Models for Analyzing Count Data with a Lot of Zeros

• Activity Number: 589
• Type: Topic Contributed
• Date/Time: Thursday, August 7, 2014 : 8:30 AM to 10:20 AM
• Sponsor: Health Policy Statistics Section
• Author(s): Dominique Lord and Srinivas Reddy Geedipally*+
• Companies: Texas A&M and Texas A&M Transportation Institute
• Keywords: negative binomial ; negative binomial-Lindley ; data with many zeros ; highly dispersed data ; 3-parameter models

Abstract

One important characteristic about crash data that has been documented in the literature is related to datasets that contained a large amount of zeros and a long or heavy tail (which creates highly dispersed data). For such datasets, the number of sites where no crash is observed is so large that traditional distributions and regression models, such as Poisson-gamma or negative binomial (NB) models cannot be used efficiently. To overcome this problem, zero-inflated (ZI) models have been proposed, but they suffer from an important methodological limitation, where one of the components has a long-term mean equal to zero. Recently, researchers have proposed distributions and/or regression models that can handle datasets with a lot of zeros, but do not have issues with a risk-free state. This presentation covers the characteristics of such models. They include the NB-Lindley (NB-L), the NB-crack (NB-CR), the Sichel (SI) and the NB-generalized exponential (NB-GE). Over the last two years, the NB-L has successfully, for example, been applied by highway safety analysts as a substitute to ZI models.