EcolRxC: Ecological inference estimation of R × C tables using latent structure approaches

Abstract

Abstract Ecological inference is a statistical technique used to infer individual behavior from aggregate data. A particularly relevant instance of ecological inference involves the estimation of the inner cells of a set of R × C related contingency tables when only their aggregate margins are known. This problem spans multiple disciplines, including quantitative history, epidemiology, political science, marketing, and sociology. This paper proposes new models for solving the problem using the latent structure theory, and presents the ecolRxC package, an R implementation of this methodology. This article exemplifies, explains, and statistically documents the new extensions and, using real inner cell election data, shows how the new models in ecolRxC lead to significantly more accurate solutions than ecol and VTR, two Stata routines suggested within this framework. ecolRxC also holds its own against ei.MD.bayes and nslphom, the two algorithms currently identified in the literature as the most accurate to solve this problem. ecolRxC records accuracies as good as those reported for ei.MD.bayes and nslphom. Besides, from a theoretical perspective, ecolRxC stands up for modeling a causal theory of political behavior to build its algorithm. This distinguishes it from other procedures proposed from different frameworks (such as ei.MD.bayes and nslphom) which model expected behaviors, instead of modeling how voters make choices based on their underlying preferences as ecolRxC does.