Supplementing Small Probability Samples with Nonprobability Samples: A Bayesian Approach
Supplementing Small Probability Samples with Nonprobability Samples: A Bayesian Approach
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DOI：
10.2478/jos-2019-0027
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发表时间：
2019-09-01
影响因子：
1.1
通讯作者：
Blom, Annelies G.
中科院分区：
文献类型：
--
作者：
Sakshaug, Joseph W.;Wisniowski, Arkadiusz;Blom, Annelies G.
精心设计的基于概率的抽样调查费用可能高得令人望而却步。因此，许多调查机构已经从使用昂贵的概率样本转向使用较便宜但可能不太准确的非概率网络样本。然而，其较低的成本和丰富的可用性使其成为传统的基于概率的样本的潜在有用的补充。我们研究这一概念，提出了一种方法，补充小概率样本与非概率样本使用贝叶斯推理。我们考虑两个半共轭信息先验分布的线性回归系数的非概率样本的基础上，一个占来自平行的概率和非概率样本的最大似然系数之间的距离，第二个取决于非概率样本的变异性和大小。该方法进行了评估，通过模拟和真实数据的应用，涉及多个概率和非概率调查同时使用相同的问卷进行比较。我们表明，该方法降低了方差和均方误差（MSE）的系数估计和基于模型的预测相对于概率只有样本。使用实际和假设的成本数据，我们还表明，该方法可以产生大量的成本节省（高达55%）为固定的MSE。
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 nonprobability 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.