zic.svs {zic}

SVS for Zero-Inflated Count Models

Description

zic.svs applies SVS to zero-inflated count models

Usage

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)

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.

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.

Details

The considered zero-inflated count model is given by

y_i^* \sim \mathrm{Poisson}[\exp(\eta^*_i)],

\eta^*_i = \alpha + x_i'\beta + \varepsilon_i,\; \varepsilon_i \sim \mathrm{N}(0,\sigma^2),

d_i^* = \gamma + x_i'\delta + \nu_i,\; \nu_i \sim \mathrm{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 \sim \mathrm{N}(0,a_0),

\beta_k\sim \mathrm{N}(0,\tau^\beta_k\kappa^\beta_k),, \quad k=1,\ldots,K,

\kappa^\beta_j\sim\textrm{Inv-Gamma}(g_0^\beta,h_0^\beta),

\tau_k^\beta \sim (1-\omega^\beta)\delta_{\nu^\beta_0}+\omega^\beta\delta_1,

\omega^\beta\sim\mathrm{Beta}(r_0^\beta,s_0^\beta),

\gamma \sim \mathrm{N}(0,c_0),

\delta_k\sim \mathrm{N}(0,\tau^\delta_k\kappa^\delta_k), \quad k=1,\ldots,K,

\kappa^\delta_k\sim\textrm{Inv-Gamma}(g_0^\delta,h_0^\delta),

\tau_k^\delta \sim (1-\omega^\delta)\delta_{\nu^\delta_0}+\omega^\delta\delta_1,

\omega^\delta\sim\mathrm{Beta}(r_0^\delta,s_0^\delta),

\sigma^2 \sim \textrm{Inv-Gamma}\left(e_0,f_0\right).

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).

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.

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.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)