Ecological inference in the social sciences

Ecological inference is a problem of partial identification, and therefore precise conclusions are rarely possible without the collection of individual level (identifying) data. Without such data, sensitivity analyses provide the only recourse. In this paper we review and critique recent approaches to ecological inference in the social sciences, and describe in detail hierarchical models, which allow both sensitivity analysis and the incorporation of individual level data into an ecological analysis. A crucial element of a sensitivity analysis in such models is prior specification, and we detail how this may be carried out. Furthermore, we demonstrate how the inclusion of a small amount of individual level data from a small number of ecological areas can dramatically improve the properties of such estimates.