LN_MeanReg function

Bayesian Estimate of the conditional Log-normal Mean

This function produces a bayesian estimate of the conditional log-normal mean assuming a GIG prior for the variance and an improper prior for the regression coefficients of the linear regression in the log scale.

Source

Fabrizi, E., & Trivisano, C. Bayesian Conditional Mean Estimation in Log-Normal Linear Regression Models with Finite Quadratic Expected Loss. Scandinavian Journal of Statistics, 43(4), 1064-1077. (2016).

LN_MeanReg(
  y,
  X,
  Xtilde,
  method = "weak_inf",
  y_transf = TRUE,
  h = NULL,
  CI = TRUE,
  alpha_CI = 0.05,
  type_CI = "two-sided",
  nrep = 1e+05
)

Arguments

• y: Vector of observations of the response variable.
• X: Design matrix.
• Xtilde: Matrix of covariate patterns for which an estimate is required.
• method: String that indicates the prior setting to adopt. Choosing "weak_inf" a weakly informative prior setting is adopted, whereas selecting "optimal" the hyperparameters are aimed at minimizing the frequentist MSE.
• y_transf: Logical. If TRUE, the y vector is already assumed as log-transformed.
• h: Leverage. With the default option NULL, the average leverage is used.
• CI: Logical. With the default choice TRUE, the posterior credibility interval is computed.
• alpha_CI: Level of alpha that determines the credibility (1-alpha_CI) of the posterior interval.
• type_CI: String that indicates the type of interval to compute: "two-sided" (default), "UCL" (i.e. Upper Credible Limit) for upper one-sided intervals or "LCL" (i.e. Lower Credible Limit) for lower one-sided intervals.
• nrep: Number of simulations.

Returns

The function returns a list including the prior and posterior parameters, the point estimate of the log-normal mean conditioned with respect to the covariate points included in Xtilde. It consists of the mean of the posterior distribution for the functional $\exp\{\tilde{x}_i^T\beta+\sigma^2/2\}$ and the posterior variance.

Details

In this function the same procedure as LN_Mean is implemented allowing for the inclusion of covariates. Bayesian point and interval estimates for the response variabile in the original scale are provided considering the model: $log(y_i)=X\beta$.

Examples

library(BayesLN)
data("fatigue")

# Design matrices
Xtot <- cbind(1, log(fatigue$stress), log(fatigue$stress)^2)
X <- Xtot[-c(1,13,22),]
y <- fatigue$cycle[-c(1,13,22)]
Xtilde <- Xtot[c(1,13,22),]
#Estimation
LN_MeanReg(y = y,
           X = X, Xtilde = Xtilde,
           method = "weak_inf", y_transf = FALSE)