Book contents
- Frontmatter
- Contents
- List of Figures
- List of Tables
- Preface
- 1 Introduction
- 2 Model Specification and Estimation
- 3 Basic Count Regression
- 4 Generalized Count Regression
- 5 Model Evaluation and Testing
- 6 Empirical Illustrations
- 7 Time Series Data
- 8 Multivariate Data
- 9 Longitudinal Data
- 10 Measurement Errors
- 11 Nonrandom Samples and Simultaneity
- 12 Flexible Methods for Counts
- Appendices
- References
- Author Index
- Subject Index
- Titles in the series
2 - Model Specification and Estimation
Published online by Cambridge University Press: 05 January 2013
- Frontmatter
- Contents
- List of Figures
- List of Tables
- Preface
- 1 Introduction
- 2 Model Specification and Estimation
- 3 Basic Count Regression
- 4 Generalized Count Regression
- 5 Model Evaluation and Testing
- 6 Empirical Illustrations
- 7 Time Series Data
- 8 Multivariate Data
- 9 Longitudinal Data
- 10 Measurement Errors
- 11 Nonrandom Samples and Simultaneity
- 12 Flexible Methods for Counts
- Appendices
- References
- Author Index
- Subject Index
- Titles in the series
Summary
Introduction
The general modeling approaches most often used in count data analysis – likelihood-based, generalized linear models, and moment-based – are presented in this chapter. Statistical inference for these nonlinear regression models is based on asymptotic theory, which is also summarized.
The models and results vary according to the strength of the distributional assumptions made. Likelihood-based models and the associated maximum likelihood estimator require complete specification of the distribution. Statistical inference is usually performed under the assumption that the distribution is correctly specified.
A less parametric analysis assumes that some aspects of the distribution of the dependent variable are correctly specified while others are not specified, or if specified are potentially misspecified. For count data models considerable emphasis has been placed on analysis based on the assumption of correct specification of the conditional mean, or on the assumption of correct specification of both the conditional mean and the conditional variance. This is a nonlinear generalization of the linear regression model, where consistency requires correct specification of the mean and efficient estimation requires correct specification of the mean and variance. It is a special case of the class of generalized linear models, widely used in the statistics literature. Estimators for generalized linear models coincide with maximum likelihood estimators if the specified density is in the linear exponential family. But even then the analytical distribution of the same estimator can differ across the two approaches if different second moment assumptions are made.
- Type
- Chapter
- Information
- Regression Analysis of Count Data , pp. 19 - 58Publisher: Cambridge University PressPrint publication year: 1998