I have a question regarding the role played by the "unstructured"
heterogeneity variable in both spatial and non-spatial models. In
particular, when I fit a model in BUGS that includes ecological
covariates and the random-effects variable, representing unstructured
heterogeneity, I get a model that fits the data WORSE than if I fit a
model to my data that includes ONLY the random-effects term. I was
perplexed by this result since in the frequentist analysis I was able to
explain 50% of the variability in my data using the ecological
regression covariates. In order to further investigate what might be
occurring I fit the following model in BUGS on a hypothetical data set
containing 20 observations, 19 of which had a value of 1 and one with a
value of 250:
model
{
for (i in 1:N){
O[i] ~ dpos(mu[i])
log(mu[i])<- alpha + h[i] # intercept + Unstructured random effects
h[i] ~ dnorm(0,tau.h)
}
#Other priors
alpha ~ dnorm(0,0.001)
tau.h ~ dgamma(0.3612,1.29)
the results are as follows;
Observed Expected(from BUGS)
1 1.111
1 1.11
1 1.117
1 1.11
1 1.126
1 1.116
1 1.109
1 1.104
1 1.117
250 247.7
1 1.119
1 1.119
1 1.113
1 1.118
1 1.122
1 1.131
1 1.112
1 1.118
1 1.115
1 1.106
Amazing fit! After fitting this model I realized that the random
effects term was modeling the observed data TOO WELL! Unfortunately,
even though I am using the BUGS code in my modeling work in a manner
that completely copies the spatial model structures presented in the
BUGS manual, I am still getting these odd results. Can anyone out there
explain to me WHY the unstructured random effects are basically
reproducing the observed data when I thought its role was to smooth the
data towards the global mean? I'm wondering if I have somehow
mis-specified the model's structure, or if it has to do with the Gibb's
sampler fitting a model to each data point instead of averaging across
all the data? I must admit this problem has got me quite confused, any
help will be appreciated.
thanks in advance,
matt
******************************
Matthew Farnsworth
Graduate Research assistant
Natural Resources Ecology Lab
Colorado State University
Fort Collins, Colorado 80523
970-491-1604 (office)
970-491-1965 (fax)
******************************
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