Empirical Bayes Small Area Prediction of Sheet and Rill Erosion Using a Zero-Inflated Lognormal Model

Abstract

In the Conservation Effects Assessment Project (CEAP), some of the variables are skewed right and have zeros. We proposed an empirical Bayes (EB) estimator for the Zero-inflated Log-normal model. We are also able to approximate the variance of the estimator by estimating the conditional variance. A Monte Carlo simulation is conducted to show the empirical properties of the EB predictor and its efficiency gain over the Plugin and Zero-ignored Minimum Mean Squared Error estimator. We also applied the method to the CEAP data of South Dakota, where there are about 15% zeros among the observed RUSLE2. The proposed method is applied to get the predicted population mean of rainfall-erosion losses from cropland at the county level for South Dakota. For data analysis, we overlaid soil map shapefile and Cropland Data Layer raster in R to obtain a list of cropland map units for South Dakota, which is our target population for small area prediction. A Shiny app visualizing the overlaying procedure is developed.