An Approximate Bayesian Approach to Improving Probability Sample Estimators Using a Supplementary Nonprobability Sample

• Activity Number: 549 - Integration of Design and Estimation Approaches in the Use of Auxiliary Data with Sample Surveys
• Type: Topic Contributed
• Date/Time: Thursday, August 11, 2022 : 10:30 AM to 12:20 PM
• Sponsor: Survey Research Methods Section
• Author(s): Yong You and Abel DaSylva and Jean-Francois Beaumont*
• Companies: Statistics Canada and Statistics Canada and Statistics Canada
• Keywords: Bayesian prediction; Informative sampling; Non-ignorable sampling; Statistical data integration

Abstract

Non-probability samples are being increasingly explored by National Statistical Offices as a complement to probability samples. We consider the scenario where the variable of interest and auxiliary variables are observed in both a probability and non-probability sample. Our objective is to use data from the non-probability sample to improve the efficiency of survey-weighted estimates obtained from the probability sample. Recently, Sakshaug, Wisniowski, Ruiz and Blom (2019) and Wisniowski, Sakshaug, Ruiz and Blom (2020) proposed a Bayesian approach to integrating data from both samples for the estimation of model parameters. In their approach, non-probability sample data are used to determine the prior distribution of model parameters, and the posterior distribution is obtained under the assumption that the probability sampling design is ignorable (or not informative). We extend this Bayesian approach to the prediction of finite population parameters under non-ignorable (or informative) sampling by conditioning on appropriate survey-weighted statistics. We illustrate the properties of our predictor through a simulation study.