Spatial Regression Modeling for Compositional Data with Many Zeros

• Activity Number: 345
• Type: Topic Contributed
• Date/Time: Tuesday, August 6, 2013 : 10:30 AM to 12:20 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Thomas Leininger*+ and Alan E. Gelfand and Jenica Allen and John Silander, Jr.
• Companies: Duke University and Duke University and University of Connecticut and University of Connecticut
• Keywords: areal data ; conditionally autoregressive model ; continuous ranked probability score ; hierarchical modeling ; Markov Chain Monte Carlo

Abstract

Compositional data analysis considers vectors of nonnegative-valued variables subject to a unit-sum constraint. Our interest lies in spatial compositional data, in particular, land use/land cover (LULC) data in the northeast United States. Here, the observations are vectors providing the proportions of LULC types observed in each 3km x 3km grid cell. On the same grid cells, we have an additional compositional dataset supplying forest fragmentation proportions. Potentially useful covariates include elevation range, population, median household income, and housing levels. We propose a spatial regression model that captures flexible dependence among the components of the observation at each location and spatial dependence across the locations. A key issue is the high incidence of observed zero proportions for the LULC dataset, requiring incorporation of local point masses at 0. We build a hierarchical model prescribing a power scaling first stage and using latent variables with spatial dependence at the second stage. Analyses for the LULC and forest fragmentation data illustrate the interpretation of the regression coefficients and the benefit of incorporating spatial smoothing.