Alleviating Ecological Bias in Poisson Models Using Optimal Subsampling

Abstract

In many situations, data are available at some aggregate level, but one wishes to estimate the individual-level association between a response and an explanatory variable (or variables). Unfortunately, this endeavor is fraught with difficulties because of the ecological level of the data. The only reliable approach for overcoming the inherent identifiability problem associated with the analysis of ecological data is to supplement the ecological data with individual-level data. In this article, the authors illustrate the benefits of gathering individual-level data in the context of a Poisson modeling framework. Additionally, they derive optimal designs that allow the individual samples to be chosen so that information with respect to a particular model is maximized. The methods are illustrated using Robinson’s classic data on illiteracy rates. The authors show that the optimal design, if used with an appropriate model, produces accurate inference with respect to estimation of relative risks, with ecological bias removed.