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 7.1 Bayesian zero-inflated Poisson model in R using JAGS

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

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

set.seed(141)
nobs <- 1000

x1 <- runif(nobs)
xb <- 1 + 2.0*x1
xc <- 2 - 5.0*x1


exb <- exp(xb)
exc <- 1/(1+exp(-xc))


zipy <- rzipois(n=nobs, lambda=exb, pstr0=exc)
zipdata <- data.frame(zipy,x1)

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

model.data <- list(Y = zipdata$zipy,                      # response
                              Xc = Xc,                                   # covariates
                              Kc = Kc,                                   # number of betas
                              Xb = Xb,                                   # covariates
                              Kb = Kb,                                   # number of gammas
                              N = nobs)

ZIPOIS<-"model{
    # Priors - count and binary components
    for (i in 1:Kc) { beta[i] ~ dnorm(0, 0.0001)}
    for (i in 1:Kb) { gamma[i] ~ dnorm(0, 0.0001)}

    # Likelihood
    for (i in 1:N) {
        W[i] ~ dbern(1 - Pi[i])
        Y[i] ~ dpois(W[i] * mu[i])
        log(mu[i]) <- inprod(beta[], Xc[i,])
        logit(Pi[i]) <- inprod(gamma[], Xb[i,])
    }
}"

W <- zipdata$zipy
W[zipdata$zipy > 0] <- 1

inits <- function() {
      list(beta = rnorm(Kc, 0, 0.1),
            gamma = rnorm(Kb, 0, 0.1),
            W = W)}

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

ZIP <- jags(data = model.data,
                    inits = inits,
                    parameters = params,
                    model = textConnection(ZIPOIS),
                    n.thin = 1,
                    n.chains = 3,
                    n.burnin = 4000,
                    n.iter = 5000)

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

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GET SOURCE

Output on screen:

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

    each with 5000 iterations (first 4000 discarded)

    n.sims = 3000 iterations saved

 

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

beta[1]               1.019       0.045            0.932              1.104         1.103          25

beta[2]               1.955       0.058            1.843              2.066         1.096          26

gamma[1]          1.913       0.166            1.588              2.241         1.013        160

gamma[2]         -4.828       0.319           -5.472            -4.208         1.014        150

deviance       3095.598     11.563      3079.409        3122.313         1.004        710

 

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 = 66.7 and DIC = 3162.3

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