Journal of Applied Mathematics and Decision Sciences 
Volume 2006 (2006), Article ID 38358, 18 pages
doi:10.1155/JAMDS/2006/38358

Unravelling ecological analysis

D. G. Steel,1 M. Tranmer,2 and D. Holt3

 1School of Mathematics and Applied Statistics, University of Wollongong, Wollongong 2522, NSW, Australia
2Cathie Marsh Centre for Census and Survey Research, University of Manchester, Manchester M13 9PL, United Kingdom
3Department of Social Statistics, University of Southampton, Southampton SO17 1BJ, United Kingdom
Received 10 February 2004; Accepted 25 May 2005

Abstract

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.