Dear all,
I'm trying to implement a spatial Weibull model for child mortality in WinBUGS. I have a sample of children born in the same year. Age of death was recorded if a child died by age 5. Children were clustered within a number of different census tracts. The X-Y coordinates of the centroid of each tract was also recorded. Part of the data looks like the following:
t[] c[] tract.id[] x[] y[]
NA 5 1 177.45 212.12
2 0 1 177.45 212.12
1 0 2 178.19 211.30
4 0 2 178.19 211.30
NA 5 2 178.19 211.30
1 0 3 178.60 210.27
NA 5 3 178.60 210.27
t = year of death if a child died by age 5; t = NA if a child was right-censored (i.e. not dead by age 5).
c = 0 if a child died by age 5; c = 5 if a child was right-censored.
tract.id denotes the IDs of the census tracts in which children lived.
The goal is to model time to death while adjusting for potential spatial correlations. Instead of using a CAR prior, I prefer an exponential spatial distribution as specified by the spatial.exp function. In this way, I can learn more about how the spatial correlation decays as the distance between two census tracts increases. My WinBUGS code looks like the following:
model
{
for(i in 1:N) {
t[i] ~ dweib(alpha,lambda[i]) I(c[i] ,)
lambda[i] <- exp(mu[i])
mu[i] <- b.0+theta[tract.id[i]]
}
# Priors for alpha
alpha ~ dexp(.001)
# Priors for intercept
b.0 ~ dnorm(0, 0.01);
# Spatial part
theta[1:M] ~ spatial.exp(mu.M[],x[],y[],tau,phi,1)
for(i in 1:M){mu.M[i] <- 0}
tau ~ dgamma(0.1,0.1)
phi ~ dunif(0.1,10)
}
When I ran the model, WinBUGS gave an error message "value of weibull t[1] must be greater than lower bound". I'm not sure what went wrong and how to correct it. Any ideas and suggestions are highly appreciated.
Thanks,
Hongwei
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