Randomized response (RR) is a well-known method for measuring sensitive behavior. Yet this method is not often applied because: (i) of its lower efficiency and the resulting need for larger sample sizes which make applications of RR costly; (ii) despite its privacy-protection mechanism the RR design may not be followed by every respondent; and (iii) the incorrect belief that RR yields estimates only of aggregate-level behavior but that these estimates cannot be linked to individual-level covariates. This paper addresses the efficiency problem by applying item randomized-response (IRR) 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 allow for more powerful analyses of individual differences than available from univariate RR data. Response behavior that does not follow the RR design is approached by introducing mixture components in the IRR models with one component consisting of respondents who answer truthfully and another component consisting of respondents who do not provide truthful responses. An analysis of data from two large-scale Dutch surveys conducted among recipients of invalidity insurance benefits shows that the willingness of a respondent to answer truthfully is related to the educational level of the respondents and the perceived clarity of the instructions. A person is more willing to comply when the expected benefits of noncompliance are minor and social control is strong.