New estimation techniques for ordinal sensitive variables

Abstract

Methods to analyze multicategorical variables are extensively used in sociological, medical and educational research. Nonetheless, they have a very sparse presence in finite population sampling when sensitive topics are investigated and data are obtained by means of the randomized response technique (RRT), a survey method based on the principle that sensitive questions must not be asked directly to the respondents. The RRT is used with the aim of reducing social desirability bias, which is defined as the respondent tendency to release personal information according to what is socially acceptable. This nonstandard data-collection approach was originally developed to deal with dichotomous responses to sensitive questions. Later, the idea has been extended to multicategory responses. In this paper we consider ordinal variables with more than two response categories. In particular, we first discuss the theoretical framework for estimating the frequency of ordinal categories when data are subjected to misclassification due to the use of a particular RRT. Then, we show how it is possible to improve the efficiency of the inferential process by employing auxiliary information at the estimation stage through the calibration approach. Finally, we assess the performance of the proposed estimators in a Monte Carlo simulation study.