Dear list and in particular those working in spatial modelling
hello,
I was hoping one of you might have the answer or might have observed
something similar to a problem I encountered while using the CAR
distribution in winBUGS 1.3 to locally smooth geographic variation of
suicide mortality across areas in Britain.
I'll try to keep it brief:
I have two levels of geography: constituencies, with a total of around
600 areas and the much smaller one, wards, with a total of around 10
000 areas. It is important to know that as suicide is rare, at that
geographic level a lot of areas, in fact more than half in certain
age/sex groups have no deaths at all.
I usually run 4 chains with different initial values. The basic model
incorporating both structured and unstructured variability is:
O[i] ~ dpois(mu[i])
log(mu[i]) <- log(E[i]) + const + H[i] + S[i]
H[i] ~ dnorm(0,v.inv)
S[1:N] ~ car.normal(adj[], weights[], neigh[], vstar.inv)
As the variances of the unstructured and structuted components are not
directly comparable, I calculate (as suggested at the Disease mapping
and ecological regression course in London) their empirical variances
and then their ratio.
sdemp.star<-sd(S[])
varemp.star<-pow(sdemp.star, 2)
sdemp<-sd(H[])
varemp<- pow(sdemp, 2)
ratio<-varemp.star/(varemp+varemp.star)
This works fine at the constituency level. But at ward level, although
the variance of the CAR dn converges fine and behaves normally in
general, the empirical variance does not and there is an obvious
increasing trend either in all or in certain chains producing a highly
skewed posterior (and sometimes on the contary of what is usually
expected, the empirical variance turns out to be greater than the
comditional variance).
While at ward level the convolution model has various problems in
general since when a structured component is included, the unstructured
component is having difficulties converging (possibly because it is not
necessary and we are overfitting the model), this is not the reason the
empirical variance of the structured component behaves badly as it also
does when fitting a model with only a CAR component.
Any ideas what is actually going on? Can I still use the empirical
variances to make inferences about the importance of each component,
possibly using the median instead?
Thanks a lot,
Nicos Middleton
-------------------
Nicos Middleton
Department of Social Medicine
University of Bristol
Canynge Hall
Whiteladies Road
Bristol BS8 2PR
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