Flexible Regression Models for Dispersed Count Data

Speaker: Kimberly Sellers, Georgetown University

Abstract: Poisson regression is a popular tool for modeling count data and is applied in a vast array of disciplines. Real data, however, are often over- or under-dispersed relative to a Poisson model and, thus, are not conducive to Poisson regression. This talk introduces the Conway-Maxwell-Poisson (CMP) regression, which generalizes the well-known Poisson and logistic regressions, and is suitable for fitting count data with a wide range of dispersion levels. With a generalized linear model approach that takes advantage of exponential family properties, we discuss model estimation, inference, diagnostics, and interpretation, and present a test for determining the need for a CMP regression over a standard Poisson regression. Additional work considers the incorporation of a zero-inflated CMP model to address excess zeroes, broader model development via a sum-of-CMPs (SCMP) and a zero-inflated analog (ZISCMP) regression, and development of a CMP model to incorporate random effects for analysis of longitudinal count data. We demonstrate the models’ flexibility via simulated and real data examples, and (time permitting) the associated R package for such analyses.