A Bottom-Up Approach for Ecological Inference

Abstract

The ecological inference canonical problem in the social sciences consists of estimating the unobserved internal counts of a global RxC table from the known margins of a set of units. This paper proposes a new, computation-based strategy designed to better exploit the information contained in the unit margins. This approach can be integrated into any ecological inference method that explicitly estimates unit tables and accounts for differences in unit size. We evaluate its performance using as a baseline the fastest ecological inference linear programming method, relying on real electoral data from over 550 datasets where true contingency tables are known. In this extensive assessment, the proposed strategy reduces average global errors by more than 21% relative to the baseline, outperforming it in 95% of cases. It also improves upon nslphom—identified in the literature as the most accurate algorithm for this dataset—reducing average global errors by over 5% and outperforming it in 60% of cases. The versatility of the approach is further illustrated by also integrating it into three more computationally intensive methods, including the two main statistical ecological inference models—ei.MD.bayes and BPF—and nslphom, yielding consistent improvements over their respective baselines in a small set of examples.