Package 'zic'

Demand for Health Care Data

Description

This data set gives the number of doctor visits in the last three months for a sample of German male individuals in 1994. The data set is taken from Riphahn et al. (2003) and is a subsample of the German Socioeconomic Panel (SOEP). In contrast to Riphahn et al. (2003) only male individuals from the last wave are considered. See Jochmann (2013) for further details.

Usage

data(docvisits)

Format

This data frame contains 1812 observations on the following 22 variables:

docvisits

number of doctor visits in last 3 months

age

age

agesq

age squared / 1000

age30

1 if age >= 30

age35

1 if age >= 35

age40

1 if age >= 40

age45

1 if age >= 45

age50

1 if age >= 50

age55

1 if age >= 55

age60

1 if age >= 60

health

health satisfaction, 0 (low) - 10 (high)

handicap

1 if handicapped, 0 otherwise

hdegree

degree of handicap in percentage points

married

1 if married, 0 otherwise

schooling

years of schooling

hhincome

household monthly net income, in German marks / 1000

children

1 if children under 16 in the household, 0 otherwise

self

1 if self employed, 0 otherwise

civil

1 if civil servant, 0 otherwise

bluec

1 if blue collar employee, 0 otherwise

employed

1 if employed, 0 otherwise

public

1 if public health insurance, 0 otherwise

addon

1 if add-on insurance, 0 otherwise

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.

Riphahn, R. T., Wambach, A., Million, A. (2003). “Incentive Effects in the Demand for Health Care: A Bivariate Panel Count Data Estimation”, Journal of Applied Econometrics, 18, 387–405.

Wagner, G. G., Frick, J. R., Schupp, J. (2007). “The German Socio-Economic Panel Study (SOEP) – Scope, Evolution and Enhancements”, Schmollers Jahrbuch, 127, 139–169.

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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

$y_i^* \sim \mathrm{Poisson}[\exp(\eta_i^*)],$

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

$d_i^* = \gamma + x_i'\delta + \nu_i,\; \nu_i \sim \mathrm{N}(0,1),$

$y_i = 1(d_i^*>0)y_i^*,$

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

$\alpha \sim \mathrm{N}(0,a_0),$

$\beta_k \sim \mathrm{N}(0,b_0), \quad k=1,\ldots,K,$

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

$\delta_k \sim \mathrm{N}(0,d_0), \quad k=1,\ldots,K,$

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

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).
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)

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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)

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