Poisson regression is one of a number of regression models for dependent variables that are counts (non-negative integers). A more general model is negative binomial regression. Both have numerous variants.
Poisson regression is a regression in which the dependent variable is a count variable. The Poisson regression is a based on the Poisson distribution. In order to apply the Poisson Regression the Equidispersion Property has to be fulfilled: E[X] = Var[X]. If the Equidispersion Property is not fulfilled the Negative Binomial Regression might be a better approach.
Common variants of the Poisson regression are:
- Zero-inflated Poisson Regression
The dependent variable is a count variable, but many values take on the variable 0.
- Hurdle model with a Poisson hurdle
The dependent variable is a count variable, but many values take on the variable 0. In contrast to the Zero-Inflated Poisson Regression this is a two step procedure with a hurdle process (e.g. Probit hurdle) and a Poisson regression.
- Zero-truncated Poisson
The dependent variable is a count variable which can never take on the variable 0. An example are the number of days a person stays in hospital.
Literature:
Greene, William H. (2003). Econometric Analysis (Fifth ed.). Prentice-Hall. pp. 740–752. ISBN 0130661899.
Paternoster R, Brame R (1997). "Multiple routes to delinquency? A test of developmental and general theories of crime". Criminology. 35: 45–84. doi:10.1111/j.1745-9125.1997.tb00870.x.
Berk R, MacDonald J (2008). "Overdispersion and Poisson regression" (PDF). Journal of Quantitative Criminology. 24 (3): 269–284. doi:10.1007/s10940-008-9048-4.
Ver Hoef, JAY M.; Boveng, Peter L. (2007-01-01). "Quasi-Poisson vs. Negative Binomial Regression: How should we model overdispersed count data?". Ecology. 88 (11): 2766–2772. Retrieved 2016-09-01. Further reading[edit]
Cameron, A. C.; Trivedi, P. K. (1998). Regression analysis of count data. Cambridge University Press. ISBN 0-521-63201-3.
Christensen, Ronald (1997). Log-linear models and logistic regression. Springer Texts in Statistics (Second ed.). New York: Springer-Verlag. ISBN 0-387-98247-7. MR 1633357.
Gouriéroux, Christian (2000). "The Econometrics of Discrete Positive Variables: the Poisson Model". Econometrics of Qualitative Dependent Variables. New York: Cambridge University Press. pp. 270–83. ISBN 0-521-58985-1.
Greene, William H. (2008). "Models for Event Counts and Duration". Econometric Analysis (8th ed.). Upper Saddle River: Prentice Hall. pp. 906–944. ISBN 978-0-13-600383-0.
Hilbe, J. M. (2007). Negative Binomial Regression. Cambridge University Press. ISBN 978-0-521-85772-7.
Jones, Andrew M.; et al. (2013). "Models for count data". Applied Health Economics. London: Routledge. pp. 295–341. ISBN 978-0-415-67682-3.
Wooldridge, J. M. (2002). Econometric analysis of cross section and panel data. Cambridge, Mass: MIT Press. p. 646-656.
Cameron, A. C. and Trivedi, P. K. 2009. Microeconometrics Using Stata. College Station, TX: Stata Press.
Cameron, A. C. and Trivedi, P. K. 1998. Regression Analysis of Count Data. New York: Cambridge Press.
Cameron, A. C. Advances in Count Data Regression Talk for the Applied Statistics Workshop, March 28, 2009. http://cameron.econ.ucdavis.edu/racd/count.html .
Dupont, W. D. 2002. Statistical Modeling for Biomedical Researchers: A Simple Introduction to the Analysis of Complex Data. New York: Cambridge Press.
Long, J. S. 1997. Regression Models for Categorical and Limited Dependent Variables. Thousand Oaks, CA: Sage Publications.
Long, J. S. and Freese, J. 2006. Regression Models for Categorical Dependent Variables Using Stata, Second Edition. College Station, TX: Stata Press.
Software implementations:
- Rodriguez, G., Poisson Model in Stata. Princeton University.
- Rodriguez, G., Poisson Model in R. Princeton University.
- Some useful examples from UCLA with Code in Stata, SAS, SPSS, MPlus and R
gmmcommand in Stata
