A Review of Regression Procedures for Randomized Response Data, Including Univariate and Multivariate Logistic Regression, the Proportional Odds Model and Item Response Model, and Self-Protective Responses

M. J.L.F. Cruyff, U. Böckenholt, P. G.M. van der Heijden*, L. E. Frank

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contribution

7 Scopus citations

Abstract

In survey research, it is often problematic to ask people sensitive questions because they may refuse to answer or they may provide a socially desirable answer that does not reveal their true status on the sensitive question. To solve this problem Warner (1965) proposed randomized response (RR). Here, a chance mechanism hides why respondents say yes or no to the question being asked. Thus far RR has been mainly used in research to estimate the prevalence of sensitive characteristics. It is not uncommon that researchers wrongly believe that the RR procedure has the drawback that it is not possible to relate the sensitive characteristics to explanatory variables. Here, we provide a review of the literature of regression procedures for dichotomous RR data. Univariate RR data can be analyzed with a version of logistic regression that is adapted so that it can handle data collected by RR. Subsequently the manuscript presents extensions towards repeated cross-sectional data that allowed for a change in the design with which the RR data are collected. We also review regression procedures for multivariate dichotomous RR data, such as the model by Glonek and McCullagh (1995), a model for the sum of a set of dichotomous RR data, and a model from item response theory that assumes a latent variable that explains the answers on the RR variables. We end with a discussion of a recent development in the analysis of multivariate RR data, namely models that take into account that there may be respondents that do not follow the instructions of the RR design by answering no whatever the sensitive question asked. These are coined self-protective responses.

Original languageEnglish (US)
Title of host publicationData Gathering, Analysis and Protection of Privacy Through Randomized Response Techniques
Subtitle of host publicationQualitative and Quantitative Human Traits, 2016
EditorsArijit Chaudhuri, Tasos C. Christofides, C.R. Rao
PublisherElsevier
Pages287-315
Number of pages29
ISBN (Print)9780444635709
DOIs
StatePublished - Jan 1 2016

Publication series

NameHandbook of Statistics
Volume34
ISSN (Print)0169-7161

Keywords

  • Item response model
  • Logistic regression
  • Multivariate
  • Proportional odds model
  • Randomized response
  • Randomized response data
  • Self-protective responses

ASJC Scopus subject areas

  • Statistics and Probability
  • Modeling and Simulation
  • Applied Mathematics

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    Cruyff, M. J. L. F., Böckenholt, U., van der Heijden, P. G. M., & Frank, L. E. (2016). A Review of Regression Procedures for Randomized Response Data, Including Univariate and Multivariate Logistic Regression, the Proportional Odds Model and Item Response Model, and Self-Protective Responses. In A. Chaudhuri, T. C. Christofides, & C. R. Rao (Eds.), Data Gathering, Analysis and Protection of Privacy Through Randomized Response Techniques: Qualitative and Quantitative Human Traits, 2016 (pp. 287-315). (Handbook of Statistics; Vol. 34). Elsevier. https://doi.org/10.1016/bs.host.2016.01.016