B0875
Title: Spatial Bayesian hierarchical model for small area estimation of proportions with constraint
Authors: Zhengyuan Zhu - Iowa State University (United States) [presenting]
Abstract: Motivated by the need to produce small area estimates for the National Resources Inventory survey, we develop a spatial hierarchical Bayesian model based on a generalized Dirichlet distribution 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 used to obtain more efficient predictors. At the observation level, the standard survey estimators of the proportions are assumed to follow the generalized Dirichlet (GD) distribution. After proper transformation of the survey 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 random effects with spatial structure through a conditionally autoregressive (CAR) process. Three special cases of the Bayesian hierarchical model, with different random effects structures, are compared using Bayesian model comparisons tools. In the application, the survey data are from the National Resources Inventory survey, and the covariate is derived from the Cropland Data Layer (CDL), a land cover map based on satellite data. In a design-based evaluation study, the Bayesian estimators are shown to have smaller relative root mean squared error than direct estimators.
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