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

Maarten J L F Cruyff, Ulf Böckenholt, Ardo van den Hout, Peter G M van der Heijden

Research output: Contribution to journalArticle

15 Scopus citations

Abstract

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

Original languageEnglish (US)
Pages (from-to)316-331
Number of pages16
JournalAnnals of Applied Statistics
Volume2
Issue number1
DOIs
StatePublished - Mar 2008

Keywords

  • Poisson regression
  • Randomized response
  • Regulatory noncompliance
  • Self-protective responses
  • Zero-inflation

ASJC Scopus subject areas

  • Statistics and Probability
  • Modeling and Simulation
  • Statistics, Probability and Uncertainty

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