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D. James Greiner & Kevin M. Quinn, R x C Ecological Inference: Bounds, Correlations, Flexibility, and Transparency of Assumptions, 172 J. Royal Stat. Soc’y: Series A (Stat. in Soc'y) 67 (2009).

Abstract: Despite its potential pitfalls, ecological inference is an unavoidable part of some quantitative settings, including US voting rights litigation. In such applications, the analyst will typically encounter two-way tables with more than two rows and columns. Although several ecological inference methods are currently available for 2×2 tables, there are fewer options for analysing general R×C tables, and virtually none that model counts as opposed to fractions. We propose a count R×C method that respects the bounds deterministically, that allows for complex relationships between internal cell quantities, that is easily extensible and that results from transparent assumptions. We study the method via simulation, and then apply it to an example that is drawn from the state of Texas relevant to recent redistricting litigation there.