Although several methods exist to produce synthetic estimates none has been found to be uniformly superior. One well suited method uses a fitted regression model to predict quantitative characteristics of the area of interest. The dependent variable in such a model is the characteristic for which the small area estimate is to be obtained (dependency) while the explanatory variables are predictors available externally to the estimation process (e.g, age, sex, race, income, marital status, or living arrangement).
This approach has been widely used. The first detailed conceptual and empirical basis for the use of regression models for estimating population size was presented by Erickson (1973, 1974). Methods developed by Kalsbeek (1973) and Cohen et al. (1977) extended this idea. Gonzalez and Hoza (1978) applied Ericksen's regression method to the estimation of unemployment for selected Standard Metropolitan Areas, while Nicholls (1977) followed the regression method in estimating population sizes for Statistical Divisions in Queensland, Australia. Levy (1979) evaluated a regression-adjusted synthetic estimator. Royall (1977) introduced the prediction approach to small area estimation based on an assumed regression model. Holt (1979) and Laake (1979) have subsequently extended this prediction approach under several basic population models. DiGaetano and associates (1980) used synthetic and regression procedures to produce estimates at local levels using NHIS data. Heeringa (1982) examined the roles that a model may play in small area estimation based on sample survey data sets and discussed current perceptions of the strength and weaknesses of model-based small area estimation methods. Diffendal and colleagues (1983) used the synthetic and regression methods for small area adjustment methodologies applied to the 1980 Census. Unger and Weissert (1988), as previously noted, developed a regression-based technique for estimating state-level estimates of functionally dependent elderly.