2016/10/26 by Suneel Babu Chatla, Galit Shmueli, Chatla, Suneel Babu +1
Mathematics · Computer Science · #Statistical Methods and Bayesian Inference #Statistical Methods and Inference #Bayesian Methods and Mixture Models
paper · pdf · doi:10.48550/arxiv.1610.08244
The Conway-Maxwell-Poisson (CMP) or COM-Poison regression is a popular model\nfor count data due to its ability to capture both under dispersion and over\ndispersion. However, CMP regression is limited when dealing with complex\nnonlinear relationships. With today's wide availability of count data,\nespecially due to the growing collection of data on human and social behavior,\nthere is need for count data models that can capture complex nonlinear\nrelationships. One useful approach is additive models; but, there has been no\nadditive model implementation for the CMP distribution. To fill this void, we\nfirst propose a flexible estimation framework for CMP regression based on\niterative reweighed least squares (IRLS) and then extend this model to allow\nfor additive components using a penalized splines approach. Because the CMP\ndistribution belongs to the exponential family, convergence of IRLS is\nguaranteed under some regularity conditions. Further, it is also known that\nIRLS provides smaller standard errors compared to gradient-based methods. We\nillustrate the usefulness of this approach through extensive simulation studies\nand using real data from a bike sharing system in Washington, DC.\n