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Models, assumptions and model checking in ecological regressions

Ecological regression is based on assumptions that are untestable from aggregate data. However, these assumptions seem more questionable in some applications than in others. There has been some research on implicit models of individual data underlying aggregate ecological regression modelling. We discuss ways in which these implicit models can be checked from aggregate data. We also explore the differences in applications of ecological regressions in two examples: estimating the effect of radon on lung cancer in the United States and estimating voting patterns for different ethnic groups in New York City.