A new non-randomized multi-category response model for surveys with a single sensitive question: Design and analysis

In this article, we develop a non-randomized multi-category response model for a single sensitive survey question with multiple outcomes. Unlike existing randomized response models, our proposed model does not require any randomizing device and the respondents are merely asked to answer a non-sensitive question. It thus reduces cost, ensures reproducibility of respondents' answer (i.e., the same respondent gives the same answer if the survey is re-conducted under the non-randomized multi-category model), enhances respondents' trust on the privacy policy, and motivates respondents' cooperation. We show maximum likelihood estimates (MLEs) of cell probabilities can be obtained in closed-form. Bootstrap standard errors and confidence intervals (CIs) of the cell probabilities or their functions are then given. Bayesian estimation via the data augmentation algorithm is developed when prior information on the parameters of interest is available. Simulation studies are conducted to evaluate the performance of the MLEs and CI estimates. A real data set from a questionnaire on sexual activities in Korean adolescents is used to illustrate the proposed design and analysis methods.