Block Weighted Least Squares Estimation for Nonlinear Cost-based Split Questionnaire Design

Yang Li, Le Qi, Yichen Qin, Cunjie Lin, Yuhong Yang

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Pages (from-to)459-487
Number of pages29
JournalJournal of Official Statistics
Issue number4
StatePublished - Dec 1 2023

Bibliographical note

Publisher Copyright:
© 2023 Yang Li et al., published by Sciendo.


  • Block weighted least squares estimation
  • block-wise missing data
  • large-scale survey
  • nonlinear cost function
  • split questionnaire design


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