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From: Bayesian Models for Astrophysical Data, Cambridge Univ. Press

(c) 2017,  Joseph M. Hilbe, Rafael S. de Souza and Emille E. O. Ishida

you are kindly asked to include the complete citation if you used this material in a publication

Code 6.24 Zero Truncated Negative binomial with 0-trick using JAGS - direct

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require(MASS)
require(R2jags)
require(VGAM)

set.seed(123579)
nobs <- 1000

x1 <- rbinom(nobs,size=1,0.7)
x2 <- runif(nobs)

xb <- 1 + 2*x1 - 4*x2
exb <- exp(xb)

alpha = 5

rztnb <- function(n, mu, size){
p <- runif(n, dzinegbin(0, munb=mu, size=size),1)
ztnb <- qzinegbin(p, munb=mu, size=size)
return(ztnb)
}

ztnby <- rztnb(nobs, exb, size=1/alpha)
ztnb.data <-data.frame(ztnby, x1, x2)

X <- model.matrix(~ x1 + x2, data = ztnb.data)
K <- ncol(X)

model.data <- list(Y = ztnb.data\$ztnby,
X = X,
K = K,                                                   # number of betas
N = nobs,
Zeros = rep(0, nobs))                            # sample size

ZTNB <- "
model{
for (i in 1:K) {beta[i] ~ dnorm(0, 1e-4)}

alpha ~ dgamma(1e-3,1e-3)

# Likelihood with zero trick
C <- 10000
for (i in 1:N) {
# Log likelihood function using zero trick:
Zeros[i] ~ dpois(Zeros.mean[i])
Zeros.mean[i] <- -L[i] + C
l1[i] <- 1/alpha * log(u[i])
l2[i] <- Y[i] * log(1 - u[i])
l3[i] <- loggam(Y[i] + 1/alpha)
l4[i] <- loggam(1/alpha)
l5[i] <- loggam(Y[i] + 1)
l6[i] <- log(1 - (1 + alpha * mu[i])^(-1/alpha))
L[i] <- l1[i] + l2[i] + l3[i] - l4[i] - l5[i] - l6[i]
u[i] <- 1/(1 + alpha * mu[i])
log(mu[i]) <- inprod(X[i,], beta[])
}
}"

inits <- function () {
list(beta = rnorm(K, 0, 0.1))}

params <- c("beta","alpha")

ZTNB1 <- jags(data = model.data,
inits = inits,
parameters = params,
model = textConnection(ZTNB),
n.thin = 1,
n.chains = 3,
n.burnin = 2500,
n.iter = 5000)

print(ZTNB1, intervals=c(0.025, 0.975), digits=3)

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Output on screen:

Inference for Bugs model at "3", fit using jags, 3 chains,

each with 5000 iterations (first 2500 discarded)

n.sims = 7500 iterations saved

mu.vect     sd.vect                     2.5%                  97.5%        Rhat    n.eff

alpha                           4.619        1.198                    2.936                   7.580       1.032       81

beta[1]                        1.099        0.199                    0.664                    1.445      1.016      150

beta[2]                        1.823        0.131                    1.564                    2.074      1.004      600

beta[3]                      -3.957         0.199                  -4.345                   -3.571      1.008       290

deviance      20004596.833         2.861      20004593.165      20004603.978      1.000           1

For each parameter, n.eff is a crude measure of effective sample size,

and Rhat is the potential scale reduction factor (at convergence, Rhat=1).

DIC info (using the rule, pD = var(deviance)/2)

pD = 4.1 and DIC = 20004600.9

DIC is an estimate of expected predictive error (lower deviance is better).

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