LN_QuantReg {BayesLN} | R Documentation |

## Bayesian estimate of the log-normal conditioned quantiles

### Description

This function produces a point estimate for the log-normal distribution quantile of fixed level `quant`

.

### Usage

```
LN_QuantReg(
y,
X,
Xtilde,
quant,
method = "weak_inf",
guess_s2 = NULL,
y_transf = TRUE,
CI = TRUE,
method_CI = "exact",
alpha_CI = 0.05,
type_CI = "two-sided",
rel_tol_CI = 1e-05,
nrep_CI = 1e+05
)
```

### Arguments

`y` |
Vector of observations of the response variable. |

`X` |
Design matrix. |

`Xtilde` |
Covariate patterns of the units to estimate. |

`quant` |
Number between 0 and 1 that indicates the quantile of interest. |

`method` |
String that indicates the prior setting to adopt. Choosing |

`guess_s2` |
Specification of a guess for the variance if available. If not, the sample estimate is used. |

`y_transf` |
Logical. If |

`CI` |
Logical. With the default choice |

`method_CI` |
String that indicates if the limits should be computed through the logSMNG
quantile function |

`alpha_CI` |
Level of credibility of the posterior interval. |

`type_CI` |
String that indicates the type of interval to compute: |

`rel_tol_CI` |
Level of relative tolerance required for the |

`nrep_CI` |
Number of simulations for the C.I. in case of |

### Details

The function allows to carry out Bayesian inference for the conditional quantiles of a sample that is assumed log-normally distributed.
The design matrix containing the covariate patterns of the sampled units is `X`

, whereas `Xtilde`

contains the covariate patterns of the unit to predict.

The classical log-normal linear mixed model is assumed and the quantiles are estimated as:

`\theta_p(x)=exp(x^T\beta+\Phi^{-1}(p))`

.

A generalized inverse Gaussian prior is assumed for the variance in the log scale `\sigma^2`

, whereas a
flat improper prior is assumed for the vector of coefficients `\beta`

.

Two alternative hyperparamters setting are implemented (choice controlled by the argument `method`

): a weakly
informative proposal and an optimal one.

### Value

The function returns the prior parameters and their posterior values, summary statistics of the parameters `\beta`

and `\sigma^2`

, and the estimate of the specified quantile:
the posterior mean and variance are provided by default. Moreover the user can control the computation of posterior intervals.

#'@source

Gardini, A., C. Trivisano, and E. Fabrizi. *Bayesian inference for quantiles of the log-normal distribution.* Biometrical Journal (2020).

*BayesLN*version 0.2.10 Index]