ZIP_model_jags.txt

# Zero-inflated Poisson model (ZIP) 
# Adapted from Ntzoufras (2009) "Bayesian Modeling Using WinBUGS: An Introduction"
# Chapter 8
# http://stat-athens.aueb.gr/~jbn/winbugs_book/

model {
	# Likelihood
	for(i in 1:n) { 

		y[i] ~ dpois(mu[i])
    		mu[i] <- (1-u[i])*lambda.ind[i] + 0.0001
          			# when u[i] = 1, observation i is an "excess" zero
			  	# when u[i] = 0, observation i is from Poisson 
         		 	# adding 0.0001 is a hack required for JAGS, per Bolker

		log(lambda.ind[i]) <- beta[1] + beta[2]*gender[i] # regression for count model 

		u[i]~dbern(p0[i]) # model for excess zeros
		logit(p0[i]) <- gamma[1] + gamma[2]*gender[i] # regression for zero-inflation model
	}	

	# Priors 
	for (j in 1:2) {
		beta[j] ~ dnorm(0, 0.01) # weak priors on regression coefs
		gamma[j] ~ dnorm(0, 0.01)
	}

	# Things to monitor for inference and model checks
	lambda[1] <- exp(beta[1]) # monitor mean of Poisson for females (gender=0) 
	lambda[2] <- exp(beta[1]+beta[2]) # ditto for males (gender=1)
	lambda.diff <- lambda[2] - lambda[1] # difference between means for genders
	for (i in 1:n) { resid[i] <- y[i] - mu[i] } # calculate residuals
}