Nonparametric Model-Assisted Estimation from Quantitative Randomized Response Models

• Activity Number: 54 - Record Linkage, Data Integration, and Improving Survey Measurement
• Type: Contributed
• Date/Time: Sunday, August 8, 2021 : 3:30 PM to 5:20 PM
• Sponsor: Survey Research Methods Section
• Author(s): Sayed Mostafa*
• Companies: North Carolina A&T State University
• Keywords: randomized response model; complex surveys; model-assisted estimation; local linear regression; Horvitz-Thompson estimation

Abstract

The randomized response technique is a survey method that has been proven effective in reducing potential bias resulting from nonresponse and untruthful responses when asking questions about sensitive behaviors or beliefs. This paper considers estimating the finite population mean of a sensitive variable from complex sample surveys in the presence of non-sensitive auxiliary information. We define and study a class of nonparametric model-assisted estimators for the mean of a sensitive study variable whose sample values are only observed in a scrambled form through a general linear randomized response model. The proposed estimators are shown to have the desirable asymptotic properties of traditional model-assisted estimators. The finite sample performance of the new estimators is studied via Monte Carlo simulations accounting for a wide range of forms for the relationship between the study variable and auxiliary variable. The empirical results support the theoretical analyses and suggest that our proposed estimators outperform many standard estimators, e.g, ratio and regression estimators, in most cases. We also discuss the problem of variance estimation for the proposed estimators.