, 67:251 | Cite as

Two new models for survey sampling with sensitive characteristic: design and analysis

  • Jun-Wu Yu
  • Guo-Liang TianEmail author
  • Man-Lai Tang


Sensitive topics or highly personal questions are often being asked in medical, psychological and sociological surveys. This paper proposes two new models (namely, the triangular and crosswise models) for survey sampling with the sensitive characteristics. We derive the maximum likelihood estimates (MLEs) and large-sample confidence intervals for the proportion of persons with sensitive characteristic. The modified MLEs and their asymptotic properties are developed. Under certain optimality criteria, the designs for the cooperative parameter are provided and the sample size formulas are given. We compare the efficiency of the two models based on the variance criterion. The proposed models have four advantages: neither model requires randomizing device, the models are easy to be implemented for both interviewer and interviewee, the interviewee does not face any sensitive questions, and both models can be applied to both face-to-face personal interviews and mail questionnaires.


Maximum likelihood estimate Randomizing device Randomized response technique Sensitive questions Warner’s model 


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Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  1. 1.School of Mathematics and Computational ScienceHunan University of Science and TechnologyXiangtanPeople’s Republic of China
  2. 2.Division of BiostatisticsUniversity of Maryland Greenebaum Cancer CenterBaltimoreUSA
  3. 3.Department of MathematicsHong Kong Baptist UniversityKowloon TongPeople’s Republic of China

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