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Comparison of Poisson and Quasi-Poisson Regression: A Simulation study

Poisson regression is often used to model count data. However, it requires the assumption of equidispersion which not always met in the real application data. Quasi-Poisson can be considered as an alternative to handle this problem. The objective of this essay is to explain about the Quasi-Poisson regression, the likelihood construction, parameter estimation, and its implementation in real life data. The numerical method used in this study is Newton-Raphson which is equivalent to Iterative Weighted Least Square (IWLS) at the end of calculation. The simulation results for the data with the above problem showed that, in case of overdispersion, Quasi-Poisson regression with Maximum Quasi-Likelihood method provided a good fit to the data compared to Poisson regression.