The generalization of the non-randomized parallel model and item count technique in surveys with sensitive questions

Abstract

Sensitive issues are often arose in medical, psychological and sociological surveys, such as sex, abortion, illegitimate birth, AIDs, illegal betting, shoplifting, drug-taking, tax evasion, annual income, family violence, students’ cheating behavior and so on. Owing to preserving their own privacy, respondents may refuse to answer or even may provide wrong answers when sensitive questions are being asked directly. In order to encourage truthful answers as well as protect individuals’ personal information, the randomized response techniques (RRTs), item count techniques (ICTs) and the non-randomized response techniques (NRRTs) are proposed during the past decades in dealing with such surveys with sensitive characteristics.

The newly presented non-randomized parallel model (Tian, 2014) is a landmark in the area of NRRTs. It not only could resolve the estimation of the sensitive proportion when both the two possible outcomes of the question of interest are sensitive, it also has been proved numerically and theoretically showed that it is more efficient than the existing non-randomized crosswise and triangular designs in certain situations. However, the sample size formulae associated with testing hypotheses for the parallel model are not yet available. Since the sample size determination is a crucial step in survey practices, the main objective of Chapter 2 is to develop the sample size formulae with the parallel design by using the power analysis method for both the one- and two-sample problems.

In addition, it was noted that all these findings in Tian (2014) are based on the assumption of known proportions θ = Pr(U = 1) and p = Pr(W = 1). However, in survey practice, it is usually difficult to choose an appropriate non-sensitive dichotomous variate U with known θ = Pr(U = 1). The main goal of Chapter 3 is to propose a variant of the parallel model with unknown θ = Pr(U = 1).

Furthermore, although some hidden logit regression models were proposed based on the randomized response techniques. In practice, the randomized response techniques still have some limitations which will impede the survey implementation. Thus, the major objective of Chapter 4 is to develop a so-called hidden logistic regression based on the non-randomized parallel model to investigate the relationship between a sensitive binary response variable and a set of non-sensitive covariates. And also, in this Chapter, we will show that the hidden logistic regression based on the parallel model can be used to study such association.

Lastly, we propose a new Poisson–Poisson ICT, which is an extension of the Poisson ICT of Tian et al. (2015) from estimating the proportion associated with a sensitive binary variable to estimating the Poisson mean associated with a sensitive qualitative variable. The Poisson–Poisson ICT can be used to collect and analyze sensitive qualitative data, where an independent non-sensitive Poisson random variable with mean parameter λ is introduced to facilitate the data collection.

The performances of all the methods in this thesis are evaluated through simulation studies and the analysis of some real data sets.