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.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Abul-Ela AA, Greenberg BG, Horvitz DG (1967) A multi-proportions randomized response model. J Am Stat Assoc 62:990–1008
Bourke PD (1982) Randomized response multivariate designs for categorical data. Commun Stat A Theory Methods 11:2889–2901
Chaudhuri A, Mukerjee R (1988) Randomized response: theory and techniques. Marcel Dekker, New York
Chaudhuri A, Stenger H (1992) Survey sampling: theory and methods. Marcel Dekker, New York
Cochran WG (1977) Sampling techniques, 3rd edn. Wiley, New York
Daniel WW (1993) Collecting sensitive data by randomized response: an annotated bibliography, 2nd edn. Research Monograph No. 107. Georgia State University Business Press, Atlanta
Devore JL (1977) A note on the randomized response technique. Commun Stat A Theory Methods 6:1525–1529
Dowling TA, Shachtman RH (1975) On the relative efficiency of randomized response models. J Am Stat Assoc 70:84–87
Eriksson SA (1973) A new model for randomized response. Int Stat Rev 41:101–113
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
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
Franklin LA (1989) Randomized response sampling from dichotomous populations with continuous randomization. Surv Methodol 15:225–235
Franklin LA (1998) Randomized response techniques. In: Armitage P, Colton T (eds) Encyclopedia of biostatistics. Wiley, New York, pp 3696–3703
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
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
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
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
Hedayat AS, Sinha BK (1991) Design and inference in finite population sampling. Wiley, New York
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
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
Horvitz DG, Greenberg BG, Abernathy JR (1976) Randomized response: a data gathering device for sensitive questions. Int Stat Rev 44:181–196
Kim JM, Warde WD (2004) A stratified Warner’s randomized response model. J Stat Plann Infer 120: 155–165
Kim JM, Elam ME (2005) A two-stage stratified Warner’s randomized response model using optimal allocation. Metrika 61:1–7
Kong SY (1997) Survey sampling for sensitive questions. Unpublished Ph.D. dissertation, Renmin University, Beijing, P. R. China
Levy KJ (1976) Reducing the occurrence of omitted or untruthful responses when testing hypotheses concerning proportions. Psychol Bull 83:759–761
Liu PT, Chow LP (1976) The efficiency of the multiple trial randomized response technique. Biometrics 32:607–618
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
Moors JJA (1971) Optimization of the unrelated question randomized response model. J Am Stat Assoc 66:627–629
Moors JJA (1981) Inadmissibility of linearly invariant estimators in truncated parameter spaces. J Am Stat Assoc 76:910–915
Saha A (2006) Optimal randomized response in stratified unequal probability sampling—a simulation based numerical study with Kuk’s method. Test (in press)
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
Warner SL (1965) Randomized response: a survey technique for eliminating evasive answer bias. J Am Stat Assoc 60:63–69
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Yu, JW., Tian, GL. & Tang, ML. Two new models for survey sampling with sensitive characteristic: design and analysis. Metrika 67, 251–263 (2008). https://doi.org/10.1007/s00184-007-0131-x
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00184-007-0131-x