# Hierarchical Bayesian multiple regression model incorporating genotype uncertainty (HBMR) for binary traits

### Description

The function implements HBMR using a Gibbs sampler with probit link function for binary traits.

### Usage

1 2 |

### Arguments

`pheno` |
A phenotypic vector ( |

`geno` |
An |

`qi` |
An optional |

`fam` |
fam=1 for family samples. In this case, a relatedness matrix should be given. See kin. |

`kin` |
In the case of fam=1, kin is an |

`iter` |
The number of MCMC iterations. The default value is 10000. |

`burnin` |
The number of burn-ins. The default value is 500. |

`gq` |
A cutoff for |

`imp` |
A cutoff for imputed genotype ( |

`cov` |
An optional |

`maf` |
An optional minor allele frequency information vector ( |

`pa` |
The positive hyper-parameter |

`pb` |
The positive hyper-parameter |

### Value

`BF ` |
The Bayes factor of |

`BF_RB ` |
The BF estimated by using Rao-Blackwellization theorem |

`p_upper ` |
For a BF larger than 2, we calculate p_upper that is the upper bound of the p value corresponding to the BF based on the connection |

`mean ` |
The mean of the posterior of |

`var ` |
The inverse of the mean of posterior of precision 1/ |

`est_geno ` |
The number of genotypes whose uncertainty are considered in estimation |

`var_ran ` |
The estimated variance of the random effect for family design |

`rv_mean_es ` |
The means of the posterior of |

`rv_sd_es ` |
The standard deviations of the posterior of |

`mean_cov ` |
The means of the posterior of for the |

### Author(s)

Liang He

### References

He, L., Pitk<e4>niemi, J., Sarin, A. P., Salomaa, V., Sillanp<e4><e4>, M. J., & Ripatti, S. (2015). Hierarchical Bayesian Model for Rare Variant Association Analysis Integrating Genotype Uncertainty in Human Sequence Data. Genetic epidemiology, 39(2), 89-100.

Albert, J. H., & Chib, S. (1993). Bayesian analysis of binary and polychotomous response data. Journal of the American statistical Association, 88(422), 669-679.

### Examples

1 2 3 | ```
data(hbmr_bin_data)
hbmr_bin(hbmr_bin_data$pheno[1:500], hbmr_bin_data$geno[1:500,1:3], fam=1,
kin= hbmr_bin_data$kin[1:500,1:500], iter=800, burnin=200)
``` |