bayesQRsurvey (version 0.1.4)

bqr.svy: Bayesian quantile regression for complex survey data

Description

bqr.svy implements Bayesian methods for estimating quantile regression models for complex survey data analysis regarding single (univariate) outputs. To improve computational efficiency, the Markov Chain Monte Carlo (MCMC) algorithms are implemented in 'C++'.

Usage

bqr.svy(
  formula,
  weights = NULL,
  data = NULL,
  quantile = 0.5,
  method = c("ald", "score", "approximate"),
  prior = NULL,
  niter = 50000,
  burnin = 0,
  thin = 1,
  verbose = TRUE,
  estimate_sigma = FALSE
)

Value

An object of class "bqr.svy", containing:

beta

Posterior mean estimates of regression coefficients.

draws

Posterior draws from the MCMC sampler.

accept_rate

Average acceptance rate (if available).

warmup, thin

MCMC control parameters used during sampling.

quantile

The quantile(s) fitted.

prior

Prior specification used.

formula, terms, model

Model specification details.

runtime

Elapsed runtime in seconds.

method

Estimation method

estimate_sigma

Logical flag indicating whether the scale parameter \(\sigma^2\) was estimated (TRUE) or fixed at 1 (FALSE).

Arguments

formula

a symbolic description of the model to be fit.

weights

an optional numerical vector containing the survey weights. If NULL, equal weights are used.

data

an optional data frame containing the variables in the model.

quantile

numerical scalar or vector containing quantile(s) of interest (default=0.5).

method

one of "ald", "score" and "approximate" (default="ald").

prior

a bqr_prior object of class "prior". If omitted, a vague prior is assumed (see prior).

niter

number of MCMC draws.

burnin

number of initial MCMC draws to be discarded.(default = 0)

thin

thinning parameter, i.e., keep every keepth draw (default=1).

verbose

logical flag indicating whether to print progress messages (default=TRUE).

estimate_sigma

logical flag indicating whether to estimate the scale parameter when method = "ald" (default=FALSE and \(\sigma^2\) is set to 1)

Details

The bqr.svy function can estimate three types of models, where the quantile regression coefficients are defined at the super-population level, and their estimators are built upon the survey weights.

• "ald" – The asymmetric Laplace distribution as working likelihood.

• "score" – A score based likelihood function.

• "approximate" – A pseudolikelihood function based on a Gaussian approximation.

References

Nascimento, M. L. & Gonçalves, K. C. M. (2024). Bayesian Quantile Regression Models for Complex Survey Data Under Informative Sampling. Journal of Survey Statistics and Methodology, 12(4), 1105–1130. doi:10.1093/jssam/smae015

Examples

# \donttest{
# Generate population data
set.seed(123)
N    <- 10000
x1_p <- runif(N, -1, 1)
x2_p <- runif(N, -1, 1)
y_p  <- 2 + 1.5 * x1_p - 0.8 * x2_p + rnorm(N)

# Generate sample data
n <- 500
z_aux <- rnorm(N, mean = 1 + y_p, sd = .5)
p_aux <- 1 / (1 + exp(2.5 - 0.5 * z_aux))
s_ind <- sample(1:N, n, replace = FALSE, prob = p_aux)
y_s   <- y_p[s_ind]
x1_s  <- x1_p[s_ind]
x2_s  <- x2_p[s_ind]
w     <- 1 / p_aux[s_ind]
data  <- data.frame(y = y_s, x1 = x1_s, x2 = x2_s, w = w)

# Basic usage with default method ('ald') and priors (vague)
fit1 <- bqr.svy(y ~ x1 + x2, weights = w, data = data)

# Specify informative priors
prior <- prior(
  beta_x_mean = c(2, 1.5, -0.8),
  beta_x_cov  = diag(c(0.25, 0.25, 0.25)),
  sigma_shape = 1,
  sigma_rate  = 1
)
fit2 <- bqr.svy(y ~ x1 + x2, weights = w, data = data, prior = prior)

# Specify different methods
fit_score  <- bqr.svy(y ~ x1 + x2, weights = w, data = data, method = "score")
fit_approx <- bqr.svy(y ~ x1 + x2, weights = w, data = data, method = "approximate")
# }