Small area estimation using multilevel models

Moura, Fernando Antonio da Silva (1994) Small area estimation using multilevel models. University of Southampton, Doctoral Thesis.

Abstract

Mixed Models have been shown to be useful for improving the efficiency of the small area estimates. Battese Harter and Fuller (1981) have proposed the random intercept model for making small area estimates. Prasad and Rao(1990) have studied model-based properties of some mixed linear small area estimators and provided approximate expression for the Mean Square Error (MSE) of each small area estimate and a corresponding MSE estimator. Model-based simulation studies (Prasad and Rao(1990) ) as well as design-based simulation studies (Ghosh and Rao(1993) ) show the superiority of mixed-models over conventional approaches.

The first aim of this thesis is to extend Prasad and Rao's(1990) results obtained for the random intercept model in two ways: (a) allowing all regression coefficients to be random and (b) introducing small area level auxiliary covariates which help to model the between area components of variance. Small area predictors are also provided together with an approximation to the MSE for each small area and an estimator for the MSE.

The second aim is to derive design-based precision measurements of the small area predictors and their corresponding estimators.

Model-based simulation studies carried out using real data sets show that the extra random components can improve the small area estimates and the MSE approximation is satisfactory. Further numerical results, within the repeated sampling framework demonstrate that underlying model assumptions are important and the use of small area level variables are preferable to explain some of the small area intra-class correlation rather than simply treating them as unexplained sources of variation. (DX184,267)

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