Introduction

Gary King and Margaret Roberts

Introduction: Ecological Inference

This program provides methods of inferring individual behavior from aggregate data. It implements the statistical procedures, diagnostics, and graphics from the Gary King, A Solution to the Ecological Inference Problem: Reconstructing Individual Behavior from Aggregate Data (Princeton: Princeton University Press, 1997), http://j.mp/ecinfbook; Ori Rosen, Wenxin Jiang, Gary King, and Martin A. Tanner (2001) ``Bayesian and Frequentist Inference for Ecological Inferece: The RxC Case.’’ (Statistica Neerlandica, Vol.55, nr.2, pp 134-156), http://j.mp/eiRxC; and from our own ongoing work. Except where indicated, all references to page, section, chapter, table, and figure numbers in this document refer to the the first reference.

Ecological inference is the process of using aggregate (i.e., “ecological”) data to infer discrete individual-level relationships of interest when individual-level data are not available. Ecological inferences are required in political science research when individual-level surveys are unavailable (e.g., local or comparative electoral politics), unreliable (racial politics), insufficient (political geography), or infeasible (political history). They are also required in public policy (e.g., for applying the Voting Rights Act) and other academic disciplines ranging from epidemiology and marketing to sociology and quantitative history. Most researchers using aggregate data have encountered some form of the ecological inference problem.

Because the ecological inference problem is caused by the lack of individual-level information, no method of ecological inference, including that estimated by this program, will always produce accurate results. However, potential difficulties are reduced by models that include more available information, diagnostics to evaluate when assumptions need to be modified, easy methods of modifying the assumptions, and uncertainty estimates for quantities of interest. We recommend reviewing Chapter 16 while using this program for actual research. Model dependence defines ecological inference when going anywhere beyond the bounds and tomography plots, and so we have added new graphical procedures for evaluating the degree of model dependence.

ei is a unifed program that contains methods for both the 2x2 ecological inference case and the RxC case. We will begin by explaining how to use eiR in the 2x2 case, and then move on to RxC examples.