Note of a forthcoming Royal Statistical Society (RSS) meeting.
Stephen Senn
ORDINARY MEETING, Wednesday, November 12, 2003, at 5 pm
J. Wakefield (University of Washington, Seattle)
Ecological inference for 2 x 2 tables
A fundamental problem in many disciplines, including political science,
sociology and epidemiology, is the examination of the association between
two binary variables across a series of 2 x 2 tables, when only the margins
are observed, and one of the margins is fixed. Two unobserved fractions are
of interest, with only a single response per table, and it is this
non-identifiability that is the fundamental difficulty lying at the heart
of ecological inference. Many methods have been suggested for ecological
inference, often without a probabilistic model; we clarify the form of the
sampling distribution and critique previous approaches within a formal
statistical framework, thus allowing clarification and examination of the
assumptions that are required under all approaches. A particularly
difficult problem is choosing between models with and without contextual
effects. Various Bayesian hierarchical modelling approaches are proposed to
allow the formal inclusion of supplementary data, and/or prior information,
without which ecological inference is unreliable. Careful choice of the
prior within such models is required, however, since there may be
considerable sensitivity to this choice, even when the model assumed is
correct and there are no contextual effects. This sensitivity is shown to
be a function of the number of areas and the distribution of the
proportions in the fixed margin across areas. By explicitly providing a
likelihood for each table, the combination of individual level survey data
and aggregate level data is straightforward and we illustrate that survey
data can be highly informative, particularly if these data are from a
survey of the minority population within each area. This strategy is
related to designs that are used in survey sampling and in epidemiology. An
approximation to the suggested likelihood is discussed, and various
computational approaches are described. Some extensions are outlined
including the consideration of multiway tables, spatial dependence and
area-specific (contextual) variables. Voter registration - race data from
64 counties in the US state of Louisiana are used to illustrate the methods.
Venue:
The Royal Statistical Society
12 Errol Street, London, EC1Y 8LX.
Tea will be served from 4.30pm
A preprint is available at
http://www.rss.org.uk/publications/preprints.html
==============================================
Stephen Senn
Professor of Statistics
Department of Statistics
15 University Gardens
<http://www.gla.ac.uk>University of Glasgow
G12 8QQ
Tel: +44 (0)141 330 5141
Fax: +44(0)141 330 4814
email [log in to unmask]
Private webpage: http://www.senns.demon.co.uk/home.html
===============================================
|