zic.svs: SVS for Zero-Inflated Count Models
In zic: Bayesian Inference for Zero-Inflated Count Models

Description Usage Arguments Details Value References Examples

zic.svs applies SVS to zero-inflated count models

zic.svs(formula, data,
        a0, g0.beta, h0.beta, nu0.beta, r0.beta, s0.beta, e0, f0, 
        c0, g0.delta, h0.delta, nu0.delta, r0.delta, s0.delta, 
        n.burnin, n.mcmc, n.thin, tune = 1.0, scale = TRUE)

`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.
`g0.beta`	The shape parameter for the inverse gamma prior on kappa_k^beta.
`h0.beta`	The inverse scale parameter for the inverse gamma prior on kappa_k^beta.
`nu0.beta`	Prior parameter for the spike of the hypervariances for the beta_k.
`r0.beta`	Prior parameter of omega^beta.
`s0.beta`	Prior parameter of omega^beta.
`e0`	The shape parameter for the inverse gamma prior on sigma^2.
`f0`	The inverse scale parameter the inverse gamma prior on sigma^2.
`c0`	The prior variance of gamma.
`g0.delta`	The shape parameter for the inverse gamma prior on kappa_k^delta.
`h0.delta`	The inverse scale parameter for the inverse gamma prior on kappa_k^delta.
`nu0.delta`	Prior parameter for the spike of the hypervariances for the delta_k.
`r0.delta`	Prior parameter of omega^delta.
`s0.delta`	Prior parameter of omega^delta.
`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.

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, tau_k^beta * kappa_k^beta), k=1,...,K

kappa_k^β ~ Inv-Gamma(g0^beta,h0^beta),

tau_k^β ~ (1-ω^beta) delta_(nu0^β)+ omega^beta delta_1,

omega^beta ~ Beta(r0^beta,s0^beta),

gamma ~ N(0,c0)

delta_k ~ N(0, tau_k^delta * kappa_k^delta), k=1,...,K,

kappa_k^δ ~ Inv-Gamma(g0^delta,h0^delta),

tau_k^δ ~ (1-ω^delta) delta_(nu_0^δ)+ omega^delta delta_1,

omega^delta ~ Beta(r0^delta,s0^delta),

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

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

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).
`I.beta`	Posterior draws of indicator whether tau_j^beta is one (coda mcmc object).
`I.delta`	Posterior draws of indicator whether tau_j^delta is one (coda mcmc object).
`omega.beta`	Posterior draws of omega^beta (coda mcmc object).
`omega.delta`	Posterior draws of omega^delta (coda mcmc object).
`acc`	Acceptance rate of the Metropolis-Hastings step.

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.

## Not run: 
data( docvisits )
mdl <- docvisits ~ age + agesq + health + handicap + hdegree + married + schooling +
                    hhincome + children + self + civil + bluec + employed + public + addon
post <- zic.ssvs( mdl, docvisits,
                  10.0, 5.0, 5.0, 1.0e-04, 2.0, 2.0, 1.0, 1.0,
                  10.0, 5.0, 5.0, 1.0e-04, 2.0, 2.0,
                  1000, 10000, 10, 1.0, TRUE )
## End(Not run)