Regression analysis using scrambled responses

This paper investigates the general linear regression model Y = Xβ + e assuming the dependent variable is observed as a scrambled response using Eichhorn & Hayre's (1983) approach to collecting sensitive personal information. The estimates of the parameters in the model remain unbiased, but the variances of the estimates increase due to scrambling. The Wald test of the null hypothesis H₀: β = β₀, against the alternative hypothesis H_α: β ≠ β₀, is also investigated. Parameter estimates obtained from scrambled responses are compared to those from conventional or direct-question surveys, using simulation. The coverage by nominal 95% confidence intervals is also reported.