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Abstract 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 calledviscover(available athttps://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.
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This content will become publicly available on August 5, 2026
Accounting for Mismatch Error in Small Area Estimation with Linked Data
Abstract In small area estimation, different data sources are integrated in order to produce reliable estimates of target parameters (e.g., a mean or a proportion) for a collection of small subsets (areas) of a finite population. Regression models such as the linear mixed effects model or M-quantile regression are often used to improve the precision of survey sample estimates by leveraging auxiliary information for which means or totals are known at the area level. In many applications, the unit-level linkage of records from different sources is probabilistic and potentially error-prone. In this article, we present adjustments of the small area predictors that are based on either the linear mixed effects model or M-quantile regression to account for the presence of linkage error. These adjustments are developed from a two-component mixture model that hinges on the assumption of independence of the target and auxiliary variable given incorrect linkage. Estimation and inference is based on composite likelihoods and machinery revolving around the Expectation-Maximization Algorithm. For each of the two regression methods, we propose modified small area predictors and approximations for their mean squared errors. The empirical performance of the proposed approaches is studied in both design-based and model-based simulations that include comparisons to a variety of baselines.
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- Award ID(s):
- 2120318
- PAR ID:
- 10647989
- Publisher / Repository:
- Oxford University Press
- Date Published:
- Journal Name:
- Journal of Survey Statistics and Methodology
- ISSN:
- 2325-0984
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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