# bayesModel.fit: Bayesian regression model with mixture of two scaled inverse... In BayesH: Bayesian Regression Model with Mixture of Two Scaled Inverse Chi Square as Hyperprior

## 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 `matrix` of model. `y` the vector of response variable of the model. `nu0` the degree of freedom hyperparameter(s) `nu0` for all mixture components. `s0` the scale hyperparameter(s) `s0` for all mixture components. `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, [email protected]

## See Also

`get.scale.bayesH`

## Examples

 ```1 2 3 4 5 6``` ```data(example) mod = bayesModel.fit(X = X, y = y, nu0 = c(3,30,20), s0 = c(1e-10,0.1, 0.5), niter = 2000, burnin = 300, type = "bayesH" ) summary(mod) ```

BayesH documentation built on May 1, 2019, 6:28 p.m.