I have a microdata recipient survey and a macro (aggregate) donor. How can I fuse the (binary categorical) data? The Statistical Matching techniques/software I'm familiar with are micro-to-micro. Furthermore, a web search revealed nothing (but perhaps my terms were wrong).
One (possibly over-simplified/naive) approach is:
Build a probability distribution of the donor's response in question, broken out into (harmonized) common variables like age, income, etc...
A respondent in the recipient that most closely matches donor profile X (e.g.: Nearest Neighbor) is assigned a "yes" response with probability X (based on #1).
Any pointers, comments on the above, references and software (R is a good one) are greatly appreciated.
The most conservative approach here would be to aggregate your micro data into summary statistics, and test for differences between the groups. I think that the reason you can't find anything is because most people in this situation would step back and do macro-macro comparisons. You've lost information from the donor dataset that won't come back, so I'd be very wary of trying to reconstruct the original set from your summaries.
My instinctive first response was to construct a set of pseudo-observations by generating 'samples' from your summary statistics, using correlation information to match the pseudo-observations more closely to the real ones from which you found your summary statistics. Of course, that's not a useful approach here.