# Bayesian regression model with mixture of two scaled inverse chi square as hyperprior distribution.

### Description

Performs Gibbs Sampling algorithm for fitting the Bayesian regression model with mixture of two scaled inverse chi square as hyperprior distribution for variance of each regression coefficients.

### Usage

1 2 | ```
bayesModel.fit(X, y, nu0, s0, niter = 2000, burnin = 500, type="bayesH")
``` |

### Arguments

`X` |
the incidence |

`y` |
the vector of response variable of the model. |

`nu0` |
the degree of freedom hyperparameter(s) |

`s0` |
the scale hyperparameter(s) |

`niter` |
the number of iterations of Gibbs Sampling algorithm. |

`burnin` |
the number of 'burn in' in a Gibbs Sampling algorithm. |

`type` |
it is a string which if were defined as “ridge” the function performs Bayesian ridge regression, otherwise, Bayes H model. |

### Details

For bayesian ridge regression (type == "ridge"), the prior distribution for the error
variance and the hyperprior distribution for variance of the regression coefficients
follows scaled inverse chi square with same hyperparameters `(nu0[1], s0[1])`

and `(nu0[2], s0[2])`

, respectively.On the other hand, for hierarchical regression
model (type == "bayesH") is assumed that each the regression coefficient has different variance
and each one of them follows a mixture of scaled inverse chi square with hyperparameters
(`nu0[1]`

; `s0[1]`

) and (`nu0[2]`

; `s0[2]`

), respectively.
In this case, the prior distribution for error variance also follows scaled inverse
chi square with hyperparameters `nu0[3]`

and `s0[3]`

. NA's in the incidence
matrix are not allowed. All elements of vector `s0`

must be greater than zero.

### Value

The output is an object of class `BayesH`

that contains the
posterior distribution of intercept, posterior distribution of variance error,
posterior mean of regression coefficients and posterior mean of predicted values.

### Author(s)

Renato Rodrigues Silva, renato.rrsilva@ufg.br

### See Also

`get.scale.bayesH`

### Examples

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