Modeling Mixtures of Three States of a Count Process: A Zero-State and Two Poisson Count States

• Activity Number: 3
• Type: Invited
• Date/Time: Sunday, August 3, 2008 : 2:00 PM to 3:50 PM
• Sponsor: Section on Statistics and the Environment
• Author(s): Mary C. Christman*+
• Companies: University of Florida
• Keywords: Poisson Process ; spatial models ; zero-inflation

Abstract

In conservation biology it is important to identify spatial regions with both high biodiversity and endemics (species found only in one place). When species richness is low, usually due to detectability issues, the unobserved true diversity needs to be predicted in order to develop appropriate management plans. We develop an extension to the zero-inflated Poisson regression model that simultaneously models the counts as a mixture of three processes: a zero state, a Poisson count state for the majority of observations, and a second Poisson count state for the very high species richness counts. The estimators of the regression coefficients are obtained using a Bayesian hierarchical approach with non-informative priors. We show that this approach has better predictive capability than the two-part zero-inflated count model and elucidates the underlying mechanisms determining diversity.