Measuring noncompliance in insurance benefit regulations with randomized response methods for multiple items

摘要

Randomized response (RR) is a well known method for measuring sensitive behavior. Yet it is not often applied. Two possible reasons for this are (ⅰ) its lower efficiency and the resulting need for larger sample sizes, making applications of RR expensive, (ⅱ) the notion that in many applications the RR design may not be followed by every respondent ('cheating'). This paper addresses the efficiency problem by proposing item response theory (IRT) models for the analysis of multivariate RR data. In these models a person parameter is estimated based on multiple measures of a sensitive behavior under study which yields a more efficient and powerful analysis of individual differences than available from univariate RR data. Cheating in a RR study is approached by introducing additional mixture components in the IRT models with one component consisting of respondents who answer truthfully and other components consisting of respondents who do not provide truthful responses to all or a subset of the items. The resulting IRT model is applied to data from a Dutch survey conducted under receivers of disablement insurance benefit (DIB) who are interviewed about their compliance behavior to rules that are a prerequisite for receiving DIB.