# Separately modelling of multiple response variables taking values from (0,1] when there are multiple random variables in the linear predictors of the link functions

### Description

Internal function to be called by function zoib. Separately models multiple (0,1]-bounded variables with inflation at 1 when there are multiple random variables in the linear predictors of the link functions

### Usage

1 2 3 | ```
sep.2z1(y, n, xmu.1, p.xmu, xsum.1, p.xsum, x1.1, p.x1, zdummy, qz, nz0, m, rid,
EUID, nEU, prior1, prior2, prior.beta, prior.Sigma, prec.int, prec.DN,
lambda.L1, lambda.L2, lambda.ARD, scale.unif, scale.halft, link, n.chain,inits, seed)
``` |

### Arguments

`y` |
>=2 response variables taking value from (0, 1]. |

`n` |
Number of rows in the data set. |

`xmu.1` |
Design matrix associated with the fixed effects in the linear predictor of g(mean of the beta piece), where g() is a link function. |

`p.xmu` |
Number of columns in xmu.1. |

`xsum.1` |
Design matrix associated with fixed effects in linear predictor of the log(dispersion parameter of the beta piece). |

`p.xsum` |
Number of columns in xsum.1. |

`x1.1` |
Design matrix associated with the fixed effects in the linear predictor of g(Pr(y=1)), where g() is a link function. |

`p.x1` |
Number of columns in x1.1. |

`zdummy` |
Design matrix associated with the random effects. |

`qz` |
Number of columns in zdummy. |

`nz0` |
Number of original random variables (before dummy coding). |

`m` |
A vector with nz0 element that contains the number of levels of each random varaibles. |

`rid` |
A vector containing information on which linear predictors have a random component. |

`EUID` |
Listing of experimental unit ID for each row of the data set. |

`nEU` |
Number of experimental units. |

`prior1` |
A vector containing information on the prior choice for the regression coefficients in each of the 4 linear predictors of the 4 link functions. |

`prior2` |
A matrix containing information on the prior choice for the covariance structure of the random variables. |

`prior.beta` |
Prior choice for the regression coefficients in each of the 4 link functions. |

`prior.Sigma` |
Prior choice for the Covariance structure of the random variables. |

`prec.int` |
The precision parameter of the prior distributions (diffuse normal) of the intercepts in the linear predictors. |

`prec.DN` |
The precision parameter of the prior distributions of the regression coefficients in the linear predictors if the diffuse normal prior is chosen. |

`lambda.L1` |
The scale parameter in the prior distributions of the regression coefficients in the linear predictors if the L1-like prior is chosen. |

`lambda.L2` |
The scale parameter in the prior distributions of the regression coefficients in the linear predictors if the L2-like prior is chosen. |

`lambda.ARD` |
The scale parameter in the prior distributions of the regression coefficients in the linear predictors if the ARD prior is chosen. |

`scale.unif` |
The upper bound of the uniform distribution for the standard deviation of each random variable. |

`scale.halft` |
The scale parameter of the half-Cauchy distribution for the standard deviation of each random variable. |

`link` |
A vector containing the information on the choice of link function for the mean of the beta piece. |

`n.chain` |
Number of chains for the MCMC sampling. |

`inits` |
initial parameter for model parameters. |

`seed` |
seeds for results reproducibility |

### Value

Internal function. Returned values are used internally

### Author(s)

Fang Liu (fang.liu.131@nd.edu)

### See Also

See Also as `zoib`