Published by Oxford University Press on behalf of the International Epidemiological Association © The Author 2009; all rights reserved.
Editorial |
Multi-level modelling, the ecologic fallacy, and hybrid study designs
Departments of Statistics and Biostatistics, University of Washington, Box 357232, Seattle, WA 98195-7232, USA. E-mail: jonno@u.washington.edu
Accepted 10 March 2009
| The first 150 words of the full text of this article appear below. |
The ecologic fallacy
In this issue, Robinson's highly influential paper is reprinted,1 along with a paper advocating the use of multi-level thinking by Subramanian et al.2, and commentaries by Oakes3 and Firebaugh.4
On re-reading Robinson's paper, I was again struck by the clarity of the basic take-home message: ecological data can estimate individual associations in only very rare situations. Robinson illustrated the ecologic fallacy using correlation coefficients applied at different levels of aggregation, whereas more recent work has focused on loglinear models.5,6 For common (in a statistical sense) outcomes, such as the illiteracy-race example considered in Robinson's paper, a logistic form is more appropriate (and is used by Subramanian et al.) but this form is less amenable to analytic study.7 There has been an abundance of work on the myriad causes of ecologic bias on estimates of individual-level associations, which include within-area variability in exposure, and within-area confounding.8–13 One might think
Hybrid designs
Multi-level models
Exploratory data analysis
Prior choice
Stage 1: observed data model
Stage 2: random effects model
Stage 3: hyperpriors
Interpretation
Markov chain Monte Carlo
Supplementary Data
Funding
Appendix 1
Prior choice
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