model{
#observation model
for(t in 1:T){
y[t]~dbern(p[t])
logit(p[t])<-beta0[t]+beta1[t]*I[t]+beta2[t]*L[t]+beta3[t]*IL[t]
}
#state model
for(t in 2:T){
beta0[t]~dnorm(mu.0[t],tau0)
beta1[t]~dnorm(mu.1[t],tau1)
beta2[t]~dnorm(mu.2[t],tau2)
beta3[t]~dnorm(mu.3[t],tau3)
mu.0[t]<-alp0*beta0[t-1]+gam0*E[t]
mu.1[t]<-alp1*beta1[t-1]+gam1*E[t]
mu.2[t]<-alp2*beta2[t-1]+gam2*E[t]
mu.3[t]<-alp3*beta3[t-1]+gam3*E[t]
}
#end of t
#priors on observation model
beta0[1]~dnorm(0.0,1.0)
beta1[1]~dnorm(0.0,1.0)
beta2[1]~dnorm(0.0,1.0)
beta3[1]~dnorm(0.0,1.0)
gam0~dnorm(0.0,1.0)
gam1~dnorm(0.0,1.0)
gam2~dnorm(0.0,1.0)
gam3~dnorm(0.0,1.0)
alp0~dnorm(0.0,1.0)
alp1~dnorm(0.0,1.0)
alp2~dnorm(0.0,1.0)
alp3~dnorm(0.0,1.0)
tau~dgamma(1.0,1.0)
tau0~dgamma(1.0,1.0)
tau1~dgamma(1.0,1.0)
tau2~dgamma(1.0,1.0)
tau3~dgamma(1.0,1.0)
sgm<-1/tau
sgm0<-1/tau0
sgm1<-1/tau1
sgm2<-1/tau2
sgm3<-1/tau3
}
#end of model
Data
list(T=9,
y=c(0,1,1,1,1,1,1,1,0),
I=c(0.38,0.39,0.40,0.42,0.43,0.45,0.46,0.48,0.50),
L=c(90,88,86,85,83,82,81,80,78),
IL=c(34.2,34.32,34.4,35.7,35.69,36.9,37.26,38.4,39),
E=c(10,10,10,10,9,9,9,8,8))
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