csSampling: An R Package for Bayesian Models for Complex Survey Data

TL;DR

csSampling is an R package that enables Bayesian modeling of complex survey data by integrating survey design information with probabilistic programming, providing accurate uncertainty estimates and frequentist properties.

Contribution

It introduces a method to incorporate survey weights into Bayesian models using Stan and brms, with asymptotic covariance correction for design effects.

Findings

Provides asymptotic covariance correction for survey weights

Ensures Bayesian inference with frequentist coverage properties

Integrates survey design with probabilistic programming in R

Abstract

We present csSampling, an R package for estimation of Bayesian models for data collected from complex survey samples. csSampling combines functionality from the probabilistic programming language Stan (via the rstan and brms R packages) and the handling of complex survey data from the survey R package. Under this approach, the user creates a survey-weighted model in brms or provides a custom weighted model via rstan. Survey design information is provided via the svydesign function of the survey package. The cs_sampling function of csSampling estimates the weighted stan model and provides an asymptotic covariance correction for model mis-specification due to using survey sampling weights as plug-in values in the likelihood. This is often known as a ``design effect'' which is the ratio between the variance from a complex survey sample and a simple random sample of the same size. The resulting adjusted posterior draws can then be used for the usual Bayesian inference while also achieving frequentist properties of asymptotic consistency and correct uncertainty (e.g. coverage).