Amid historically low response rates, survey researchers seek ways to reduce respondent burden while measuring desired concepts with precision. We propose to ask fewer questions of respondents and impute missing responses via probabilistic matrix factorization. A variance-minimizing active learning criterion chooses the most informative questions per respondent. In simulations of our matrix sampling procedure on real-world surveys as well as a Facebook survey experiment, we find active question selection achieves efficiency gains over baselines. The reduction in imputation error is heterogeneous across questions and depends on the latent concepts they capture. Modeling responses with the ordered logit likelihood improves imputations and yields an adaptive question order. We find for the Facebook survey that potential biases from order effects are likely to be small. With our method, survey researchers obtain principled suggestions of questions to retain and, if desired, can automate the design of shorter instruments.

中文翻译：

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主动矩阵分解

在历史上较低的响应率的背景下，调查研究人员寻求各种方法来减轻响应者的负担，同时精确地测量所需的概念。我们建议询问较少的受访者问题，并通过概率矩阵分解归因于缺失的回答。最小化方差的主动学习准则会为每个受访者选择信息量最大的问题。在现实世界调查中进行的矩阵抽样程序模拟以及Facebook调查实验中，我们发现积极的问题选择可提高基准效率。插补错误的减少在各个问题上是异质的，并且取决于它们捕获的潜在概念。用有序对数似然对响应进行建模可以改善估算并产生自适应问题顺序。我们在Facebook调查中发现，订单效应带来的潜在偏差可能很小。使用我们的方法，调查研究人员可以获得保留问题的原则性建议，并且，如果需要，可以使较短仪器的设计自动化。