Book contents
- Frontmatter
- Contents
- Preface
- Introduction
- 1 Overview of count response models
- 2 Methods of estimation
- 3 Poisson regression
- 4 Overdispersion
- 5 Negative binomial regression
- 6 Negative binomial regression: modeling
- 7 Alternative variance parameterizations
- 8 Problems with zero counts
- 9 Negative binomial with censoring, truncation, and sample selection
- 10 Negative binomial panel models
- Appendix A Negative binomial log-likelihood functions
- Appendix B Deviance functions
- Appendix C Stata negative binominal – ML algorithm
- Appendix D Negative binomial variance functions
- Appendix E Data sets
- References
- Author Index
- Subject Index
9 - Negative binomial with censoring, truncation, and sample selection
Published online by Cambridge University Press: 05 June 2012
- Frontmatter
- Contents
- Preface
- Introduction
- 1 Overview of count response models
- 2 Methods of estimation
- 3 Poisson regression
- 4 Overdispersion
- 5 Negative binomial regression
- 6 Negative binomial regression: modeling
- 7 Alternative variance parameterizations
- 8 Problems with zero counts
- 9 Negative binomial with censoring, truncation, and sample selection
- 10 Negative binomial panel models
- Appendix A Negative binomial log-likelihood functions
- Appendix B Deviance functions
- Appendix C Stata negative binominal – ML algorithm
- Appendix D Negative binomial variance functions
- Appendix E Data sets
- References
- Author Index
- Subject Index
Summary
There are many times when certain data elements are lost, discarded, ignored, or are otherwise excluded from analysis. Truncated and censored models have been developed to deal with these types of data. Both models take two forms, truncation or censoring from below, and truncation or censoring from above. Count model forms take their basic logic from truncated and censored continuous response data, in particular from Tobit (Amemiya, 1984) and censored normal regression (Goldberger, 1983) respectively.
Count sample selection models also deal with data situations in which the distribution is confounded by an external condition. We shall address sample selection models at the end of the chapter.
The traditional parameterization used for truncated and censored count data can be called the econometric parameterization. This is the form of model discussed in standard econometric texts and is the form found in current econometric software implementations. I distinguish this from what I term a survival parameterization, the form of which is derived from standard survival models. This parameterization only relates to censored Poisson and censored negative binomial models. I shall first address the more traditional econometric parameterization. In addition, I shall not use subscripts for this chapter; they are understood as presented in the earlier chapters.
Censored and truncated models – econometric parameterization
Censored and truncated count models are related, with only a relatively minor algorithmic difference between the two. The essential difference relates to how response values beyond a user-defined cut point are handled.
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- Negative Binomial Regression , pp. 179 - 197Publisher: Cambridge University PressPrint publication year: 2007