An application of a small area procedure with correlation between measurement error and sampling error to the Conservation Effects Assessment Project

TL;DR

This paper develops a small area estimation method for county-level erosion estimates, accounting for correlation between measurement error in covariates and sampling error, improving accuracy over traditional models.

Contribution

It introduces a novel small area model that incorporates correlation between measurement error and sampling error, with validation through simulations showing improved predictions.

Findings

Proposed predictor outperforms traditional models in simulations.

Accounting for measurement error correlation improves estimation accuracy.

Method is applicable when covariate data is estimated from the same survey.

Abstract

County level estimates of mean sheet and rill erosion from the Conservation Effects Assessment Project (CEAP) are useful for program development and evaluation. Since county sample sizes in the CEAP survey are insufficient to support reliable direct estimators, small area estimation procedures are needed. The quantity of water runoff is a useful covariate but is unavailable for the full population. We use an estimate of mean runoff from the CEAP survey as a covariate in a small area model with sheet and rill erosion as the response. As the runoff and sheet and rill erosion are estimators from the same survey, the measurement error in the covariate is important as is the correlation between the measurement error and the sampling error. We conduct a detailed investigation of small area estimation in the presence of a correlation between the measurement error in the covariate and the sampling error in the response. In simulations, the proposed predictor is superior to small area predictors that assume the response and covariate are uncorrelated or that ignore the measurement error entirely.