of Truncated Poisson
C Software
References
Author Index
Subject Index
