Combining Individual Level and R x C Ecological Data
Cross-level or 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. To do so, we extend and study a hybrid model that addresses two-way tables of arbitrary dimension. We apply the hybrid model to our 400-pollster exit poll, taken in 39 polling locations in the City of Boston and covering four contests in November 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 in realistic settings.