Unravelling ecological analysis

Ecological analysis involves analysing aggregate data for groups of individuals to make inferences about relationships at the individual level. Often the results of such analyses give badly biased estimates. This paper will consider the sources of bias in linear regression analysis using aggregate data. The role of variation of the individual level relationships between groups and the consequent within-group correlations and how these are related to auxiliary variables that characterise the differences between groups is considered. A method of adjusting ecological regression for the effects of auxiliary variables is described and evaluated using data from the 1991 Australian Census.