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There have been various studies in the literature on investigating the relationship between a count response and several covariates. Most researchers study count variables and use traditional methods (i.e. generalized linear models- GLM). However, GLM is limited when dealing with outliers and nonlinear relationships. Generalized Additive Models (GAM) is an extension of GLM, where the assumptions on the link functions and components are additive and smooth, respectively. Our aim is to propose a flexible extension of GLM and demonstrate the usefulness and performance of GAMs for the analysis of Poisson data set including outliers in the response variable through extensive Monte Carlo Simulations and using three applications.
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