The multidimensional randomized response design: Estimating different aspects of the same sensitive behavior.

Maarten J L F Cruyff,Peter G M Van Der Heijden,Ulf Böckenholt

doi:10.3758/s13428-015-0583-2

Abstract

The conventional randomized response design is unidimensional in the sense that it measures a single dimension of a sensitive attribute, like its prevalence, frequency, magnitude, or duration. This paper introduces a multidimensional design characterized by categorical questions that each measure a different aspect of the same sensitive attribute. The benefits of the multidimensional design are (i) a substantial gain in power and efficiency, and the potential to (ii) evaluate the goodness-of-fit of the model, and (iii) test hypotheses about evasive response biases in case of a misfit. The method is illustrated for a two-dimensional design measuring both the prevalence and the magnitude of social security fraud.

Highlights

In surveys and questionnaires, sensitive questions are the major source of evasive responses
In “The model” section, we derive the statistical model for the multidimensional design, and in “Power study” section we present a power study comparing the uni- and multidimensional designs
This paper introduced a multidimensional design for randomized response studies

Summary

Introduction

Sensitive questions are the major source of evasive responses. This is not a satisfactory situation, and several multivariate models for the unidimensional design have been proposed that allow for the estimation of response biases. The transition probabilities denoting the probability of the observed answer given the respondent’s true state, are computed as the sum of a truthful and a forced responses.

Results

Conclusion