Estimation of small-area proportions using covariates and survey data

Data gathered in surveys often are used to estimate characteristics for subsets of the survey population. If the sample from a subset is small, then a traditional design-based survey estimator may have unacceptably large variance. Small-area estimation reduces the variance of estimators by "borrowing strength" across subsets. Here we compare estimators based on two models, one that uses simple geographic clustering and demographic data and one that uses more elaborate covariate information that relates subsets to one another. Data are from a survey conducted by the Gallup Organization. The methods incorporate survey weight information and are appropriate for rare events. Empirical Bayes estimation techniques are used. Covariates for the second model are selected in a step-wise manner until addition of another covariate does not yield a decrease in an objective criterion.