When private or stigmatizing characteristics are included in sample surveys, direct questions result in low cooperation of the respondents. To increase cooperation, indirect questioning procedures have been established in the literature. Nonrandomized response methods are one group of such procedures and have attracted much attention in recent years. In this article, we consider four popular nonrandomized response schemes and present a possibility to improve the estimation precision of these schemes. The basic idea is to require multiple indirect answers from each respondent. We develop a Fisher scoring algorithm for the maximum likelihood estimation in the presented new schemes and show the better efficiency of the new schemes compared with the original designs.
For repeated randomized response procedures, it is often difficult to find an explicit formula for the maximum likelihood estimator. Therefore, an iterative method to maximize the log-likelihood is needed. The EM algorithm is one convenient method. In the first part of this online appendix, we describe the computation of maximum likelihood estimates by the EM algorithm. In the second part, we address the asymptotic estimation variance.
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