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

Authors:
Ardo van den Hout;Peter Kooiman
Affiliations:
Department of Methodology and Statistics, Faculty of Social Sciences, Utrecht University, P.O. box 80140, 3508 TC Utrecht, The Netherlands;Department Labour Market and Welfare State, CPB Netherlands Bureau for Economic Policy Analysis, P.O. Box 80510, 2508 GM Den Haag, The Netherlands
Venue:
Computational Statistics & Data Analysis
Year:
2006

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Abstract

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.