Regression analysis aims at modelling the relationship between dependent variable and explanatory variable(s). In regular regression models, the distribution of the dependent variable Y is assumed to be a continuous distribution especially normal distribution with mean zero and constant variance. However, there are many dependent variables that no matter how many transformations you try, you cannot get to be normally distributed such as count variables. Especially in actuarial science, biostatistics and demography we may be interested in the number of events that occur in a certain time period. Poisson regression model is used in these cases where the dependent variable Y is count or rate variables. Poisson regression model is a kind of generalized linear model. Therefore, the model parameter estimators are obtained by using maximum likelihood estimation. However, in general there are no closed form of solutions, so iterative methods are performed such as Newton-Raphson or iteratively reweighted least square method. In this study, we give general information about Poisson regression and other alternatives such as Negative binomial regression and Quasi-Poisson regression model. We also apply these models to an actuarial data related with insurance policy number and make a comparison with standard Ordinary Least Square Method (in transformed data).
Anahtar Kelimeler: Poisson Regression, Negative Binomial Regression, Quasi-Poisson Regression, Count Variable, Rate Variable