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A Theory of Higher Order Interactions Between Sensitive Variables: Empirical Evidences and an Application to a Variety of Smoking

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  • Oluwaseun L. Olanipekun
  • JuLong Zhao
  • Rongdong Wang
  • Stephen A.Sedory
  • Sarjinder Singh

Abstract

In carrying out surveys involving sensitive characteristics, randomized response models have been considered among the best techniques since they provide the maximum privacy protection to the respondents and procure honest responses. Over the years, researchers have carried out studies on the estimation of proportions of the population possessing sensitive characteristics. However, there is a paucity of research studies that have addressed higher order interactions between these sensitive characters. In this article, we develop a new theory based on three proposed randomized response models which we name as: simple model, semi-crossed model, and fully crossed model. Twenty-one new unbiased estimators of seven parameters are introduced, their variance expressions are derived, and unbiased estimators of variances are developed. The three models are compared under various values of the parameters by computing the percent relative efficiency of one model over another model. The most efficient model is then applied to study the population proportions of three varieties of smoking habits among students, and their first- and second-order interactions. The last four sections (Ninth to Twelfth) are verifications of theoretical results using the Cramer–Rao lower bounds of variances for the developed 21 new estimators in randomized response sampling.

Suggested Citation

  • Oluwaseun L. Olanipekun & JuLong Zhao & Rongdong Wang & Stephen A.Sedory & Sarjinder Singh, 2023. "A Theory of Higher Order Interactions Between Sensitive Variables: Empirical Evidences and an Application to a Variety of Smoking," Sociological Methods & Research, , vol. 52(2), pages 642-763, May.
  • Handle: RePEc:sae:somere:v:52:y:2023:i:2:p:642-763
    DOI: 10.1177/0049124120986203
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    References listed on IDEAS

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    1. van den Hout, Ardo & van der Heijden, Peter G.M. & Gilchrist, Robert, 2007. "The logistic regression model with response variables subject to randomized response," Computational Statistics & Data Analysis, Elsevier, vol. 51(12), pages 6060-6069, August.
    2. Sarjinder Singh & Stephen A. Sedory, 2012. "A true simulation study of three estimators at equal protection of respondents in randomized response sampling," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 66(4), pages 442-451, November.
    3. Cheon-Sig Lee & Shu-Ching Su & Katrina Mondragon & Veronica I. Salinas & Monique L. Zamora & Stephen Andrew Sedory & Sarjinder Singh, 2016. "Comparison of Cramer–Rao lower bounds of variances for at least equal protection of respondents," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 70(2), pages 80-99, May.
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    Cited by:

    1. Daryan Naatjes & Stephen A. Sedory & Sarjinder Singh, 2023. "New Randomised Response Models for Two Sensitive Characteristics: Theory and Application," International Statistical Review, International Statistical Institute, vol. 91(3), pages 511-534, December.

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