An error-components model for prediction of county crop areas using survey and satellite data
Knowledge of the area under different crops is important to the U.S. Department of Agriculture. Sample surveys have been designed to estimate crop areas for large regions, such as crop-reporting districts, individual states, and the United States as a whole. Predicting crop areas for small areas such as counties has generally not been attempted, due to a lack of available data from farm surveys for these areas. The use of satellite data in association with farm-level survey observations has been the subject of considerable research in recent years. This article considers (a) data for 12 Iowa counties, obtained from the 1978 June Enumerative Survey of the U.S. Department of Agriculture and (b) data obtained from land observatory satellites (LANDSAT) during the 1978 growing season. Emphasis is given to predicting the area under corn and soybeans in these counties. A linear regression model is specified for the relationship between the reported hectares of corn and soybeans within sample segments in the June Enumerative Survey and the corresponding satellite determination for areas under corn and soybeans. A nested-error model defines a correlation structure among reported crop hectares within the counties. Given this model, the mean hectares of the crop per segment in a county is defined as the conditional mean of reported hectares, given the satellite determinations and the realized (random) county effect. The mean hectares of the crop per segment is the sum of a fixed component, involving unknown parameters to be estimated and a random component to be predicted. Variance-component estimators in the nested-error model are defined, and the generalized least-squares estimators of the parameters of the linear model are obtained. Predictors of the mean crop hectares per segment are defined in terms of these estimators. An estimator of the variance of the error in the predictor is constructed, including terms arising from the estimation of the parameters of the model. Predictions of mean hectares of corn and soybeans per segment for the 12 Iowa counties are presented. Standard errors of the predictions are compared with those of competing predictors. The suggested predictor for the county mean crop area per segment has a standard error that is considerably less than that of the traditional survey regression predictor.