There seems to be some concern that this data collection strategy is, by its nature, analytically restrictive. However, in this note the authors demonstrate how the quantitative, unrelated question model of randomized response can be reformulated into a measurement error model, which in turn allows a wide range of multivariate approaches. Last, they illustrate through a simulated correlation experiment the type of adjustment that need only be made to manipulate randomized response data more powerfully than has been the practice in the past. Tables, equations, and 22 references are supplied. (Author abstract modified)