The Poisson regression model
- Count data:
- Regressors: \mathbf
Equation (2.1) is the pdf of the Poisson distribution with mean .
The model implies that the conditional mean is given by
The standard estimator for the Poisson regression model is the MLE. The log-likelihood function is
Similar to OLS, inference can be performed under assumptions about just the mean and possibly variance.
Because Equation 2.3 implies that , we can define an estimator that is the solution to the Equation 2.6, the corresponding moment condition in the sample.
- Cameron, A.C. and Trivedi, P.K. (2013) Regression Analysis of Count Data. 2nd edn. Cambridge: Cambridge University Press (Econometric Society Monographs). doi:10.1017/CBO9781139013567.