Generalized Scrambling in Quantitative Optional Randomized Response Models

Huang (2010) proposed an optional randomized response model using a linear combination scrambling which is a generalization of the multiplicative scrambling of Eichhorn and Hayre (1983) and the additive scrambling of Gupta et al. (2006, 2010). In this article, we discuss two main issues. (1) Can the Huang (2010) model be improved further by using a two-stage approach?; (2) Does the linear combination scrambling provide any benefit over the additive scrambling of Gupta et al. (2010)? We will note that the answer to the first question is yes but the answer to the second question is no.