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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

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# Data from code 7.6

rztp <- function(N, lambda){
p <- runif(N, dpois(0, lambda),1)
ztp <- qpois(p, lambda)
return(ztp)
}

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nobs <- 1000
x1 <- runif(nobs,-0.5,2.5)
xb <- 0.75 + 1.5*x1

exb <- exp(xb)
poy <- rztp(nobs, exb)
pdata <- data.frame(poy, x1)

xc <- -3 + 4.5*x1

pi <- 1/(1+exp((xc)))
bern <- rbinom(nobs,size =1, prob=1-pi)

pdata\$poy <- pdata\$poy*bern

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Code 7.9 Zero-altered negative binomial (ZANB) or NB hurdle model in R using JAGS

==================================================================

require(R2jags)

Xc <- model.matrix(~ 1 + x1, data = pdata)
Xb <- model.matrix(~ 1 + x1, data = pdata)
Kc <- ncol(Xc)
Kb <- ncol(Xb)

model.data <- list(
Y = pdata\$poy,
Xc = Xc,
Xb = Xb,
Kc = Kc,                                                        # number of betas − count
Kb = Kb,                                                        # number of gammas − binary
N = nrow(pdata),
Zeros = rep(0, nrow(pdata)))

sink("NBH.txt")

cat("
model{
# Priors beta and gamma
for (i in 1:Kc) {beta[i]  ~  dnorm(0, 0.0001)}
for (i in 1:Kb) {gamma[i]  ~  dnorm(0, 0.0001)}

# Prior for alpha
alpha ~ dunif(0.001, 5)

# Likelihood using zero trick
C <- 10000

for (i in 1:N) {
Zeros[i]  ~  dpois(-ll[i] + C)
LogTruncNB[i] <- 1/alpha * log(u[i])  +
Y[i] * log(1 - u[i]) + loggam(Y[i] + 1/alpha) -
loggam(1/alpha) - loggam(Y[i] + 1) -
log(1 - (1 + alpha * mu[i])^(-1/alpha))

z[i] <- step(Y[i] - 0.0001)
l1[i] <- (1 - z[i]) * log(1 - Pi[i])
l2[i] <- z[i] * (log(Pi[i]) + LogTruncNB[i])
ll[i] <- l1[i] + l2[i]
u[i] <- 1/(1 + alpha * mu[i])
log(mu[i]) <- inprod(beta[], Xc[i,])
logit(Pi[i]) <- inprod(gamma[], Xb[i,])
}
}"
, fill = TRUE)

sink()

inits <- function () {
list(beta = rnorm(Kc, 0, 0.1),
gamma = rnorm(Kb, 0, 0.1),
numS = rnorm(1, 0, 25),
denomS = rnorm(1, 0, 1))}

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

ZANB <- jags(data = model.data,
inits = inits,
parameters = params,
model = "NBH.txt",
n.thin = 1,
n.chains = 3,
n.burnin = 4000,
n.iter = 6000)

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

==================================================================

Anchor 1

Output on screen:

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Inference for Bugs model at "NBH.txt", fit using jags,

3 chains, each with 6000 iterations (first 4000 discarded)

n.sims = 6000 iterations saved

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

alpha                            0.002        0.001                   0.001                     0.005       1.001      4000

beta[1]                         0.733        0.031                   0.665                     0.787       1.020        150

beta[2]                         1.508        0.016                   1.481                     1.542       1.019        150

gamma[1]                   -2.926        0.228                 -3.386                    -2.491       1.001       5000

gamma[2]                    4.675        0.312                  4.097                      5.304       1.001       5700

deviance        20004176.033        3.180     20004171.871       20004183.917       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 = 5.1 and DIC = 20004181.1

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

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