Two-stage Optional Randomized Response Models.

Social desirability bias (SDB) is defined as a tendency in people to present themselves in a more socially acceptable light, when faced with sensitive questions. People with a higher degree of SDB tend to give answers that will make them look good rather than those that are accurate. Randomized Response Technique (RRT) is one of several techniques used by researchers to circumvent social desirability bias in personal interview surveys. Starting from the pioneering work of Warner (1965), many versions of RRT have been developed that can deal with both categorical and quantitative responses. In this thesis we will focus only on those RRT models that are useful for quantitative responses. We will discuss a variety of quantitative RRT models including full, partial and optional RRT models. However, our primary focus in this thesis will be on optional RRT models. Specifically we will compare one-stage optional RRT models with two-stage optional RRT models. For optional RRT models, both additive and multiplicative RRT models have been used in the literature. However, survey respondents with minimal or no mathematical background may find additive models easier to handle. In this thesis we will discuss some other advantages of using additive optional RRT models as opposed to multiplicative optional RRT models. We will develop unbiased estimators for both the mean and the sensitivity level of a quantitative response sensitive question. We will also try to validate the proposed estimators by way of a simulation study. Throughout this thesis, we will use only the simple random sampling with replacement (SRSWR) design. However, the results can also be extended to other sampling designs