Geography, Statistics, and Ecological Inference

I am grateful for such thoughtful review from these three distinguished geographers. Fotheringham provides an excellent summary of the approach offered, including how it combines the two methods that have dominated applications (and methodological analysis) for nearly half a century– the method of bounds (Duncan and Davis, 1953) and Goodman’s (1953) least squares regression. Since Goodman’s regression is the only method of ecological inference “widely used in Geography” (O’Loughlin), adding information that is known to be true from the method of bounds (for each observation) would seem to have the chance to improve a lot of research in this field. The other addition that EI provides is estimates at the lowest level of geography available, making it possible to map results, instead of giving only single summary numbers for the entire geographic region. Whether one considers the combined method offered “the” solution (as some reviewers and commentators have portrayed it), “a” solution (as I tried to describe it), or, perhaps better and more simply, as an improved method of ecological inference, is not importatnt. The point is that more data are better, and this method incorporates more. I am gratified that all three reviewers seem to support these basic points. In this response, I clarify a few points, correct some misunderstandings, and present additional evidence. I conclude with some possible directions for future research.