Some New Results on the Multinomial Randomized Response Model

ABSTRACT

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.

Key Words:

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

Mathematics Subject Classification:

• Primary 62D05
• Secondary 62F10.

Acknowledgment

The authors appreciate the suggestions from an anonymous referee and an associate editor which have led to a substantial improvement on the earlier version of this article. The authors also would like to thank Dr. Joshua M. Tebbs for helping the revision of this article.