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A covariate nonrandomized response model for multicategorical sensitive variables

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  • Groenitz, Heiko

Abstract

The diagonal method (DM) is an innovative technique to obtain trustworthy survey data on an arbitrary categorical sensitive characteristic Y∗ (e.g., income classes, number of tax evasions). The estimation of the unconditional distribution of Y∗ from DM data has already been shown. Now, a covariate extension of the DM, that is, methods to investigate the dependence of Y∗ on nonsensitive covariates, is sought. For instance, the dependence of income on gender and profession may be under study. The covariate extensions of privacy-protecting survey designs are broadened by the covariate DM, especially because existing methods focus on binary Y∗. LR-DM estimation and stratum-wise estimation are described, where the former is based on a logistic regression model, leads to a generalized linear model, and requires computer-intensive methods. The existence of a certain regression estimate is investigated. Moreover, the connection between efficiency of the LR-DM estimation and the degree of privacy protection is studied and appropriate model parameters of the DM are searched. This problem of finding suitable model parameters is rarely addressed for privacy-protecting survey methods for multicategorical Y∗. Finally, the LR-DM estimation is compared with the stratum-wise estimation. MATLAB programs that conduct the presented estimations are provided as supplemental material (see Appendix E).

Suggested Citation

  • Groenitz, Heiko, 2016. "A covariate nonrandomized response model for multicategorical sensitive variables," Computational Statistics & Data Analysis, Elsevier, vol. 103(C), pages 124-138.
    • Handle: RePEc:eee:csdana:v:103:y:2016:i:c:p:124-138
    DOI: 10.1016/j.csda.2016.04.007
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    References listed on IDEAS

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    1. Heiko Groenitz, 2017. "Valid estimates for repeated randomized response methods," Journal of Applied Statistics, Taylor & Francis Journals, vol. 44(16), pages 2994-3010, December.

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