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Last data update: 2014.03.03

R: Bayesian Inference for Zero-Inflated Count Models

zic	R Documentation

Bayesian Inference for Zero-Inflated Count Models

Description

zic fits zero-inflated count models via Markov chain Monte Carlo methods.

Usage

zic(formula, data, a0, b0, c0, d0, e0, f0, 
    n.burnin, n.mcmc, n.thin, tune = 1.0, scale = TRUE)

Arguments

`formula`	A symbolic description of the model to be fit specifying the response variable and covariates.
`data`	A data frame in which to interpret the variables in `formula`.
`a0`	The prior variance of alpha.
`b0`	The prior variance of beta_j.
`c0`	The prior variance of gamma.
`d0`	The prior variance of delta_j.
`e0`	The shape parameter for the inverse gamma prior on sigma^2.
`f0`	The inverse scale parameter the inverse gamma prior on sigma^2.
`n.burnin`	Number of burn-in iterations of the sampler.
`n.mcmc`	Number of iterations of the sampler.
`n.thin`	Thinning interval.
`tune`	Tuning parameter of Metropolis-Hastings step.
`scale`	If true, all covariates (except binary variables) are rescaled by dividing by their respective standard errors.

Details

The considered zero-inflated count model is given by

y*_i ~ Poisson[exp(eta*_i)],

eta*_i = x_i' * beta + epsilon_i, epsilon_i ~ N( 0, sigma^2 ),

d*_i = x_i' * delta + nu_i, nu_i ~ N(0,1),

y_i = 1(d*_i>0) y*_i,

where y_i and x_i are observed. The assumed prior distributions are

alpha ~ N(0,a0),

beta_k ~ N(0,b0), k=1,...,K,

gamma ~ N(0,c0)

delta_k ~ N(0,d0), k=1,...,K,

sigma^2 ~ Inv-Gamma(e0,f0).

The sampling algorithm described in Jochmann (2013) is used.

Value

A list containing the following elements:

`alpha`	Posterior draws of alpha (coda mcmc object).
`beta`	Posterior draws of beta (coda mcmc object) .
`gamma`	Posterior draws of gamma (coda mcmc object).
`delta`	Posterior draws of delta (coda mcmc object).
`sigma2`	Posterior draws of sigma^2 (coda mcmc object).
`acc`	Acceptance rate of the Metropolis-Hastings step.

References

Jochmann, M. (2013). “What Belongs Where? Variable Selection for Zero-Inflated Count Models with an Application to the Demand for Health Care”, Computational Statistics, 28, 1947–1964.

Examples

## Not run: 
data( docvisits )
mdl <- docvisits ~ age + agesq + health + handicap + hdegree + married + schooling +
                    hhincome + children + self + civil + bluec + employed + public + addon
post <- zic( f, docvisits, 10.0, 10.0, 10.0, 10.0, 1.0, 1.0, 1000, 10000, 10, 1.0, TRUE )
## End(Not run)