MRC Biostatistics UnitPoisson model...
model {
for (i in 1:6) {
for (j in 1:3) {
y[i,j] ~ dpois(mu[i])
}
log(mu[i]) <- alpha + beta*log(x[i] + 10) + gamma*x[i]
}
for (i in 1:6) {
y.pred[i] ~ dpois(mu[i])
}
alpha ~ dnorm(0, 0.0001)
beta ~ dnorm(0, 0.0001)
gamma ~ dnorm(0, 0.0001)
}
Data:
list(y = structure(.Data = c(15,21,29,16,18,21,16,26,33,27,41,60,33,38,41,20,27,42),
.Dim = c(6, 3)),
x = c(0, 10, 33, 100, 333, 1000))
Inits:
list(alpha = 0, beta = 0, gamma = 0)
node mean sd MC error 2.5% median 97.5% start sample
alpha 2.182 0.2169 0.0109 1.767 2.178 2.629 1001 20000
beta 0.3169 0.05666 0.002886 0.1993 0.3186 0.4254 1001 20000
gamma -0.001006 2.452E-4 1.06E-5 -0.001483 -0.001009 -5.044E-4 1001 20000
mu[1] 18.48 1.793 0.07912 15.23 18.39 22.35 1001 20000
mu[2] 22.74 1.571 0.05453 19.78 22.69 25.99 1001 20000
mu[3] 28.29 1.506 0.01745 25.43 28.26 31.31 1001 20000
mu[4] 35.63 2.153 0.05967 31.5 35.59 39.95 1001 20000
mu[5] 40.43 2.739 0.09947 35.18 40.38 45.95 1001 20000
mu[6] 29.2 3.086 0.04847 23.52 29.07 35.68 1001 20000
y.pred[1] 18.5 4.634 0.08278 10.0 18.0 28.0 1001 20000
y.pred[2] 22.76 5.027 0.0633 14.0 23.0 33.0 1001 20000
y.pred[3] 28.33 5.543 0.04162 18.0 28.0 40.0 1001 20000
y.pred[4] 35.61 6.316 0.07021 24.0 35.0 49.0 1001 20000
y.pred[5] 40.45 6.929 0.1133 27.0 40.0 55.0 1001 20000
y.pred[6] 29.17 6.276 0.06318 18.0 29.0 42.0 1001 20000
Negative binomial model...
model {
for (i in 1:6) {
for (j in 1:3) {
y[i,j] ~ dnegbin(p[i], r)
}
p[i] <- r/(mu[i] + r)
log(mu[i]) <- alpha + beta*log(x[i] + 10) + gamma*x[i]
}
for (i in 1:6) {
y.pred[i] ~ dnegbin(p[i], r)
}
r ~ dcat(pi[])
for (i in 1:max) {
pi[i] <- 1/max
}
alpha ~ dnorm(0, 0.0001)
beta ~ dnorm(0, 0.0001)
gamma ~ dnorm(0, 0.0001)
}
Data:
list( max = 1000,
y = structure(.Data = c(15,21,29,16,18,21,16,26,33,27,41,60,33,38,41,20,27,42),
.Dim = c(6, 3)),
x = c(0, 10, 33, 100, 333, 1000))
Inits:
list(alpha = 0, beta = 0, gamma = 0, r = 10)
node mean sd MC error 2.5% median 97.5% start sample alpha 2.183 0.3206 0.01339 1.581 2.176 2.843 4001 100000 beta 0.3166 0.08655 0.00366 0.1374 0.3188 0.4774 4001 100000 gamma -9.956E-4 3.794E-4 1.38E-5 -0.001721 -0.001009 -2.066E-4 4001 100000 mu[1] 18.56 2.61 0.09437 14.12 18.34 24.36 4001 100000 mu[2] 22.78 2.253 0.06098 18.76 22.63 27.67 4001 100000 mu[3] 28.32 2.269 0.02043 24.18 28.21 33.16 4001 100000 mu[4] 35.73 3.505 0.09056 29.25 35.58 43.19 4001 100000 mu[5] 40.66 4.505 0.1405 32.35 40.45 50.25 4001 100000 mu[6] 29.67 4.876 0.06402 21.39 29.21 40.64 4001 100000 r 72.24 145.3 0.8461 8.0 27.0 617.0 4001 100000 y.pred[1] 18.54 6.389 0.09668 8.0 18.0 33.0 4001 100000 y.pred[2] 22.78 7.17 0.06429 10.0 22.0 39.0 4001 100000 y.pred[3] 28.35 8.32 0.03032 14.0 28.0 47.0 4001 100000 y.pred[4] 35.77 10.29 0.09455 18.0 35.0 59.0 4001 100000 y.pred[5] 40.65 11.62 0.1454 20.0 40.0 66.0 4001 100000 y.pred[6] 29.69 9.736 0.06814 14.0 29.0 52.0 4001 100000