Some new results on the multinomial randomized response model

Jong Min Kim, William D. Warde

Research output: Contribution to journalArticlepeer-review

25 Scopus citations


The randomized response technique is an effective survey method designed to elicit sensitive information while ensuring the privacy of the respondents. In this article, we present some new results on the randomization response model in situations wherein one or two response variables are assumed to follow a multinomial distribution. For a single sensitive question, we use the well-known Hopkins randomization device to derive estimates, both under the assumption of truthful and untruthful responses, and present a technique for making pairwise comparisons. When there are two sensitive questions of interest, we derive a Pearson product moment correlation estimator based on the multinomial model assumption. This estimator may be used to quantify the linear relationship between two variables when multinomial response data are observed according to a randomized-response protocol.

Original languageEnglish (US)
Pages (from-to)847-856
Number of pages10
JournalCommunications in Statistics - Theory and Methods
Issue number4
StatePublished - Jun 13 2005


  • Confidentiality
  • Multinomial distribution
  • Multiple comparisons
  • Product-moment correlation
  • Randomized response design matrix
  • Sensitive questions


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