Estimating the linear regression model with categorical covariates subject to randomized response

The maximum likelihood estimation of the iid normal linear regression model where some of the covariates are subject to randomized response is discussed. Randomized response (RR) is an interview technique that can be used when sensitive questions have to be asked and respondents are reluctant to answer directly. RR variables are described as misclassified categorical variables where conditional misclassification probabilities are known. The likelihood of the linear regression model with RR covariates is derived and a fast and straightforward EM algorithm is developed to obtain maximum likelihood estimates. The basis of the algorithm consists of elementary weighted least-squares steps. A simulation example demonstrates the feasibility of the method.