Multivariate Small Area Estimation of Social Indicators: the Case of Continuous and Binary Variables

Large-scale sample surveys are not designed to produce reliable estimates for small areas. Here, small area estimation methods can be applied to estimate population parameters of target variables to detailed geographic scales. Small area estimation for noncontinuous variables is a topic of great interest in the social sciences where such variables can be found. Generalized linear mixed models are widely adopted in the literature. Interestingly, the small area estimation literature shows that multivariate small area estimators, where correlations among outcome variables are taken into account, produce more efficient estimates than do the traditional univariate techniques. In this article, the author evaluate a multivariate small area estimator on the basis of a joint mixed model in which a small area proportion and mean of a continuous variable are estimated simultaneously. Using this method, the author “borrows strength” across response variables. The author carried out a design-based simulation study to evaluate the approach where the indicators object of study are the income and a monetary poverty (binary) indicator. The author found that the multivariate approach produces more efficient small area estimates than does the univariate modeling approach. The method can be extended to a large variety of indicators on the basis of social surveys.