An Individual-Level Story and Ecological Inference 

 I blogged some last year (see  here )  on whether an individual-level story is necessary, or useful, to ecological inference.  For a review of what ecological inference is, and what I mean by an individual-level story, see the end of this entry.  Last year, I stated that such a story was helpful in explaining an ecological inference technique, even if it might not be strictly necessary for modeling.  Gary disagreed that such a story was at all helpful, and we had a little debate on the subject, which you can access  here .  Lately, though, I’ve been thinking that an individual-level story really is necessary for good modeling, not just for communication of a model.  In particular, it seems like an individual-level model is required to incorporate survey information into an ecological inference model.  Survey data is, after all, data collected at the level of the individual, and with only an aggregate-level model, it’s hard to see how one could incorporate it.  Any thoughts from anyone out there? 


 To review:  ecological inference is the effort to predict the values of the internal cells of contingency tables (usually assumed to be exchangeable) when only the margins are observed.  A classic example is in voting, where one observes how many (say) black, white, and Hispanic potential voters there are in each precinct, and one also observes how many votes were cast for Democratic and Republican candidates.  What one wants to know if, say, how many blacks voted Democrat.  By an individual-level story, I mean a model of voting behavior at the level of the individual voter and a mathematical theory of how to aggregate up to the precinct-level counts.