Studies into Non-Saturated Randomized Response Models

Abstract

Randomized response is an interview technique designed to ask sensitive questions while protecting respondents’ privacy. It reduces response bias caused by evasive answers but is not entirely effective, as respondents sometimes fail to follow instructions. This dissertation develops statistical models to correct for such bias, focusing on non-saturated randomized response designs, specifically the Extended Crosswise Model (ECWM) and the Ever/Last year design. Besides an introductory chapter, this dissertation consists of five chapters. Chapters 2, 3, and 4 focus on the ECWM. Chapter 2 introduces a refined randomizer using numerical sequences to minimize response bias. Three online studies (on drug use and COVID-19 regulations) showed promising results: reduced bias and higher prevalence estimates for sensitive topics. Chapter 3 presents the One-Sayers model, which corrects for systematic response bias where respondents choose the safest answer. Analysis of six doping surveys found one-saying bias ranging from 6.5% to 13.1%, with corrected prevalence estimates 1.2 to 3.8 percentage points lower than uncorrected ECWM estimates. Chapter 4 extends the ECWM and the one-sayers models to account for random answering, which biases prevalence estimates toward 50%. Correcting for this bias significantly lowered prevalence estimates. Chapter 5 introduces the multinomial model for the joint analysis of the “ever” and “last year” questions, The model has a degree of freedom that allows for a goodness-of-fit test. Chapter 6 shows the similarities between the cheater detection model and the self-protective no-sayers model, and introduces extensions to the multinomial model of Chapter 5 to correct for self-protective answering and cheating.