On use of randomized response technique for estimating sensitive subpopulation total

Abstract

In social and behavioral surveys, researchers often have interest in obtaining separate estimates for the parameters of the study variable in specific domains, categorized according to some attribute(s) such as political affiliation, income status, residency, and ethnical affiliations etc. When complete information about such attributes are not available in advance, surveyors need to include questions in interviews which provide information about such attributes. The truthful response about these attributes can easily be collected when it is nonsensitive to the respondents, but not so for sensitive attributes. The respondents may either refuse to answer the question or provide evasive response about the sensitive attributes. In such cases, reliable estimates for the mean or total of even a nonsensitive quantitative variable in specific domains are quite challenging as there is no truthful information about the domain membership. Consequently, either we are left with unreliable estimates for small area parameters due to nonresponse, or get biased estimates following false responses from respondents. This article emphasizes on obtaining reliable estimates for subpopulation totals using Warner’s randomized response technique. The suggested method enhances response rate by protecting confidentiality of the respondents in exposing their domain membership. A real-world data set from Pakistan Demographic Health Survey (2017–2018) is used to see the applicability of the proposed method followed by a simulation study.

Keywords:

• Small area estimation
• randomized response
• sensitive qualitative variable

Acknowledgments

The authors highly acknowledges the comments and suggestions by the reviewers and editors for improving the previous version of the article.