The Annals of Applied Statistics

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, and Peter G. M. van der Heijden

Full-text: Open access

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.

Article information

Source
Ann. Appl. Stat. Volume 2, Number 1 (2008), 316-331.

Dates
First available in Project Euclid: 24 March 2008

Permanent link to this document
https://projecteuclid.org/euclid.aoas/1206367823

Digital Object Identifier
doi:10.1214/07-AOAS135

Mathematical Reviews number (MathSciNet)
MR2415605

Zentralblatt MATH identifier
1137.62414

Keywords
Randomized response Poisson regression zero-inflation self-protective responses regulatory noncompliance

Citation

Cruyff, Maarten J. L. F.; Böckenholt, Ulf; van den Hout, Ardo; van der Heijden, Peter G. M. Accounting for self-protective responses in randomized response data from a social security survey using the zero-inflated Poisson model. Ann. Appl. Stat. 2 (2008), no. 1, 316--331. doi:10.1214/07-AOAS135. https://projecteuclid.org/euclid.aoas/1206367823.


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