A Two-stage Multilevel Randomized Response Technique With Proportional Odds Models and Missing Covariates

• Published in: Sociological methods & research Vol. 51; no. 1; pp. 439 - 467
• Main Authors: Hsieh, Shu-Hui, Lee, Shen-Ming, Li, Chin-Shang
• Format: Journal Article
• Language: English
• Published: Los Angeles, CA SAGE Publications 01.02.2022; SAGE PUBLICATIONS, INC
• Subjects: Bias; Foreign Countries; Income; Multiple imputation; Polls & surveys; Privacy; Response Rates (Questionnaires); Response Style (Tests); Simulation; Social change; Surveys; Underreporting; Weighting; Taiwan; missing at random; multiple imputation; inverse probability weighting; Taiwan Social Change Survey; multilevel randomized response technique
• ISSN: 0049-1241; 1552-8294
• DOI: 10.1177/0049124120914954

Surveys of income are complicated by the sensitive nature of the topic. The problem researchers face is how to encourage participants to respond and to provide truthful responses in surveys. To correct biases induced by nonresponse or underreporting, we propose a two-stage multilevel randomized response (MRR) technique to investigate the true level of income and to protect personal privacy. For a wide range of applications, we present a proportional odds model for two-stage MRR data and apply inverse probability weighting and multiple imputation methods to deal with covariates on some subjects that are missing at random. A simulation study is conducted to investigate the effects of missing covariates and to evaluate the performance of the proposed methods. The practicality of the proposed methods is illustrated with the regular monthly income data collected in the Taiwan Social Change Survey. Furthermore, we provide an estimate of personal regular monthly mean income.