IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v13y2025i18p2973-d1749167.html

Variant Poisson Item Count Technique with Non-Compliance

Author

Listed:
  • 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)

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.

Suggested Citation

  • Man-Lai Tang & Qin Wu & Daisy Hoi-Sze Chow & Guo-Liang Tian, 2025. "Variant Poisson Item Count Technique with Non-Compliance," Mathematics, MDPI, vol. 13(18), pages 1-16, September.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:18:p:2973-:d:1749167
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/13/18/2973/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/13/18/2973/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Jansakul, N. & Hinde, J. P., 2002. "Score Tests for Zero-Inflated Poisson Models," Computational Statistics & Data Analysis, Elsevier, vol. 40(1), pages 75-96, July.
    2. Jun-Wu Yu & Guo-Liang Tian & Man-Lai Tang, 2008. "Two new models for survey sampling with sensitive characteristic: design and analysis," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 67(3), pages 251-263, April.
    3. Feng, Ziding & McCulloch, Charles E., 1992. "Statistical inference using maximum likelihood estimation and the generalized likelihood ratio when the true parameter is on the boundary of the parameter space," Statistics & Probability Letters, Elsevier, vol. 13(4), pages 325-332, March.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Liu, Yin & Tian, Guo-Liang, 2015. "Type I multivariate zero-inflated Poisson distribution with applications," Computational Statistics & Data Analysis, Elsevier, vol. 83(C), pages 200-222.
    2. Das, Ujjwal & Das, Kalyan, 2018. "Inference on zero inflated ordinal models with semiparametric link," Computational Statistics & Data Analysis, Elsevier, vol. 128(C), pages 104-115.
    3. Carlos Barros, 2012. "Sustainable Tourism in Inhambane-Mozambique," CEsA Working Papers 105, CEsA - Centre for African and Development Studies.
    4. Andreas Lagerås & Mathias Lindholm, 2020. "How to ask sensitive multiple‐choice questions," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 47(2), pages 397-424, June.
    5. Benjamin R. Saville & Amy H. Herring, 2009. "Testing Random Effects in the Linear Mixed Model Using Approximate Bayes Factors," Biometrics, The International Biometric Society, vol. 65(2), pages 369-376, June.
    6. Abbas Moghimbeigi & Mohammed Reza Eshraghian & Kazem Mohammad & Brian Mcardle, 2008. "Multilevel zero-inflated negative binomial regression modeling for over-dispersed count data with extra zeros," Journal of Applied Statistics, Taylor & Francis Journals, vol. 35(10), pages 1193-1202.
    7. Xie, Feng-Chang & Wei, Bo-Cheng & Lin, Jin-Guan, 2009. "Score tests for zero-inflated generalized Poisson mixed regression models," Computational Statistics & Data Analysis, Elsevier, vol. 53(9), pages 3478-3489, July.
    8. Burgstaller, Lilith & Feld, Lars P. & Pfeil, Katharina, 2022. "Working in the shadow: Survey techniques for measuring and explaining undeclared work," Journal of Economic Behavior & Organization, Elsevier, vol. 200(C), pages 661-671.
    9. Liu, Juxin & Ma, Yanyuan & Johnstone, Jill, 2020. "A goodness-of-fit test for zero-inflated Poisson mixed effects models in tree abundance studies," Computational Statistics & Data Analysis, Elsevier, vol. 144(C).
    10. Kazuo Yamaguchi, 2016. "Cross-sectional and Panel Data Analyses of an Incompletely Observed Variable Derived From the Nonrandomized Method for Surveying Sensitive Questions," Sociological Methods & Research, , vol. 45(1), pages 41-68, February.
    11. Pavel Dietz & Anne Quermann & Mireille Nicoline Maria van Poppel & Heiko Striegel & Hannes Schröter & Rolf Ulrich & Perikles Simon, 2018. "Physical and cognitive doping in university students using the unrelated question model (UQM): Assessing the influence of the probability of receiving the sensitive question on prevalence estimation," PLOS ONE, Public Library of Science, vol. 13(5), pages 1-12, May.
    12. Horng-Jinh Chang & Mei-Pei Kuo, 2012. "Estimation of population proportion in randomized response sampling using weighted confidence interval construction," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 75(5), pages 655-672, July.
    13. Mario Bossler & Christopher Osiander & Julia Schmidtke & Mark Trappmann, 2023. "Free riding on short‐time work allowances? Results from an experimental survey design," Kyklos, Wiley Blackwell, vol. 76(4), pages 882-901, November.
    14. LEONIDA, Ionel, 2022. "Investigating The Dividend Policy Determinants Using A Poisson Regression," Journal of Financial and Monetary Economics, Centre of Financial and Monetary Research "Victor Slavescu", vol. 10(1), pages 108-113, October.
    15. Jodrá, P. & Jiménez-Gamero, M.D., 2016. "A note on the Log-Lindley distribution," Insurance: Mathematics and Economics, Elsevier, vol. 71(C), pages 189-194.
    16. Dankmar Böhning & Heinz Holling & Walailuck Böhning & Patarawan Sangnawakij, 2021. "Investigating heterogeneity in meta-analysis of studies with rare events," METRON, Springer;Sapienza Università di Roma, vol. 79(3), pages 259-272, December.
    17. Leonardo Bursztyn & Ingar Haaland & Nicolas Röver & Christopher Roth, 2025. "The Social Desirability Atlas," ECONtribute Discussion Papers Series 365, University of Bonn and University of Cologne, Germany.
    18. Thorben C. Kundt & Florian Misch & Birger Nerré, 2017. "Re-assessing the merits of measuring tax evasion through business surveys: an application of the crosswise model," International Tax and Public Finance, Springer;International Institute of Public Finance, vol. 24(1), pages 112-133, February.
    19. Pier Francesco Perri & Eleni Manoli & Tasos C. Christofides, 2023. "Assessing the effectiveness of indirect questioning techniques by detecting liars," Statistical Papers, Springer, vol. 64(5), pages 1483-1506, October.
    20. T. Martin Lukusa & Shen-Ming Lee & Chin-Shang Li, 2016. "Semiparametric estimation of a zero-inflated Poisson regression model with missing covariates," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 79(4), pages 457-483, May.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:13:y:2025:i:18:p:2973-:d:1749167. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.