prior: Create prior for Bayesian quantile regression models for...

In bayesQRsurvey: Bayesian Quantile Regression Models for Complex Survey Data Analysis

Create prior for Bayesian quantile regression models for complex survey data

Description

prior creates prior distributions for both single (bqr.svy) and multiple-output (mo.bqr.svy) Bayesian quantile regression models for complex survey data.

Usage

prior(
  beta_x_mean = NULL,
  beta_x_cov = NULL,
  sigma_shape = 0.001,
  sigma_rate = 0.001,
  beta_y_mean = NULL,
  beta_y_cov = NULL
)

Arguments

beta_x_mean	vector of prior means for the regression coefficients. (default = NULL).
beta_x_cov	prior covariance matrix for the regression coefficients. (default = NULL).
sigma_shape	shape parameter for inverse Gamma prior for \sigma^2. (default = 0.001).
sigma_rate	rate parameter for inverse Gamma prior for \sigma^2. (default = 0.001).
beta_y_mean	prior means for the coefficients related to the variables that emerge from the product between the orthogonal basis and the outputs (default = NULL).
beta_y_cov	prior covariance matrix for the coefficients related to the variables that emerge from the product between the orthogonal basis and the outputs. (default = NULL).

Details

The function prior builds prior distributions for the three methods implemented in the function bqr.svy and for the multiple-output quantile regression implemented in the function mo.bqr.svy. Every nonspecified prior parameter will get the default value.

• method = "ald" in function bqr.svy allow the specification of hyperparameters beta_x_mean, beta_x_cov, sigma_shape, and sigma_rate.

• method = "score" in function bqr.svy allow the specification of hyperparameters beta_x_mean and beta_x_cov.

• method = "approximate" in function bqr.svy allow the specification of hyperparameters beta_x_mean and beta_x_cov.

• In function mo.bqr.svy, the specification of hyperparameters beta_x_mean,beta_x_cov, sigma_shape, sigma_rate, beta_y_mean, and beta_y_cov are allowed.

Value

An object of class "prior".

See Also

bqr.svy, mo.bqr.svy, summary

Examples

# Simulate data
set.seed(123)
n  <- 200
x1 <- rnorm(n, 0, 1)
x2 <- runif(n, -1, 1)
w  <- runif(n, 0.5, 2)   # survey weights

y1 <- 2 + 1.5*x1 - 0.8*x2 + rnorm(n, 0, 1)
y2 <- 1 + 0.5*x1 - 0.2*x2 + rnorm(n, 0, 1)

data <- data.frame(y1 = y1, y2 = y2, x1 = x1, x2 = x2, w = w)

# Define a general informative prior
prior_general <- prior(
  beta_x_mean = c(2, 1.5, -0.8),
  beta_x_cov  = diag(c(0.25, 0.25, 0.25)),
  sigma_shape = 3,
  sigma_rate  = 2,
  beta_y_mean = 1,
  beta_y_cov  = 0.25
)

# Estimate the model parameters with informative prior
fit_ald <- bqr.svy(y1 ~ x1 + x2, weights = w, data = data,
                   prior = prior_general, method = "ald")

fit_scr <- bqr.svy(y1 ~ x1 + x2, weights = w, data = data,
                   prior = prior_general, method = "score")

fit_apx <- bqr.svy(y1 ~ x1 + x2, weights = w, data = data,
                   prior = prior_general, method = "approximate")

# Multiple-output method
fit_mo <- mo.bqr.svy(cbind(y1, y2) ~ x1 + x2, weights = w,
                     data = data, prior = prior_general, n_dir = 10)

plot(fit_ald, type = "trace", which = "x1", tau = 0.5)
plot(fit_ald, type = "trace", which = "x2", tau = 0.5)

print(fit_mo)

bayesQRsurvey documentation built on July 8, 2026, 1:08 a.m.