In this study, we advocate a two-stage framework to deal with the issues encountered in surveys with long questionnaires. In Stage I, we propose a split questionnaire design (SQD) developed by minimizing a quadratic cost function while achieving reliability constraints on estimates of means, which effectively reduces the survey cost, alleviates the burden on the respondents, and potentially improves data quality. In Stage II, we develop a block weighted least squares (BWLS) estimator of linear regression coefficients that can be used with data obtained from the SQD obtained in Stage I. Numerical studies comparing existing methods strongly favor the proposed estimator in terms of prediction and estimation accuracy. Using the European Social Survey (ESS) data, we demonstrate that the proposed SQD can substantially reduce the survey cost and the number of questions answered by each respondent, and the proposed estimator is much more interpretable and efficient than present alternatives for the SQD data.

中文翻译：

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基于非线性成本的分割问卷设计的块加权最小二乘估计


在本研究中，我们提倡采用两阶段框架来处理长问卷调查中遇到的问题。在第一阶段，我们提出了一种分割问卷设计（SQD），通过最小化二次成本函数，同时实现对均值估计的可靠性约束，有效降低了调查成本，减轻了受访者的负担，并有可能提高数据质量。在第二阶段，我们开发了一个线性回归系数的块加权最小二乘（BWLS）估计器，可以与从第一阶段获得的 SQD 获得的数据一起使用。比较现有方法的数值研究在预测和估计方面强烈支持所提出的估计器准确性。使用欧洲社会调查 (ESS) 数据，我们证明所提出的 SQD 可以大大降低调查成本和每个受访者回答的问题数量，并且所提出的估计量比现有的 SQD 数据替代方案更具可解释性和效率。