Arkadiusz Wiśniowski, Joseph W. Sakshaug, Diego Andres Perez Ruiz, Annelies G. Blom
Integrating Probability and Nonprobability Samples for Survey Inference

Journal of Survey Statistics and Methodology, 2020: 8, issue 1, pp. 120-147
ISSN: 2325-0984 (print), 2325-0992 (online)

Survey data collection costs have risen to a point where many survey researchers and polling companies are abandoning large, expensive probability-based samples in favor of less expensive nonprobability samples. The empirical literature suggests this strategy may be suboptimal for multiple reasons, among them that probability samples tend to outperform nonprobability samples on accuracy when assessed against population benchmarks. However, nonprobability samples are often preferred due to convenience and costs. Instead of forgoing probability sampling entirely, we propose a method of combining both probability and nonprobability samples in a way that exploits their strengths to overcome their weaknesses within a Bayesian inferential framework. By using simulated data, we evaluate supplementing inferences based on small probability samples with prior distributions derived from nonprobability data. We demonstrate that informative priors based on nonprobability data can lead to reductions in variances and mean squared errors for linear model coefficients. The method is also illustrated with actual probability and nonprobability survey data. A discussion of these findings, their implications for survey practice, and possible research extensions are provided in conclusion.