Supplementing Small Probability Samples with Nonprobability Samples: A Bayesian Approach

Sakshaug Joseph W. (), Wiśniowski Arkadiusz (), Ruiz Diego Andres Perez () and Blom Annelies G. ()
Additional contact information
Sakshaug Joseph W.: University of Mannheim and Institute for Employment Research, Nuremberg, 90478Germany.
Wiśniowski Arkadiusz: University of Manchester, Manchester, M13 9PL United Kingdom.
Ruiz Diego Andres Perez: University of Manchester, Manchester, M13 9PL United Kingdom.
Blom Annelies G.: School of Social Sciences, University of Mannheim, Mannheim, 68131Germany.

Journal of Official Statistics, 2019, vol. 35, issue 3, 653-681

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.

Keywords: Bayesian inference; quota sampling; German Internet Panel; GESIS Panel; web surveys (search for similar items in EconPapers)
Date: 2019
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Persistent link: https://EconPapers.repec.org/RePEc:vrs:offsta:v:35:y:2019:i:3:p:653-681:n:7

DOI: 10.2478/jos-2019-0027

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