Multi-category parallel models in the design of surveys with sensitive questions

In the past few years, several non-randomized response (NRR) designs were introduced in sample surveys with sensitive questions. However, existing NRR models (e.g., the crosswise model, the triangular model, the hidden sensitive model and the multi-category triangular model) have certain limitations in applications, for example, they can only be applied to a situation where at least one of the population categories of interest is non-sensitive. In this paper, we propose a new NRR multi-category parallel model with a better degree of privacy protection and a wider application range, where all population categories of interest can be sensitive or one of them can be totally non-sensitive. Likelihoodbased inferences for parameters of interest are developed. In addition, an important special case of the multi-category parallel model is studied to test the association of two sensitive binary variables. Furthermore, theoretic comparisons show that the multi-category parallel model is more efficient than the multi-category triangular model for some cases. An example on the study of association between the number of sex partners and annual income is used to illustrate the proposed method.

Keywords

chi-squared test, likelihood ratio test, multi-category parallel model, multi-category triangular model, non-randomized response technique

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Published 18 March 2013