Despite its shortcomings, cross-level or ecological inference remains a
necessary part of some areas of quantitative inference, including in United
States voting rights litigation. Ecological inference suffers from a lack of
identification that, most agree, is best addressed by incorporating
individual-level data into the model. In this paper we test the limits of such
an incorporation by attempting it in the context of drawing inferences about
racial voting patterns using a combination of an exit poll and precinct-level
ecological data; accurate information about racial voting patterns is needed to
assess triggers in voting rights laws that can determine the composition of
United States legislative bodies. Specifically, we extend and study a hybrid
model that addresses two-way tables of arbitrary dimension. We apply the hybrid
model to an exit poll we administered in the City of Boston in 2008. Using the
resulting data as well as simulation, we compare the performance of a pure
ecological estimator, pure survey estimators using various sampling schemes and
our hybrid. We conclude that the hybrid estimator offers substantial benefits
by enabling substantive inferences about voting patterns not practicably
available without its use.Comment: Published in at http://dx.doi.org/10.1214/10-AOAS353 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org