1. bookVolume 35 (2019): Issue 3 (September 2019)
Journal Details
License
Format
Journal
First Published
01 Oct 2013
Publication timeframe
4 times per year
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English
access type Open Access

Supplementing Small Probability Samples with Nonprobability Samples: A Bayesian Approach

Published Online: 09 Sep 2019
Page range: 653 - 681
Received: 01 Nov 2018
Accepted: 01 Apr 2019
Journal Details
License
Format
Journal
First Published
01 Oct 2013
Publication timeframe
4 times per year
Languages
English

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

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