Robust Bayesian Inference for Non-Probability Samples Using Gaussian Process of Propensity Prediction

• Activity Number: 310 - Making Finite Population Inferences from Nonprobability Samples
• Type: Topic-Contributed
• Date/Time: Wednesday, August 11, 2021 : 3:30 PM to 5:20 PM
• Sponsor: Survey Research Methods Section
• Author(s): Ali Rafei* and Michael R. Elliott and Carol Flannagan
• Companies: University of Michigan and University of Michigan and University of Michigan
• Keywords: Non-probability sample; double robustness; Gaussian processes; prediction model; Bayesian inference

Abstract

The ubiquitous availability of unstructured data parallel to the declining response rate in probability surveys has led to a growing interest in the use of such large-scale non-probability samples for finite population inference. Existing bias adjustment approaches assume that the conditional mean structures have been correctly specified for the selection indicator or key substantive measures. Such methods may perform poorly for non-normal outcomes or when there is evidence of influential pseudo-weights. In addition, estimating the variance lacks a unified framework under these methods and often relies on complex asymptotic theories. To address these gaps, we propose alternative Bayesian approaches using a partially linear Gaussian process model. It utilizes a prediction model with a flexible function of the estimated propensity scores as a predictor to impute the outcome for units of the reference survey. We show that Gaussian process regression behaves as a non-parametric matching technique based on the estimated propensity scores. Using the posterior predictive draws of the outcome, we quantify the uncertainty of our proposed estimator based on a conditional variance method.