# Negative Binomial mean hurdle model

# data section for JAGS
data{for(i in 1:n.rec){zeros[i] <- 0}}
model{

	# Likelihood

	for(i in 1:n.rec){

	z[i] <- equals(trips[i], 0)	# I(trips = 0)

	logit(pi[i]) <- gamma[1]*intercept.rec[i] +
		gamma[2]*ski[i] +
		gamma[3]*fee[i] +
		gamma[4]*income[i]

	log(mu[i]) <- beta[1]*intercept.rec[i] + beta[2]*ski[i] +
		beta[3]*fee[i] + beta[4]*income[i]

	psi[i]<-r/(r+mu[i])

	log.like[i] <- z[i]*log(1 - pi[i]) + (1 - z[i])*(log(pi[i]) +
		loggam(trips[i]+r) - loggam(r) - loggam(trips[i]+1) +
		r*log(psi[i]) + trips[i]*log(1-psi[i]) - log(1-pow(psi[i],r)) )

	#	zeros trick

	zeros[i] ~ dpois(lambda[i])

	lambda[i] <- -log.like[i] + 10000

	}

	# prior distributions

	for(i in 1:4){

	beta[i] ~ dnorm(0, 0.001)

	gamma[i] ~ dnorm(0, 0.001)
	}
	r ~ dgamma(1, 1)


}