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.
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