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

We’re sorry, something doesn't seem to be working properly.

Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.

Abstract

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.

This is a preview of subscription content, log in to check access.

References

  1. Abul-Ela AA, Greenberg BG, Horvitz DG (1967) A multi-proportions randomized response model. J Am Stat Assoc 62:990–1008

    Article  MathSciNet  Google Scholar 

  2. Bourke PD (1982) Randomized response multivariate designs for categorical data. Commun Stat A Theory Methods 11:2889–2901

    MATH  Article  Google Scholar 

  3. Chaudhuri A, Mukerjee R (1988) Randomized response: theory and techniques. Marcel Dekker, New York

    Google Scholar 

  4. Chaudhuri A, Stenger H (1992) Survey sampling: theory and methods. Marcel Dekker, New York

    Google Scholar 

  5. Cochran WG (1977) Sampling techniques, 3rd edn. Wiley, New York

    Google Scholar 

  6. Daniel WW (1993) Collecting sensitive data by randomized response: an annotated bibliography, 2nd edn. Research Monograph No. 107. Georgia State University Business Press, Atlanta

  7. Devore JL (1977) A note on the randomized response technique. Commun Stat A Theory Methods 6:1525–1529

    Article  Google Scholar 

  8. Dowling TA, Shachtman RH (1975) On the relative efficiency of randomized response models. J Am Stat Assoc 70:84–87

    Article  Google Scholar 

  9. Eriksson SA (1973) A new model for randomized response. Int Stat Rev 41:101–113

    Google Scholar 

  10. Flingner MA, Policello GE, Singh J (1977) A comparison of two randomized response survey methods with consideration for the level of respondent protection. Commun Stat A Theory Methods 6:1511–1524

    Article  Google Scholar 

  11. Folsom RE, Greenberg BG, Horvitz DG, Abernathy JR (1973) The two alternate questions randomized response model for human surveys. J Am Stat Assoc 68:525–530

    Article  Google Scholar 

  12. Franklin LA (1989) Randomized response sampling from dichotomous populations with continuous randomization. Surv Methodol 15:225–235

    Google Scholar 

  13. Franklin LA (1998) Randomized response techniques. In: Armitage P, Colton T (eds) Encyclopedia of biostatistics. Wiley, New York, pp 3696–3703

    Google Scholar 

  14. Gould AL, Shah BV, Abernathy JR (1969) Unrelated question randomized response techniques with two trials per respondent. In: 1969 Proceedings of the Social Statistics Section, American Statistical Association, pp 351–359

  15. Greenberg BG, Abernathy JR, Horvitz DG (1986) Randomized response. In: Kotz S, Johnson NL (eds) Encyclopedia of statistical sciences, Vol. 7. Wiley, New York, pp 540–548

    Google Scholar 

  16. Greenberg BG, Abul-Ela AA, Simmons WR, Horvitz DG (1969) The unrelated question randomized response model: theoretical framework. J Am Stat Assoc 64:520–539

    Article  MathSciNet  Google Scholar 

  17. Greenberg BG, Horvitz DG, Abernathy JR (1974) Comparison of randomized response designs. In: Prochan F, Serfling RJ (eds) Reliability and biometry, statistical analysis of life length. Philadelphia, SIAM, pp 787–815

    Google Scholar 

  18. Hedayat AS, Sinha BK (1991) Design and inference in finite population sampling. Wiley, New York

    Google Scholar 

  19. Horvitz DG, Shah BV, Simmons WR (1967) The unrelated question randomized response model. In: 1967 Proceedings of the Social Statistics Section, American Statistical Association, pp 65–72

  20. Horvitz DG, Greenberg BG, Abernathy JR (1975) Recent developments in randomized designs. In: Srivastava JN (ed) A survey of statistical design and linear models. North Holland / American Elsevier Publishing Co., New York, pp 271–285

    Google Scholar 

  21. Horvitz DG, Greenberg BG, Abernathy JR (1976) Randomized response: a data gathering device for sensitive questions. Int Stat Rev 44:181–196

    MathSciNet  Article  Google Scholar 

  22. Kim JM, Warde WD (2004) A stratified Warner’s randomized response model. J Stat Plann Infer 120: 155–165

    MATH  Article  MathSciNet  Google Scholar 

  23. Kim JM, Elam ME (2005) A two-stage stratified Warner’s randomized response model using optimal allocation. Metrika 61:1–7

    MATH  Article  MathSciNet  Google Scholar 

  24. Kong SY (1997) Survey sampling for sensitive questions. Unpublished Ph.D. dissertation, Renmin University, Beijing, P. R. China

  25. Levy KJ (1976) Reducing the occurrence of omitted or untruthful responses when testing hypotheses concerning proportions. Psychol Bull 83:759–761

    Article  Google Scholar 

  26. Liu PT, Chow LP (1976) The efficiency of the multiple trial randomized response technique. Biometrics 32:607–618

    MATH  Article  Google Scholar 

  27. Liu PT, Chow LP, Mosley WH (1975) Use of the randomized response technique with a new randomizing device. J Am Stat Assoc 70:329–332

    Article  Google Scholar 

  28. Moors JJA (1971) Optimization of the unrelated question randomized response model. J Am Stat Assoc 66:627–629

    Article  Google Scholar 

  29. Moors JJA (1981) Inadmissibility of linearly invariant estimators in truncated parameter spaces. J Am Stat Assoc 76:910–915

    MATH  Article  MathSciNet  Google Scholar 

  30. Saha A (2006) Optimal randomized response in stratified unequal probability sampling—a simulation based numerical study with Kuk’s method. Test (in press)

  31. Tracy DS, Mangat NS (1996) Some developments in randomized response sampling during the last decade—a follow up of review by Chaudhuri and Mukerjee. J Appl Stat Sci 4:147–159

    MATH  Google Scholar 

  32. Warner SL (1965) Randomized response: a survey technique for eliminating evasive answer bias. J Am Stat Assoc 60:63–69

    Article  Google Scholar 

Download references

Author information

Affiliations

Authors

Corresponding author

Correspondence to Guo-Liang Tian.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Yu, J., Tian, G. & Tang, M. Two new models for survey sampling with sensitive characteristic: design and analysis. Metrika 67, 251 (2008). https://doi.org/10.1007/s00184-007-0131-x

Download citation

Keywords

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