Book contents
- Frontmatter
- Contents
- Preface to the second edition
- 1 Introduction
- 2 The concept of risk
- 3 Overview of count response models
- 4 Methods of estimation
- 5 Assessment of count models
- 6 Poisson regression
- 7 Overdispersion
- 8 Negative binomial regression
- 9 Negative binomial regression: modeling
- 10 Alternative variance parameterizations
- 11 Problems with zero counts
- 12 Censored and truncated count models
- 13 Handling endogeneity and latent class models
- 14 Count panel models
- 15 Bayesian negative binomial models
- Appendix A Constructing and interpreting interaction terms
- Appendix B Data sets, commands, functions
- References and further reading
- Index
12 - Censored and truncated count models
Published online by Cambridge University Press: 05 June 2012
- Frontmatter
- Contents
- Preface to the second edition
- 1 Introduction
- 2 The concept of risk
- 3 Overview of count response models
- 4 Methods of estimation
- 5 Assessment of count models
- 6 Poisson regression
- 7 Overdispersion
- 8 Negative binomial regression
- 9 Negative binomial regression: modeling
- 10 Alternative variance parameterizations
- 11 Problems with zero counts
- 12 Censored and truncated count models
- 13 Handling endogeneity and latent class models
- 14 Count panel models
- 15 Bayesian negative binomial models
- Appendix A Constructing and interpreting interaction terms
- Appendix B Data sets, commands, functions
- References and further reading
- 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.
The traditional parameterization used for truncated and censored count data can be called the econometric or cut-point 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.
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. Truncated models eliminate the values altogether; censored models revalue them to the value of the cut-point. In both cases the probability function and log-likelihood functions must be adjusted to account for the change in distribution of the response. We begin by considering truncation.
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- Information
- Negative Binomial Regression , pp. 387 - 406Publisher: Cambridge University PressPrint publication year: 2011