Robust Model-based Inference for Non-Probability Samples

TL;DR

This paper introduces a fully model-based Bayesian bootstrap approach for inference in non-probability samples, effectively addressing selection bias and outliers while providing reliable uncertainty estimates.

Contribution

It proposes a novel Bayesian bootstrap method with Gaussian process regression for non-probability sample inference, handling model misspecification and complex survey designs.

Findings

Method performs well in simulations under various conditions.

Accurately estimates injury rates in real-world US data.

Provides valid confidence intervals despite complex sampling.

Abstract

With the ubiquitous availability of unstructured data, growing attention is paid as how to adjust for selection bias in such non-probability samples. The majority of the robust estimators proposed by prior literature are either fully or partially design-based, which may lead to inefficient estimates if outlying (pseudo-)weights are present. In addition, correctly reflecting the uncertainty of the adjusted estimator remains a challenge when the available reference survey is complex in the sample design. This article proposes a fully model-based method for inference using non-probability samples where the goal is to predict the outcome variable for the entire population units. We employ a Bayesian bootstrap method with Rubin's combing rules to derive the adjusted point and interval estimates. Using Gaussian process regression, our method allows for kernel matching between the non-probability sample units and population units based on the estimated selection propensities when the outcome model is misspecified. The repeated sampling properties of our method are evaluated through two Monte Carlo simulation studies. Finally, we examine it on a real-world non-probability sample with the aim to estimate crash-attributed injury rates in different body regions in the United States.