Statistics and Its Interface

Volume 6 (2013)

Number 1

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

Pages: 137 – 149



Yin Liu (Department of Statistics and Actuarial Science, The University of Hong Kong)

Guo-Liang Tian (Meng Wah Complex, Pokfulam Road, Hong Kong)


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.


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

Published 18 March 2013