Abstract:
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A spatial hierarchical Bayesian model based on a Generalized Dirichlet distribution is introduced to construct small area predictors of proportions in several mutually exclusive and exhaustive land cover classes. The standard survey estimators are judged unreliable at the county level due to small sample sizes, and the hierarchical model is an effort to obtain more efficient predictors. At the first level, the design based estimators of the proportions are assumed to follow the Generalized Dirichlet distribution (GD). After proper transformation of the design based estimators, beta regression is applicable. We consider a logit mixed model for the expectation of the beta distribution, which incorporates covariates through fixed effects and spatial structure through a conditionally autoregressive (CAR) process. In the application, the survey data are from the National Resources Inventory, a longitudinal monitoring survey, and the covariate is derived from the Cropland Data Layer (CDL), a land cover map based on satellite data. In a design based simulation study, the Bayesian estimators have smaller relative root mean squared error than design based estimators.
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