Efficient Estimation of COM-Poisson Regression and Generalized Additive Model

TL;DR

This paper introduces a new efficient estimation method for COM-Poisson regression and extends it to additive models with nonlinear relationships, demonstrated through simulations and real-world data analysis.

Contribution

It develops a flexible IRLS-based estimation framework for CMP regression and introduces the first additive CMP model using penalized splines.

Findings

IRLS provides stable convergence and smaller standard errors.

The additive CMP model effectively captures complex nonlinear relationships.

Simulation and real data show improved modeling performance.

Abstract

The Conway-Maxwell-Poisson (CMP) or COM-Poison regression is a popular model for count data due to its ability to capture both under dispersion and over dispersion. However, CMP regression is limited when dealing with complex nonlinear 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 nonlinear relationships. One useful approach is additive models; but, there has been no additive model implementation for the CMP distribution. To fill this void, we first propose a flexible estimation framework for CMP regression based on iterative reweighed least squares (IRLS) and then extend this model to allow for additive components using a penalized splines approach. Because the CMP distribution belongs to the exponential family, convergence of IRLS is guaranteed under some regularity conditions. Further, it is also known that IRLS provides smaller standard errors compared to gradient-based methods. We illustrate the usefulness of this approach through extensive simulation studies and using real data from a bike sharing system in Washington, DC.