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All maps of parameter estimates are misleading
Author(s) -
Gelman Andrew,
Price Phillip N.
Publication year - 1999
Publication title -
statistics in medicine
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.996
H-Index - 183
eISSN - 1097-0258
pISSN - 0277-6715
DOI - 10.1002/(sici)1097-0258(19991215)18:23<3221::aid-sim312>3.0.co;2-m
Subject(s) - poisson distribution , sample size determination , statistics , bayesian probability , spatial variability , spatial dependence , spatial heterogeneity , sample (material) , inference , econometrics , spatial analysis , variation (astronomy) , spatial ecology , computer science , mathematics , artificial intelligence , ecology , chemistry , physics , chromatography , astrophysics , biology
Maps are frequently used to display spatial distributions of parameters of interest, such as cancer rates or average pollutant concentrations by county. It is well known that plotting observed rates can have serious drawbacks when sample sizes vary by area, since very high (and low) observed rates are found disproportionately in poorly‐sampled areas. Unfortunately, adjusting the observed rates to account for the effects of small‐sample noise can introduce an opposite effect, in which the highest adjusted rates tend to be found disproportionately in well‐sampled areas. In either case, the maps can be difficult to interpret because the display of spatial variation in the underlying parameters of interest is confounded with spatial variation in sample sizes. As a result, spatial patterns occur in adjusted rates even if there is no spatial structure in the underlying parameters of interest, and adjusted rates tend to look too uniform in areas with little data. We introduce two models (normal and Poisson) in which parameters of interest have no spatial patterns, and demonstrate the existence of spatial artefacts in inference from these models. We also discuss spatial models and the extent to which they are subject to the same artefacts. We present examples from Bayesian modelling, but, as we explain, the artefacts occur generally. Copyright © 1999 John Wiley & Sons, Ltd.