Construction of Databases for Small Area Estimation

Abstract

The demand for small area estimates can conflict with the objective of producing a multi-purpose data set. We use donor imputation to construct a database that supports small area estimation. Appropriately weighted sums of observed and imputed values produce model-based small area estimates. We develop imputation procedures for both unit-level and area-level models. For area-level models, we restrict to linear models. We assume a single vector of covariates is used for a possibly multivariate response. Each record in the imputed data set has complete data, an estimation weight, and a set of replicate weights for mean square error (MSE) estimation. We compare imputation procedures based on area-level models to those based on unit-level models through simulation. We apply the methods to the Iowa Seat-Belt Use Survey, a survey designed to produce state-level estimates of the proportions of vehicle occupants who wear a seat-belt. We develop a bivariate unit-level model for prediction of county-level proportions of belted drivers and total occupants. We impute values for the proportions of belted drivers and vehicle occupants onto the full population of road segments in the sampling frame. The resulting imputed data set returns approximations for the county-level predictors based on the bivariate model.