The Information in Aggregate Data

Abstract

Ecological analysis involves using aggregate data for a set of groups to make inferences concerning individual level relationships. Typically the data available for analysis consists of the means or totals of variables of interest for geographical areas, although the groups can be organisations such as schools or hospitals. Attention has focused on developing methods of estimating the parameters characterising the individual level relationships across the whole population, but also in some cases the relationships for each of the groups.
Applying standard methods used to analyse individual level data, such as linear or logistic regression or contingency table analysis, to aggregate data will usually produce biased estimates of individual level relationships. Thus much of the effort in ecological analysis has concentrated on developing methods of analysing aggregate data that can produce unbiased, or less biased, parameter estimates. There has been less work done on inference procedures, such as constructing confidence intervals and hypothesis testing. Fundamental to these inferential issues is the question of how much information is contained in aggregate data and what evidence such data can provide concerning important assumptions and hypotheses.

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