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The Conway-Maxwell-Poisson (CMP) or COM-Poison regression is a popular modelfor count data due to its ability to capture both under dispersion and overdispersion. However, CMP regression is limited when dealing with complexnonlinear relationships. With today's wide availability of count data,especially due to the growing collection of data on human and social behavior,there is need for count data models that can capture complex nonlinearrelationships. One useful approach is additive models; but, there has been noadditive model implementation for the CMP distribution. To fill this void, wefirst propose a flexible estimation framework for CMP regression based oniterative reweighed least squares (IRLS) and then extend this model to allowfor additive components using a penalized splines approach. Because the CMPdistribution belongs to the exponential family, convergence of IRLS isguaranteed under some regularity conditions. Further, it is also known thatIRLS provides smaller standard errors compared to gradient-based methods. Weillustrate the usefulness of this approach through extensive simulation studiesand using real data from a bike sharing system in Washington, DC.

Efficient Estimation of COM-Poisson Regression and Generalized Additive Model