Simple methods for ecological inference in 2x2 tables
This paper considers inference about the individual level relationship between two dichotomous variables based on aggregated data. It is known that such analyses suffer from 'ecological bias', caused by the lack of homogeneity of this relationship across the groups over which the aggregation occurs. Two new methods for overcoming this bias, one based on local smoothing and the other a simple semiparametric approach, are developed and evaluated. The local smoothing approach performs best when it is used with a covariate which accounts for some of the variation in the relationships across groups. The semiparametric approach performed well in our evaluation even without such auxiliary information.
Chambers, R. L. & Steel, D. G. (2001). Simple methods for ecological inference in 2x2 tables. Journal of the Royal Statistical Society. Series A (Statistics in Society), 164 (1), 175-192.