### GEORGE MASON
UNIVERSITY

DEPARTMENT OF MATHEMATICAL
SCIENCES

COLLOQUIUM

SEPTEMBER 11, 2015

**Speaker: **
Kimberly Sellers, Georgetown University

**Title: ***
A flexible regression model for count data
*

**Abstract:**
Poisson regression is a popular tool for modeling count data and is applied in a vast array of applications from the social to the physical sciences and beyond. Real data, however, are often over- or under-dispersed (i.e. the variance is greater or less the mean) and, thus, not conducive to Poisson regression. Meanwhile, excess zeroes are often thought of as a cause of data over-dispersion, yet this claim is not entirely accurate. While this results in an increased chance for data over-dispersion, the implication is not guaranteed. Thus, one should consider a flexible distribution that not only can account for excess zeroes, but can also address potential over- or under-dispersion. We propose a regression model based on the Conway-Maxwell-Poisson (COM-Poisson or CMP) distribution to address this problem. The CMP regression generalizes the well-known Poisson and logistic regression models, and is suitable for fitting count data with a wide range of dispersion levels. With a GLM 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. We compare the CMP to several alternatives and illustrate its advantages and usefulness through various data examples. Meanwhile, to address excess zeroes, we have a zero-inflated Conway-Maxwell-Poisson (ZICMP) regression to model the relationship between explanatory and response variables. This talk illustrates its flexibility, and extrapolates the corresponding likelihood ratio test for the presence of significant data dispersion, and highlights various statistical properties and model fit.

**Time:** Friday, September 11, 2015, 3:30-4:20 p.m.

**Place:** Exploratory Hall, room 4106

**Refreshments** will be served at 3:00 p.m.

Department of Mathematical Sciences

George Mason University

4400 University Drive, MS 3F2

Fairfax, VA 22030-4444

http://math.gmu.edu/

Tel. 703-993-1460, Fax. 703-993-1491