### COM-Poisson Models

Organizer: Galit Shmueli, University of MarylandSession Chair: Sarah J. Thomas, Rice University

**A Data Disclosure Policy for Count Data Based on the COM-Poisson Distribution**

Galit Shmueli

University of Maryland

Count data arise in various organizational settings. When the release of such data is sensitive, organizations need information-disclosure policies that protect data confidentiality while still providing data access. In contrast to extant disclosure policies, we describe a novel policy for count tables that is based on disclosing only the sufficient statistics of a flexible discrete distribution, the COM-Poisson. The COM-Poisson distribution is a two-parameter generalization of the Poisson distribution, which generalizes some well-known discrete distributions (Poisson, Bernoulli and geometric), allows for over- and under-dispersion, and belongs to the exponential family in both parameters. We briefly introduce the distribution, its properties, and estimation methods. We then describe a data disclosure policy for count tables based on the COM-Poisson

**Regression Models for Count Data with Constant or Observation-Level Dispersion**

Kimberly Sellers

Georgetown University

While Poisson regression is a popular tool for modeling count data, it is limited by its associated model assumptions, particularly that the response variable follows a Poisson distribution. However, over- or under-dispersion are common in practice and are not accommodated by Poisson regression. In addition, the dispersion is assumed fixed across observations, whereas in practice dispersion can vary across groups or according to some other factor. This talk will introduce an alternative regression model for count data, namely the Conway-Maxwell-Poisson (COM-Poisson) regression, based on the COM-Poisson distribution. COM-Poisson regression generalizes both Poisson and logistic regression models, and allows for over- or under-dispersed count data. The associated model structure will allow for either fixed or observation-level dispersion. We discuss model estimation, inference, diagnostics, and interpretation, and present a variable selection technique. We then compare our model to several alternatives and illustrate its advantages and usefulness using datasets with varying types and levels of dispersion.

**Marketing Applications of the COM-Poisson**

Sharad Borle

Rice University

The COM-Poisson distribution (Shmueli et al 2005), a generalization of the Poisson which accommodates both over dispersion as well as under dispersion with respect to the Poisson has found applications in modeling data in the Marketing literature. This talk discusses some applications of the COM-Poisson distribution across Marketing applications. All these applications are in the context of Bayesian models in Marketing. Of particular interest are some applications where the ability of the COM-Poisson to model under as well as over-dispersed data becomes useful.