Spatial Regression Modeling for Compositional Data With Many Zeros
- 652 Downloads
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 northeastern United States. Here, the observations are vectors providing the proportions of LULC types observed in each 3 km×3 km grid cell, yielding order 104 cells. On the same grid cells, we have an additional compositional dataset supplying forest fragmentation proportions. Potentially useful and available covariates include elevation range, road length, population, median household income, and housing levels.
We propose a spatial regression model that is also able to capture flexible dependence among the components of the observation vectors at each location as well as spatial dependence across the locations of the simplex-restricted measurements. 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 at the second stage with spatial structure for these variables supplied through a multivariate CAR specification. Analyses for the LULC and forest fragmentation data illustrate the interpretation of the regression coefficients and the benefit of incorporating spatial smoothing.
Key WordsAreal data Conditionally autoregressive model Continuous ranked probability score Hierarchical modeling Markov chain Monte Carlo
Unable to display preview. Download preview PDF.
- Fry, J. A., Coan, M. J., Homer, C. G., Meyer, D. K., and Wickham, J. (2009), “Completion of the National Land Cover Database (NLCD) 1992–2001 Land Cover Change Retrofit Product,” U.S. Geological Survey Open-File Report 2008–1379, 18 p. Google Scholar
- Haslett, J., Whiley, M., Bhattacharya, S., Salter-Townshend, M., Wilson, S. P., Allen, J. R. M., Huntley, B., and Mitchell, F. J. G. (2006), “Bayesian Palaeoclimate Reconstruction,” Journal of the Royal Statistical Society. Series A. Statistics in Society, 169, 395–438. MathSciNetCrossRefGoogle Scholar
- Minnesota Population Center (2004), “National Historical Geographic Information System: Pre-release Version, 0.1,” University of Minnesota, Minneapolis, MN, available at: http://www.nhgis.org/.
- National Oceanic Atmospheric Administration (2006), “Coastal Change Analysis Program Land Cover,” available at: http://www.csc.noaa.gov/crs/lca/northeast.html.
- Parent, J., and Hurd, J. (2010), “Landscape Fragmentation Tool (LFT v2.0).” Center for Land Use Education and Research, available at: http://clear.uconn.edu/tools/lft/lft2/index.htm.
- Plummer, M., Best, N., Cowles, K., and Vines, K. (2006), “CODA: Convergence Diagnosis and Output Analysis for MCMC,” R News, 6, 7–11. Google Scholar
- R Core Team (2012), R: A Language and Environment for Statistical Computing, R Foundation for Statistical Computing: Vienna. ISBN:3-900051-07-0. Google Scholar
- Salter-Townshend, M., and Haslett, J. (2006), “Modelling Zero Inflation of Compositional Data,” in Proceedings of the 21st International Workshop on Statistical Modelling, pp. 448–456. Google Scholar
- Tsagris, M. T., Preston, S., and Wood, A.T. (2011), “A Data-Based Power Transformation for Compositional Data,” in Proceedings of CoDaWork: 4th International Workshop on Compositional Data Analysis, eds. J. Egozcue, R. Tolosana-Delgado, and M. Ortego. Google Scholar
- Unger, D. A. (1985), “A Method to Estimate the Continuous Ranked Probability Score,” in Preprints of the Ninth Conference on Probability and Statistics in Atmospheric Sciences, Virginia Beach, Virginia, Boston: American Meteorological Society, pp. 206–213. Google Scholar
- U.S. Census Bureau (2008), “TIGER/Line Shapefiles [machine-readable data files],” available at: http://www.census.gov/geo/maps-data/data/tiger.html.
- U.S. Geological Survey (1999), “National Elevation Dataset,” available at: http://nationalmap.gov/viewer.html.