Journal of Applied Mathematics and Decision Sciences
Volume 2006 (2006), Article ID 38358, 18 pages
doi:10.1155/JAMDS/2006/38358
Unravelling ecological analysis
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
Copyright © 2006 D. G. Steel et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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.