Package {BayesQRCount}

Type:	Package
Title:	Adaptive Bayesian Quantile Regression for Count Data
Version:	0.1.0
Description:	Implements Bayesian quantile regression for count data using the jittering technique for discrete data smoothing and an asymmetric Laplace distribution likelihood. Supports adaptive variable selection via a random-bridge penalty with a beta prior on the power parameter, as well as fixed-bridge and Lasso penalties. Utilizes Markov chain Monte Carlo with Gibbs sampling and adaptive Metropolis-Hastings algorithms for posterior inference, provides Gelman-Rubin convergence diagnostics, and predicts conditional quantiles for count responses. Methodology and applications are based on the following key references: Luo, Zhou, Hu, and Li (2026, Journal of Mathematics, 2026:1543166, <doi:10.1155/jom/1543166>), Koenker and Bassett (1978, Econometrica, 46, 33-50, <doi:10.2307/1913643>), Machado and Santos Silva (2005, Journal of the American Statistical Association, 100, 1226-1237, <doi:10.1198/016214505000000330>), Yu and Moyeed (2001, Statistics and Probability Letters, 54, 437-447, <doi:10.1016/S0167-7152(01)00124-9>), Polson, Scott, and Windle (2014, Journal of the Royal Statistical Society Series B, 76, 713-733, <doi:10.1111/rssb.12042>), Park and Casella (2008, Journal of the American Statistical Association, 103, 681-686, <doi:10.1198/016214508000000337>), and Roberts and Rosenthal (2009, Journal of Computational and Graphical Statistics, 18, 349-367, <doi:10.1198/jcgs.2009.06134>).
License:	GPL (≥ 3)
Encoding:	UTF-8
RoxygenNote:	7.3.3
Depends:	R (≥ 4.0.0)
Imports:	stats, graphics, grDevices
Suggests:	testthat (≥ 3.0.0)
NeedsCompilation:	no
Packaged:	2026-07-27 18:42:36 UTC; shikhar tyagi
Author:	Shikhar Tyagi [aut, cre], Arvind Pandey [aut], Bhupendra Singh [aut], Vrijesh Tripathi [aut]
Maintainer:	Shikhar Tyagi <shikhar1093tyagi@gmail.com>
Repository:	CRAN
Date/Publication:	2026-08-05 09:30:08 UTC

Bayesian Quantile Regression for Count Data

Description

Performs Bayesian quantile regression for count data using the jittering-based asymmetric Laplace distribution (ALD) likelihood with random-bridge, fixed-bridge, or Lasso penalty priors. Implements the methodology of Luo, Zhou, Hu, and Li (2026).

Usage

bqr_count(
  y,
  X,
  tau = 0.5,
  method = c("random_bridge", "fixed_bridge", "lasso"),
  xi_fixed = 0.5,
  N_iter = 20000,
  burn_in = 10000,
  thin = 10,
  n_chains = 3,
  lambda_prior = c(a = 1, b = 1),
  xi_prior = c(e = 1, f = 1),
  delta = 0.05,
  sigma0_sq = 0.01,
  seed = NULL
)

Arguments

Value

An object of class "bqr_count", a list containing:

beta_samples

Array of posterior beta samples (n_saved x p x n_chains).

sigma_samples

Matrix of posterior sigma samples (n_saved x n_chains).

lambda_samples

Matrix of posterior lambda samples (n_saved x n_chains).

xi_samples

Matrix of posterior xi samples (n_saved x n_chains).

summary

Data frame with posterior mean, median, SD, and 95 percent HPD intervals for all parameters.

coefficients

Named numeric vector of posterior mean coefficients.

fitted_quantiles

Numeric vector of fitted quantile values.

variable_selection

Logical vector indicating selected variables (HPD excludes 0).

tau

The quantile level used.

method

The penalty method used.

n_chains

Number of chains.

y

The response data.

X_original

The original covariate matrix (without intercept).

X_design

The full design matrix (with intercept).

call

The matched function call.

Examples

set.seed(42)
n <- 100
X <- matrix(rnorm(n * 2), n, 2)
y <- rpois(n, exp(0.5 + 0.3 * X[, 1] - 0.2 * X[, 2]))
fit <- bqr_count(y, X, tau = 0.5, method = "random_bridge",
                 N_iter = 500, burn_in = 200, thin = 2, n_chains = 1)
print(fit)

Extract coefficients from bqr_count

Description

Extract coefficients from bqr_count

Usage

## S3 method for class 'bqr_count'
coef(object, ...)

Arguments

Value

A numeric vector of coefficients.

Examples

set.seed(42)
n <- 80
x1 <- rnorm(n)
x2 <- rnorm(n)
X <- cbind(x1, x2)
y <- rpois(n, exp(0.5 + 0.8 * x1))
fit <- bqr_count(y, X, tau = 0.5, method = "lasso",
                 N_iter = 500, burn_in = 200, thin = 2, n_chains = 1)
coef(fit)

Compare Multiple Bayesian Quantile Regression Models

Description

Compares two or more fitted "bqr_count" models by RMSE and MAE.

Usage

compare_models(...)

Arguments

Value

A data frame with columns: Model, Method, Tau, RMSE, MAE.

Examples

set.seed(42)
n <- 80
x1 <- rnorm(n)
x2 <- rnorm(n)
X <- cbind(x1, x2)
y <- rpois(n, exp(0.5 + 0.8 * x1))
fit1 <- bqr_count(y, X, tau = 0.5, method = "lasso",
                  N_iter = 500, burn_in = 200, thin = 2, n_chains = 1)
fit2 <- bqr_count(y, X, tau = 0.5, method = "random_bridge",
                  N_iter = 500, burn_in = 200, thin = 2, n_chains = 1)
compare_models(Lasso = fit1, RandomBridge = fit2)

Posterior Density Plots

Description

Plots kernel density estimates of posterior distributions for selected parameters.

Usage

densplot(object, pars = NULL, ...)

Arguments

Value

Invisible NULL. Called for side effects (plotting).

Examples

set.seed(42)
n <- 80
x1 <- rnorm(n)
x2 <- rnorm(n)
X <- cbind(x1, x2)
y <- rpois(n, exp(0.5 + 0.8 * x1))
fit <- bqr_count(y, X, tau = 0.5, method = "lasso",
                 N_iter = 500, burn_in = 200, thin = 2, n_chains = 1)
densplot(fit)

Extract fitted values from bqr_count

Description

Extract fitted values from bqr_count

Usage

## S3 method for class 'bqr_count'
fitted(object, ...)

Arguments

Value

A numeric vector of fitted quantiles.

Examples

set.seed(42)
n <- 80
x1 <- rnorm(n)
x2 <- rnorm(n)
X <- cbind(x1, x2)
y <- rpois(n, exp(0.5 + 0.8 * x1))
fit <- bqr_count(y, X, tau = 0.5, method = "lasso",
                 N_iter = 500, burn_in = 200, thin = 2, n_chains = 1)
fitted(fit)

Gelman-Rubin Convergence Diagnostic

Description

Computes the potential scale reduction factor (R-hat) for all model parameters from a multi-chain Bayesian quantile regression fit.

Usage

gelman_rubin(object)

Arguments

Value

A data frame with columns Parameter and Rhat.

Examples

set.seed(42)
n <- 80
x1 <- rnorm(n)
x2 <- rnorm(n)
X <- cbind(x1, x2)
y <- rpois(n, exp(0.5 + 0.8 * x1))
fit <- bqr_count(y, X, tau = 0.5, method = "lasso",
                 N_iter = 500, burn_in = 200, thin = 2, n_chains = 2)
gelman_rubin(fit)

Plot diagnostics for bqr_count

Description

Plot diagnostics for bqr_count

Usage

## S3 method for class 'bqr_count'
plot(x, which = 1, ...)

Arguments

Value

Invisible NULL.

Examples

set.seed(42)
n <- 80
x1 <- rnorm(n)
x2 <- rnorm(n)
X <- cbind(x1, x2)
y <- rpois(n, exp(0.5 + 0.8 * x1))
fit <- bqr_count(y, X, tau = 0.5, method = "lasso",
                 N_iter = 500, burn_in = 200, thin = 2, n_chains = 1)
plot(fit, which = 3)

Plot coefficient effects across different quantiles

Description

Plot coefficient effects across different quantiles

Usage

plot_effects(fits, var_names = NULL, ...)

Arguments

Value

Invisible NULL.

Examples

set.seed(42)
n <- 80
x1 <- rnorm(n)
x2 <- rnorm(n)
X <- cbind(x1, x2)
y <- rpois(n, exp(0.5 + 0.8 * x1))
fit1 <- bqr_count(y, X, tau = 0.25, method = "lasso",
                 N_iter = 500, burn_in = 200, thin = 2, n_chains = 1)
fit2 <- bqr_count(y, X, tau = 0.5, method = "lasso",
                 N_iter = 500, burn_in = 200, thin = 2, n_chains = 1)
fit3 <- bqr_count(y, X, tau = 0.75, method = "lasso",
                 N_iter = 500, burn_in = 200, thin = 2, n_chains = 1)
plot_effects(list(Q25 = fit1, Q50 = fit2, Q75 = fit3))

Predict Method for Bayesian Quantile Regression Count Models

Description

Computes predicted conditional quantiles for new or training count data using the fitted model posterior.

Usage

## S3 method for class 'bqr_count'
predict(
  object,
  newdata = NULL,
  type = c("quantile", "mean"),
  interval = c("none", "credible"),
  level = 0.95,
  ...
)

Arguments

Value

A numeric vector of predicted values (if interval = "none"), or a data frame with columns fit, lower, upper (if interval = "credible").

Examples

set.seed(42)
n <- 80
x1 <- rnorm(n)
x2 <- rnorm(n)
X <- cbind(x1, x2)
y <- rpois(n, exp(0.5 + 0.8 * x1))
fit <- bqr_count(y, X, tau = 0.5, method = "lasso",
                 N_iter = 500, burn_in = 200, thin = 2, n_chains = 1)
predict(fit)

Print method for bqr_count objects

Description

Print method for bqr_count objects

Usage

## S3 method for class 'bqr_count'
print(x, ...)

Arguments

Value

The original object invisibly.

Examples

set.seed(42)
n <- 80
x1 <- rnorm(n)
x2 <- rnorm(n)
X <- cbind(x1, x2)
y <- rpois(n, exp(0.5 + 0.8 * x1))
fit <- bqr_count(y, X, tau = 0.5, method = "lasso",
                 N_iter = 500, burn_in = 200, thin = 2, n_chains = 1)
print(fit)

Print method for summary.bqr_count

Description

Print method for summary.bqr_count

Usage

## S3 method for class 'summary.bqr_count'
print(x, ...)

Arguments

Value

The original object invisibly.

Examples

set.seed(42)
n <- 80
x1 <- rnorm(n)
x2 <- rnorm(n)
X <- cbind(x1, x2)
y <- rpois(n, exp(0.5 + 0.8 * x1))
fit <- bqr_count(y, X, tau = 0.5, method = "lasso",
                 N_iter = 500, burn_in = 200, thin = 2, n_chains = 1)
s <- summary(fit)
print(s)

Extract residuals from bqr_count

Description

Extract residuals from bqr_count

Usage

## S3 method for class 'bqr_count'
residuals(object, ...)

Arguments

Value

A numeric vector of residuals.

Examples

set.seed(42)
n <- 80
x1 <- rnorm(n)
x2 <- rnorm(n)
X <- cbind(x1, x2)
y <- rpois(n, exp(0.5 + 0.8 * x1))
fit <- bqr_count(y, X, tau = 0.5, method = "lasso",
                 N_iter = 500, burn_in = 200, thin = 2, n_chains = 1)
residuals(fit)

Variable Selection Performance Metrics

Description

Computes F1-score, precision, recall, MSE, MAE, and average bias given the true regression coefficients. Useful for simulation studies.

Usage

selection_metrics(object, true_beta, level = 0.95)

Arguments

Value

A data frame with columns: F1, Precision, Recall, MSE, MAE, Bias.

Examples

set.seed(42)
n <- 80
x1 <- rnorm(n)
x2 <- rnorm(n)
X <- cbind(x1, x2)
y <- rpois(n, exp(0.5 + 0.8 * x1))
fit <- bqr_count(y, X, tau = 0.5, method = "lasso",
                 N_iter = 500, burn_in = 200, thin = 2, n_chains = 1)
selection_metrics(fit, true_beta = c(0.8, 0))

Simulated Count Data for Bayesian Quantile Regression

Description

A simulated dataset of 200 observations with 5 covariates and a Poisson count response, designed for demonstrating Bayesian quantile regression with variable selection. The true model has three non-zero coefficients (x1, x2, x5) and two zero coefficients (x3, x4).

Usage

data(sim_count_data)

Format

A data frame with 200 rows and 6 columns:

y

Integer, count response variable generated from Poisson distribution.

x1

Numeric, covariate with true coefficient 0.8.

x2

Numeric, covariate with true coefficient -0.5.

x3

Numeric, noise covariate with true coefficient 0.

x4

Numeric, noise covariate with true coefficient 0.

x5

Numeric, covariate with true coefficient 0.3.

Details

The data were generated using: mu = exp(0.5 + 0.8*x1 - 0.5*x2 + 0*x3 + 0*x4 + 0.3*x5), y ~ Poisson(mu), with covariates drawn independently from standard normal distributions. The true intercept is 0.5. The sparsity level is 0.4 (2 out of 5 covariates are zero).

Source

Simulated data for package demonstration.

Examples

data(sim_count_data)
head(sim_count_data)
table(sim_count_data$y)

Summary method for bqr_count objects

Description

Summary method for bqr_count objects

Usage

## S3 method for class 'bqr_count'
summary(object, ...)

Arguments

Value

A summary.bqr_count object.

Examples

set.seed(42)
n <- 80
x1 <- rnorm(n)
x2 <- rnorm(n)
X <- cbind(x1, x2)
y <- rpois(n, exp(0.5 + 0.8 * x1))
fit <- bqr_count(y, X, tau = 0.5, method = "lasso",
                 N_iter = 500, burn_in = 200, thin = 2, n_chains = 1)
summary(fit)

Trace Plots for MCMC Chains

Description

Produces trace plots of MCMC samples for selected parameters.

Usage

traceplot(object, pars = NULL, ...)

Arguments

Value

Invisible NULL. Called for side effects (plotting).

Examples

set.seed(42)
n <- 80
x1 <- rnorm(n)
x2 <- rnorm(n)
X <- cbind(x1, x2)
y <- rpois(n, exp(0.5 + 0.8 * x1))
fit <- bqr_count(y, X, tau = 0.5, method = "lasso",
                 N_iter = 500, burn_in = 200, thin = 2, n_chains = 1)
traceplot(fit)

Variable Selection from Bayesian Quantile Regression

Description

Extracts variable selection results from a fitted model based on highest posterior density (HPD) intervals.

Usage

variable_select(object, level = 0.95)

Arguments

Value

A list with components:

selected

Integer vector of indices of selected covariates (relative to the original X matrix, excluding intercept).

selected_names

Character vector of names of selected covariates.

coefficients

Named numeric vector of posterior mean coefficients for selected covariates.

n_selected

Integer, number of selected covariates.

Examples

set.seed(42)
n <- 80
x1 <- rnorm(n)
x2 <- rnorm(n)
X <- cbind(x1, x2)
y <- rpois(n, exp(0.5 + 0.8 * x1))
fit <- bqr_count(y, X, tau = 0.5, method = "lasso",
                 N_iter = 500, burn_in = 200, thin = 2, n_chains = 1)
variable_select(fit)