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In 2004 the Dutch Department of Social Affairs conducted a survey to assessthe extent of noncompliance with social security regulations. The survey wasconducted among 870 recipients of social security benefits and included aseries of sensitive questions about regulatory noncompliance. Due to thesensitive nature of the questions the randomized response design was used.Although randomized response protects the privacy of the respondent, it isunlikely that all respondents followed the design. In this paper we introduce amodel that allows for respondents displaying self-protective response behaviorby consistently giving the nonincriminating response, irrespective of theoutcome of the randomizing device. The dependent variable denoting the totalnumber of incriminating responses is assumed to be generated by the applicationof randomized response to a latent Poisson variable denoting the true number ofrule violations. Since self-protective responses result in an excess ofobserved zeros in relation to the Poisson randomized response distribution,these are modeled as observed zero-inflation. The model includes predictors ofthe Poisson parameters, as well as predictors of the probability ofself-protective response behavior.

Accounting for self-protective responses in randomized response data from a social security survey using the zero-inflated Poisson model