# Probit Hierarchial Level Model

### Description

Performs modeling procedure for a Probit Hierarchial Level Model.

### Usage

1 2 3 4 |

### Arguments

`unique_subject_ids` |
A |

`subject_ids` |
A |

`choices_nk` |
A |

`fixed_effects_design` |
A |

`rv_effects_design` |
A |

`B_elem_plus1` |
A V[[1]] dimensional column |

`gamma` |
A |

`beta` |
A |

`theta` |
A |

`zeta_rv` |
A |

`WtW` |
A |

`Z_c` |
A |

`Wzeta_0` |
A |

`inv_Sigma_gamma` |
A |

`mu_gamma` |
A |

`Sigma_zeta_inv` |
A |

`S0` |
A |

`mu_beta` |
A |

`sigma_beta_inv` |
A |

### Details

The function is implemented to decrease the amount of vectorizations necessary.

### Value

A `matrix`

that is an inverse wishart distribution.

A `list`

that contains:

`zeta_1`

A

`vector`

of length N`sigma_zeta_inv_1`

A

`matrix`

of dimensions V x V`gamma_1`

A

`vector`

of length P`beta_1`

A

`vector`

of length V`B`

A

`matrix`

of length V

### Author(s)

Steven A Culpepper, James J Balamuta

### See Also

`rwishart`

and `TwoPLChoicemcmc`