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Poisson and negative binomial item count techniques for surveys with sensitive question.

Guo-Liang Tian1, Man-Lai Tang2, Qin Wu3

  • 11 Department of Statistics and Actuarial Science, The University of Hong Kong, Hong Kong, P. R. China.

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Summary

New survey designs enhance privacy for sensitive questions. The Poisson and negative binomial item count techniques offer improved respondent protection and simplified survey administration.

Keywords:
EM algorithmPoisson item count techniqueitem count techniquenegative binomial item count techniquesensitive questions

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Area of Science:

  • Survey Methodology
  • Statistical Privacy

Background:

  • The original item count technique (ICT) offers privacy benefits for sensitive survey questions but has design flaws.
  • Existing ICT designs may not fully protect respondents with the sensitive characteristic of interest.

Purpose of the Study:

  • To propose novel survey designs that enhance respondent privacy in sensitive surveys.
  • To introduce the Poisson item count technique and negative binomial item count technique.
  • To improve upon the privacy protections and design simplicity of the original ICT.

Main Methods:

  • Replaced multiple Bernoulli random variables in the original ICT with a single Poisson or negative binomial random variable.
  • Developed new models for sensitive survey data collection.
  • Utilized statistical modeling to ensure privacy and accuracy.

Main Results:

  • The proposed Poisson and negative binomial item count techniques provide closed-form variance estimates and confidence intervals within [0, 1] for sensitive proportions.
  • The new designs simplify the survey administration process compared to the original ICT.
  • Empirical results demonstrate satisfactory performance, yielding accurate parameter estimates and confidence intervals.

Conclusions:

  • The proposed Poisson and negative binomial item count techniques effectively protect respondent privacy.
  • These novel methods offer a more robust and user-friendly approach to collecting data on sensitive topics.
  • The new designs address the privacy defect in the original item count technique, ensuring better data security.