A variant of the parallel model for sample surveys with sensitive characteristics

A new non-randomized response (NRR) model (called a variant of the parallel model) is proposed. The survey design and corresponding statistical inferences including likelihood-based methods, Bayesian methods and bootstrap methods are provided. Theoretical and numerical comparisons showed that the proposed variant of the parallel model over-performs two existing NRR crosswise and triangular models for most of the possible parameter ranges. An outline for handling the possible non-compliance behavior in the proposed model is provided. An illustrative example from an existing survey on ‘sexual practices’ in San Francisco, Las Vegas and Portland is used to demonstrate the proposed statistical analysis methods. Two real surveys on the cheating behavior in examinations at the University of Hong Kong are conducted and are used to illustrate the proposed design and analysis methods.