Dear All,
I currently trying to model the number accidents involving motorbikes using a Poisson time series model with an AR(1) process (e.g. Hay and Pettitt 2001, biostatistics, page 433-44: Bayesian analysis of a time series
of count with covariates: an application to the control of an infectious disease)
model{
# model for t=1
y[1]~dpois(mu[1])
log(mu[1])<-alpha[1]+alpha[2]*x[1]+alpha[3]*xsin[1]+alpha[4]*xcos[1]+w[1]
w[1]<-u[1]/sqrt(1-phi*phi)
for (t in 2:n)
{
y[t]~dpois(mu[t])
log(mu[t])<-alpha[1]+alpha[2]*x[t]+alpha[3]*xsin[t]+alpha[4]*xcos[t]+w[t]
w[t]<-phi*w[t-1]+u[t]
}
# priors and residuals
for (t in 1:n)
{
u[t]~dnorm(0,tau)
y.res[t]<-(y[t]-mu[t])/sqrt(mu[t])
}
for (i in 1:4)
{
alpha[i]~dnorm(0,0.0001)
}
phi~dunif(-0.999,0.999)
tau<-1/tauinv
tauinv~dgamma(0.001,0.001)
rr<-exp(alpha[2])
}
The regression parameter estimates (i.e. alpha[1],alpha[2],alpha[3],alpha[4]) are very close to those obtain from a standard poisson regression (ignoring any autocorrelation) but the parameter tau has a posterior
mean of about 50,000,000 with a 95% credability interval of (21.8 to 6.4E+11)!
Has anyone else tried these models and have they run into similar problems? or can anybody offer an explanation as to why the variance of u[t] is so small?
Best wishes
Allan
=========================
Dr Allan Clark
Senior Lecturer in Medical Statistics
University of East Anglia
Norwich
NR4 7TJ
t: 01603 593629