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

Author

Listed:
  • Li Yang
  • Qi Le
  • Lin Cunjie

    (1 Renmin University of China, Center for Applied Statistics and School of Statistics, att: Cunjie Lin, 59 Zhongguancun St, Beijing, 100872, China .)

  • Qin Yichen

    (2 University of Cincinnati, Department of Operations, Business Analytics, and Information Systems Cincinnati, Ohio, U.S.A .)

  • Yang Yuhong

    (3 University of Minnesota, School of Statistics Minneapolis, U.S.A .)

Abstract

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.

Suggested Citation

  • Li Yang & Qi Le & Lin Cunjie & Qin Yichen & Yang Yuhong, 2023. "Block Weighted Least Squares Estimation for Nonlinear Cost-based Split Questionnaire Design," Journal of Official Statistics, Sciendo, vol. 39(4), pages 459-487, December.
    • Handle: RePEc:vrs:offsta:v:39:y:2023:i:4:p:459-487:n:2
    DOI: 10.2478/jos-2023-0022
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    References listed on IDEAS

    as
    1. Ledoit, Olivier & Wolf, Michael, 2004. "A well-conditioned estimator for large-dimensional covariance matrices," Journal of Multivariate Analysis, Elsevier, vol. 88(2), pages 365-411, February.
    2. James O. Chipperfield & Margo L. Barr & David. G. Steel, 2018. "Split Questionnaire Designs: collecting only the data that you need through MCAR and MAR designs," Journal of Applied Statistics, Taylor & Francis Journals, vol. 45(8), pages 1465-1475, June.
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