Combining Data from Probability and Non-Probability Samples Using Penalized Spline of Propensity Prediction

• Activity Number: 126 - Interpreting Nonprobability Samples: Discoveries and Challenges
• Type: Topic-Contributed
• Date/Time: Monday, August 9, 2021 : 1:30 PM to 3:20 PM
• Sponsor: Survey Research Methods Section
• Author(s): Michael R. Elliott* and Ali Rafei and Carol Flannagan
• Companies: University of Michigan and University of Michigan and University of Michigan
• Keywords: Double robustness; Non-parametric Bayesian modeling; Augmented inverse propensity weighting

Abstract

Population inference using combinations of probability and non-probability samples is an increasingly critical area of research. A variety of “doubly-robust” methods that combine model-based prediction estimators with estimators weighted to account for selection bias have been developed. Here we propose a Bayesian approach using partially linear Gaussian process regression that uses a prediction model with a flexible function of the estimated propensity scores as a predictor to impute the outcome for either non-sampled units of the population or units of the reference survey. We will use this method in a simulation study common to the other papers presented in this session. This study will use two sampling frames, one a subset of the other, using survey completes from a study of Arts and Culture during COVID-19. Frame 1 will be the full population frame, consisting of all survey completes, from which probability samples will be selected. Frame 2 will be a nonrandom subset of Frame 1 with known coverage biases from which non-probability samples will be selected. Assessments of the proposed method will be undertaken via estimates of bias, interval coverage, and mean square error.