Many variables of interest in agricultural or economical surveys have skewed distributions and can equal zero. Our data are measures of sheet and rill erosion called Revised Universal Soil Loss Equation - 2 (RUSLE2). Small area estimates of mean RUSLE2 erosion are of interest. We use a zero-inflated lognormal mixed effects model for small area estimation. The model combines a unit-level lognormal model for the positive RUSLE2 responses with a unit-level logistic mixed effects model for the binary indicator that the response is nonzero. In the Conservation Effects Assessment Project (CEAP) data, counties with a higher probability of nonzero responses also tend to have a higher mean among the positive RUSLE2 values. We capture this property of the data through an assumption that the pair of random effects for a county are correlated. We develop empirical Bayes (EB) small area predictors and a bootstrap estimator of the mean squared error (MSE). In simulations, the proposed predictor is superior to simpler alternatives. We then apply the method to construct EB predictors of mean RUSLE2 erosion for South Dakota counties. To obtain auxiliary variables for the population of cropland in South Dakota, we integrate a satellite-derived land cover map with a geographic database of soil properties. We provide an R Shiny application called viscover (available at https://lyux.shinyapps.io/viscover/) to visualize the overlay operations required to construct the covariates. On the basis of bootstrap estimates of the mean square error, we conclude that the EB predictors of mean RUSLE2 erosion are superior to direct estimators.

中文翻译：

---

具有相关随机区域效应的零膨胀对数正态模型下的经验贝叶斯小区域预测

农业或经济调查中许多感兴趣的变量都有偏态分布，并且可能为零。我们的数据是片状和细沟侵蚀的测量，称为修订的通用土壤流失方程 - 2 (RUSLE2)。对平均 RUSLE2 侵蚀的小面积估计很有意义。我们使用零膨胀对数正态混合效应模型进行小区域估计。该模型将正 RUSLE2 响应的单位级对数正态模型与响应非零二元指标的单位级逻辑混合效应模型相结合。在保护效果评估项目 (CEAP) 数据中，非零响应概率较高的县也往往在 RUSLE2 正值中具有较高的平均值。我们通过假设一个县的一对随机效应是相关的来捕捉数据的这一特性。我们开发了经验贝叶斯 (EB) 小区域预测器和均方误差 (MSE) 的自举估计器。在模拟中，所提出的预测器优于更简单的替代方案。然后，我们应用该方法构建南达科他州各县平均 RUSLE2 侵蚀的 EB 预测因子。为了获得南达科他州农田人口的辅助变量，我们将卫星生成的土地覆盖图与土壤特性的地理数据库相结合。我们提供了一个名为 viscover 的 R Shiny 应用程序（可在 https://lyux.shinyapps.io/viscover/ 获取）来可视化构建协变量所需的覆盖操作。根据均方误差的 bootstrap 估计，我们得出结论，平均 RUSLE2 侵蚀的 EB 预测器优于直接估计器。