<abstract xmlns="http://www.w3.org/1999/xhtml"><p>Carefully designed probability-based sample surveys can be prohibitively expensive to conduct. As such, many survey organizations have shifted away from using expensive probability samples in favor of less expensive, but possibly less accurate, nonprobability web samples. However, their lower costs and abundant availability make them a potentially useful supplement to traditional probability-based samples. We examine this notion by proposing a method of supplementing small probability samples with nonprobability samples using Bayesian inference. We consider two semi-conjugate informative prior distributions for linear regression coefficients based on nonprobability samples, one accounting for the distance between maximum likelihood coefficients derived from parallel probability and non-probability samples, and the second depending on the variability and size of the nonprobability sample. The method is evaluated in comparison with a reference prior through simulations and a real-data application involving multiple probability and nonprobability surveys fielded simultaneously using the same questionnaire. We show that the method reduces the variance and mean-squared error (MSE) of coefficient estimates and model-based predictions relative to probability-only samples. Using actual and assumed cost data we also show that the method can yield substantial cost savings (up to 55%) for a fixed MSE.</p></abstract>

Carefully designed probability-based sample surveys can be prohibitively expensive to conduct. As such, many survey organizations have shifted away from using expensive probability samples in favor of less expensive, but possibly less accurate, nonprobability web samples. However, their lower costs and abundant availability make them a potentially useful supplement to traditional probability-based samples. We examine this notion by proposing a method of supplementing small probability samples with nonprobability samples using Bayesian inference. We consider two semi-conjugate informative prior distributions for linear regression coefficients based on nonprobability samples, one accounting for the distance between maximum likelihood coefficients derived from parallel probability and non-probability samples, and the second depending on the variability and size of the nonprobability sample. The method is evaluated in comparison with a reference prior through simulations and a real-data application involving multiple probability and nonprobability surveys fielded simultaneously using the same questionnaire. We show that the method reduces the variance and mean-squared error (MSE) of coefficient estimates and model-based predictions relative to probability-only samples. Using actual and assumed cost data we also show that the method can yield substantial cost savings (up to 55%) for a fixed MSE.

Supplementing Small Probability Samples with Nonprobability Samples: A Bayesian Approach

University of Mannheim and Institute for Employment Research

Journal of Official Statistics

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Carefully designed probability-based sample surveys can be prohibitively expensive to conduct. As such, many survey organizations have shifted away from using...

Supplementing Small Probability Samples with Nonprobability Samples: A Bayesian Approach

Published Online: Sep 09, 2019

Page range: 653 - 681

Received: Nov 01, 2018

Accepted: Apr 01, 2019

DOI: https://doi.org/10.2478/jos-2019-0027

Keywords
Bayesian inference, quota sampling, German Internet Panel, GESIS Panel, web surveys

© 2019 Joseph W. Sakshaug et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Supplementing Small Probability Samples with Nonprobability Samples: A Bayesian Approach

Published Online: Sep 09, 2019

Page range: 653 - 681

Received: Nov 01, 2018

Accepted: Apr 01, 2019

DOI: https://doi.org/10.2478/jos-2019-0027

KeywordsBayesian inference, quota sampling, German Internet Panel, GESIS Panel, web surveys

© 2019 Joseph W. Sakshaug et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
Bayesian inference, quota sampling, German Internet Panel, GESIS Panel, web surveys