# Bayesian Inference for Zero-Inflated Count Models

### Description

`zic`

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

### Usage

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### 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 |

`a0` |
The prior variance of |

`b0` |
The prior variance of |

`c0` |
The prior variance of |

`d0` |
The prior variance of |

`e0` |
The shape parameter for the inverse gamma prior on |

`f0` |
The inverse scale parameter the inverse gamma prior on |

`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 |

`beta` |
Posterior draws of |

`gamma` |
Posterior draws of |

`delta` |
Posterior draws of |

`sigma2` |
Posterior draws of |

`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

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