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:

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