LN_QuantReg {BayesLN} | R Documentation |
This function produces a point estimate for the log-normal distribution quantile of fixed level quant
.
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
)
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 |
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.
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).