model {
for (j in 1:8) {
for (i in offset[j]:offset[j+1]-1) {
d[i] <- d.com[j]; x[i] <- x.com[j]; z[i] <- z.com[j]
}
}
for (j in 9:12) {
for (i in offset[j]:offset[j+1]-1) {
d[i] <- d.inc[j-8]; x[i] <- x.inc[j-8]
}
}
for (i in 1:n) {
d[i] ~ dbern(p[i])
logit(p[i]) <- beta0 + beta*z[i]
z[i] ~ dbern(psi)
x[i] ~ dbern(phi[z1[i], d1[i]])
z1[i] <- z[i] + 1
d1[i] <- d[i] + 1
}
for (j in 1:2) {
for (k in 1:2) {
phi[j, k] ~ dunif(0, 1)
}
}
psi ~ dunif(0, 1)
beta0 ~ dnorm(0, 0.0001)
beta ~ dnorm(0, 0.0001)
}

Inits:
list(psi = 0.5, beta0 = 0, beta = 0,
phi = structure(.Data = c(0.5,0.5,0.5,0.5), .Dim = c(2,2)))

Data:
list(
n = 2044,
d.com = c(1,1,1,1,0,0,0,0),
z.com = c(0,0,1,1,0,0,1,1),
x.com = c(0,1,0,1,0,1,0,1),
d.inc = c(0,0,1,1),
x.inc = c(0,1,0,1),
offset = c(1,14,17,22,40,73,84,100,116,817,1352,1670,2045)
)

   node   mean   sd   MC error   2.5%   median   97.5%   start   sample
   beta   0.6213   0.3617   0.01924   -0.09153   0.6188   1.345   1001   20000
   beta0   -0.9059   0.199   0.01045   -1.321   -0.8996   -0.5283   1001   20000
   phi[1,1]   0.3177   0.05309   0.00199   0.2109   0.3186   0.4199   1001   20000
   phi[1,2]   0.2212   0.08055   0.003301   0.07556   0.2188   0.3884   1001   20000
   phi[2,1]   0.5691   0.06352   0.002116   0.4428   0.5683   0.6941   1001   20000
   phi[2,2]   0.7638   0.06187   0.002506   0.6409   0.7646   0.8806   1001   20000
   psi   0.4923   0.04304   0.001771   0.4057   0.4929   0.5771   1001   20000