Variant Poisson Item Count Technique with Non-Compliance

Man-Lai Tang, Qin Wu (), Daisy Hoi-Sze Chow and Guo-Liang Tian
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Man-Lai Tang: Department of Physics, Astronomy and Mathematics, University of Hertfordshire, Hatfield AL10 9AB, UK
Qin Wu: School of Mathematical Sciences, South China Normal University, Guangzhou 510631, China
Daisy Hoi-Sze Chow: Cheers Psychological Consultancy Services, Hong Kong, China
Guo-Liang Tian: Department of Statistics and Data Science, Southern University of Science and Technology, Shenzhen 518055, China

Mathematics, 2025, vol. 13, issue 18, 1-16

Abstract: In this article, we propose a variant Poisson item count technique (VPICT) that explicitly accounts for respondent non-compliance in surveys involving sensitive questions. Unlike the existing Poisson item count technique (PICT), the proposed VPICT (i) replaces the sensitive item with a triangular model that combines the sensitive and an additional non-sensitive item; (ii) utilizes data from both control and treatment groups to estimate the prevalence of the sensitive characteristic, thereby improving the accuracy and efficiency of parameter estimation; and (iii) limits the occurrence of the floor effect to cases where the respondent neither possesses the sensitive characteristic nor meets the non-sensitive condition, thus protecting a subset of respondents from privacy breaches. The method introduces a mechanism to estimate the rate of non-compliance alongside the sensitive trait, enhancing overall estimation reliability. We present the complete methodological framework, including survey design, parameter estimation via the EM algorithm, and hypothesis testing procedures. Extensive simulation studies are conducted to evaluate performance under various settings. The practical utility of the proposed approach is demonstrated through an application to real-world survey data on illegal drug use among high school students.

Keywords: poisson item count technique; non-compliance; EM algorithm; hypothesis test; stochastic representation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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