A covariate nonrandomized response model for multicategorical sensitive variables

The diagonal method (DM) is an innovative technique to obtain trustworthy survey data on an arbitrary categorical sensitive characteristic Y∗Y∗ (e.g., income classes, number of tax evasions). The estimation of the unconditional distribution of Y∗Y∗ from DM data has already been shown. Now, a covariate extension of the DM, that is, methods to investigate the dependence of Y∗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∗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∗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).