Rgbp: An R Package for Gaussian, Poisson, and Binomial Random Effects Models with Frequency Coverage Evaluations

TL;DR

Rgbp is an R package that offers estimation and confidence interval evaluation for random effects in hierarchical models across Gaussian, Poisson, and Binomial data, emphasizing coverage accuracy and model checking.

Contribution

The paper introduces Rgbp, an R package that employs approximate Bayesian methods with improper priors to improve coverage and provides tools for synthetic data generation to validate interval estimates.

Findings

Rgbp achieves good repeated sampling coverage for random effects.

The package allows for model checking via synthetic data generation.

It provides inference for hyper-parameters, including regression coefficients.

Abstract

Rgbp is an R package that provides estimates and verifiable confidence intervals for random effects in two-level conjugate hierarchical models for overdispersed Gaussian, Poisson, and Binomial data. Rgbp models aggregate data from k independent groups summarized by observed sufficient statistics for each random effect, such as sample means, possibly with covariates. Rgbp uses approximate Bayesian machinery with unique improper priors for the hyper-parameters, which leads to good repeated sampling coverage properties for random effects. A special feature of Rgbp is an option that generates synthetic data sets to check whether the interval estimates for random effects actually meet the nominal confidence levels. Additionally, Rgbp provides inference statistics for the hyper-parameters, e.g., regression coefficients.