Small area estimation using multilevel models - ARCHIVED

In this paper a general multilevel model framework is used to provide estimates for small areas using survey data. This class of models allows for variation between areas because of: (i) differences in the distributions of unit level variables between areas, (ii) differences in the distribution of area level variables between areas (iii) area specific components of variance which make provision for additional local variation which cannot be explained by unit-level or area-level covariates. Small area estimators are derived for this multilevel model formulation and an approximation to the mean square error (MSE) of each small area estimates for this general class of mixed models is provided together with an estimator of this MSE. Both the approximations to the MSE and the estimator of MSE take into account three sources of variation: (i) the prediction MSE assuming that both the fixed and components of variance terms in the multilevel model are knows, (ii) the additional component due to the fact that the fixed coefficients must be estimated, and (iii) the further component due to the fact that the components of variance in the model must be estimated. The proposed methods are estimated using a large data set as a basis for numerical investigation. The results confirm that the extra components of variance contained in multilevel models as well as small area covariates can improve small area estimates and that the MSE approximation and estimator are satisfactory.