title: Poisson and negative binomial item count techniques for surveys with sensitive question.
abstract: Although the item count technique is useful in surveys with sensitive questions, privacy of those respondents who possess the sensitive characteristic of interest may not be well protected due to a defect in its original design. In this article, we propose two new survey designs (namely the Poisson item count technique and negative binomial item count technique) which replace several independent Bernoulli random variables required by the original item count technique with a single Poisson or negative binomial random variable, respectively. The proposed models not only provide closed form variance estimate and confidence interval within [0, 1] for the sensitive proportion, but also simplify the survey design of the original item count technique. Most importantly, the new designs do not leak respondents' privacy. Empirical results show that the proposed techniques perform satisfactorily in the sense that it yields accurate parameter estimate and confidence interval.
authors.affiliation: 1 Department of Statistics and Actuarial Science, The University of Hong Kong, Hong Kong, P. R. China.
authors.forename: Guo-Liang
authors.initials: GL
authors.lastname: Tian
authors.affiliation: 2 Department of Mathematics and Statistics, Hang Seng Management College, Hong Kong, P. R. China.
authors.forename: Man-Lai
authors.initials: ML
authors.lastname: Tang
authors.affiliation: 3 School of Mathematical Sciences, South China Normal University, Guangzhou, P. R. China.
authors.forename: Qin
authors.initials: Q
authors.lastname: Wu
authors.affiliation: 1 Department of Statistics and Actuarial Science, The University of Hong Kong, Hong Kong, P. R. China.
authors.forename: Yin
authors.initials: Y
authors.lastname: Liu
mesh_terms: D000465:Algorithms; D001499:Bayes Theorem; D056808:Biostatistics / Q000379:methods; D016009:Chi-Square Distribution; D002681:China; D003198:Computer Simulation; D016001:Confidence Intervals; D003219:Confidentiality; D003627:Data Interpretation, Statistical; D006801:Humans; D015233:Models, Statistical; D016012:Poisson Distribution; D018401:Sample Size; D012725:Sexual Behavior / Q000706:statistics & numerical data; D011795:Surveys and Questionnaires
keywords: EM algorithm; Poisson item count technique; item count technique; negative binomial item count technique; sensitive questions