A local convergent ecological inference algorithm for RxC tables

Abstract

ABSTRACT Over the years, a number of methods have been proposed to forecast the unknown inner-cell values of a set of related RxC contingency tables when only their margins are known. This is a classical problem that emerges in many areas, from economics to quantitative history, being particularly ubiquitous when dealing with electoral data in sociology and political science. However, the two current major algorithms to solve this problem, based on Bayesian statistics and iterative linear programming depend on adjustable (hyper-)parameters and do not yield a unique solution: their estimates tend to fluctuate (when convergence is reached) around a stationary distribution. Within the linear programming framework, this paper proposes a new algorithm (lclphom) that always converges to a unique solution, having no adjustable parameters. This characteristic makes it easy to use and robust to claims of hacking. Furthermore, after assessing lclphom with real and simulated data, lclphom is found to yield estimates of (almost) similar accuracy to the current major solutions, being more preferable to the other lphom-family algorithms the more heterogeneous the row-fraction distributions of the tables are. Interested practitioners can easily use this new algorithm as it has been programmed in the R-package lphom.