A moment substitution approach to fitting linear regression models with categorical covariates subject to randomized response.

Abstract

In this paper, we present an alternative approach to estimating linear regression models where some of the covariates are subjected to randomized response. Specifically, we examine categorical covariates which are subjected to Warner's (1965) scheme of randomization. Our approach essentially consists of replacing the affected entries in the usual least squares estimator for the centred model with their associated unbiased estimates. Assuming the above randomization scheme, we show that this substitution approach is equivalent to Selen's (1986) estimator under appropriate distributional assumptions. More generally, we further show that our approach is asymptotically equivalent to the measurement error model estimate given by Fuller (1987) under suitable transformations.