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

Abstract

County level estimates of mean sheet and rill erosion from the Conservation Effects Assessment Project (CEAP) survey are useful for program development and evaluation. As a result of small county sample sizes, small area estimation procedures are needed.One variable that is related to sheet and rill erosion is the quantity of water runoff. The runoff is collected in the CEAP survey 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 for sheet and rill erosion. 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. The proposed methodology has a genuine need in CEAP, where the same survey that supplies the response also provides auxiliary information. 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. We conclude with practical recommendations.