Non-randomized Response Model Research Articles

Sample size determination for interval estimation of the prevalence of a sensitive attribute under non-randomized response models.

A sufficient number of participants should be included to adequately address the research interest in the surveys with sensitive questions. In this paper, sample size formulas/iterative algorithms are developed from the perspective of controlling the confidence interval width of the prevalence of a sensitive attribute under four non-randomized response models: the crosswise model, parallel model, Poisson item count technique model and negative binomial item count technique model. In contrast to the conventional approach for sample size determination, our sample size formulas/algorithms explicitly incorporate an assurance probability of controlling the width of a confidence interval within the pre-specified range. The performance of the proposed methods is evaluated with respect to the empirical coverage probability, empirical assurance probability and confidence width. Simulation results show that all formulas/algorithms are effective and hence are recommended for practical applications. A real example is used to illustrate the proposed methods.

Sample Size Planning for Estimating Prevalence of Sensitive Attributes Using a Non-Randomized Response Model

Abstract It is well known that prevalence of a sensitive attribute may be underestimated based on direct inquiry of subjects. A non-randomized response model has thus been proposed and shown to be efficient in estimating the prevalence of sensitive attributes in surveys. Since most surveys are conducted to obtain precise estimates, herein we derive a sample size formula for this model based on confidence interval estimation rather than hypothesis testing as estimation is of most relevance in this context. In contrast to the conventional approach to sample size estimation, which does not explicitly consider the chance of achieving the precision, we incorporate an assurance probability into the formula by treating confidence interval width as random. Exact evaluation demonstrates that our formula performs well. Keywords : Confidence Interval; Prevalence; Proportion; Random Response

Non-randomized response model for sensitive survey with noncompliance.

Collecting representative data on sensitive issues has long been problematic and challenging in public health prevalence investigation (e.g. non-suicidal self-injury), medical research (e.g. drug habits), social issue studies (e.g. history of child abuse), and their interdisciplinary studies (e.g. premarital sexual intercourse). Alternative data collection techniques that can be adopted to study sensitive questions validly become more important and necessary. As an alternative to the famous Warner randomized response model, non-randomized response triangular model has recently been developed to encourage participants to provide truthful responses in surveys involving sensitive questions. Unfortunately, both randomized and non-randomized response models could underestimate the proportion of subjects with the sensitive characteristic as some respondents do not believe that these techniques can protect their anonymity. As a result, some authors hypothesized that lack of trust and noncompliance should be highest among those who have the most to lose and the least to use for the anonymity provided by using these techniques. Some researchers noticed the existence of noncompliance and proposed new models to measure noncompliance in order to get reliable information. However, all proposed methods were based on randomized response models which require randomizing devices, restrict the survey to only face-to-face interview and are lack of reproductivity. Taking the noncompliance into consideration, we introduce new non-randomized response techniques in which no covariate is required. Asymptotic properties of the proposed estimates for sensitive characteristic as well as noncompliance probabilities are developed. Our proposed techniques are empirically shown to yield accurate estimates for both sensitive and noncompliance probabilities. A real example about premarital sex among university students is used to demonstrate our methodologies.

A covariate nonrandomized response model for multicategorical sensitive variables

The diagonal method (DM) is an innovative technique to obtain trustworthy survey data on an arbitrary categorical sensitive characteristic Y∗ (e.g., income classes, number of tax evasions). The estimation of the unconditional distribution of Y∗ from DM data has already been shown. Now, a covariate extension of the DM, that is, methods to investigate the dependence of Y∗ on nonsensitive covariates, is sought. For instance, the dependence of income on gender and profession may be under study. The covariate extensions of privacy-protecting survey designs are broadened by the covariate DM, especially because existing methods focus on binary Y∗. LR-DM estimation and stratum-wise estimation are described, where the former is based on a logistic regression model, leads to a generalized linear model, and requires computer-intensive methods. The existence of a certain regression estimate is investigated. Moreover, the connection between efficiency of the LR-DM estimation and the degree of privacy protection is studied and appropriate model parameters of the DM are searched. This problem of finding suitable model parameters is rarely addressed for privacy-protecting survey methods for multicategorical Y∗. Finally, the LR-DM estimation is compared with the stratum-wise estimation. MATLAB programs that conduct the presented estimations are provided as supplemental material (see Appendix E).

Algorithm for estimating a sensitive proportion by using a non- randomized response model

In this paper, a new non-randomized response model is proposed. Two unrelated questions are used in the proposed model to estimate a single sensitive question in surveys. The estimated proportion of a sensitive characteristic in an unknown population can be calculated using the obtained maximum likelihood equation from the maximum likelihood method. The performance of the proposed estimation is evaluated by the Monte Carlo simulation method. The model proposed here proved to be more efficient than the randomized response model studied by Warner (1965) and the non-randomized model presented by Yu et al. (2008). A simulation example demonstrates the feasibility of the method.

A new non‐randomized response model: The parallel model

Despite certain advances for non‐randomized response (NRR) techniques in the past 6 years, the existing non‐randomized crosswise and triangular models have several limitations in practice. In this paper, I propose a new NRR model, called the parallel model with a wider application range. Asymptotical properties of the maximum likelihood estimator (and its modified version) for the proportion of interest are explored. Theoretical comparisons with the crosswise and triangular models show that the parallel model is always more efficient than the two existing NRR models for most of the possible parameter ranges. Bayesian methods for analyzing survey data from the parallel model are developed. A case study on college students' premarital sexual behavior at Wuhan and a case study on plagiarism at the University of Hong Kong are conducted and are used to illustrate the proposed methods. © 2014 The Authors. Statistica Neerlandica © 2014 VVS.

Using prior information in privacy-protecting survey designs for categorical sensitive variables

To gather data on sensitive characteristics, such as annual income, tax evasion, insurance fraud or students’ cheating behavior, direct questioning is problematic, because it often results in answer refusal or untruthful responses. For this reason, several randomized response (RR) and nonrandomized response (NRR) survey designs, which increase cooperation by protecting the respondents’ privacy, have been proposed in the literature. In the first part of this paper, we present a Bayesian extension of a recently published, innovative NRR method for multichotomous sensitive variables. With this extension, the investigator is able to incorporate prior information on the parameter, e.g., based on a previous study, into the estimation and to improve the estimation precision. In particular, we derive different point and interval estimates by the EM algorithm and data augmentation. The performance of the considered estimators is evaluated in a simulation study. In the second part of this article, we show that for any RR or NRR model addressing the estimation of the distribution of a categorical sensitive characteristic, the design matrices of the model play the central role for the Bayes estimation whereas the concrete answer scheme is irrelevant. This observation enables us to widely generalize the calculations from the first part and to establish a common approach for Bayes inference in RR and NRR designs for categorical sensitive variables. This unified approach covers even multi-stage models and models that require more than one sample.

Flexible non-randomized response models for survey with sensitive question

Non-randomized response (NRR) models have recently been developed for analyzing sensitive questions. Unlike traditional randomized response models, NRR models do not require a randomizing device, which limits the survey format and reproductivity of results. On the other hand, NRR models introduce a non-sensitive question with binary outcomes in the questionnaire in order to protect privacy and encourage cooperation from respondents. Unfortunately, the proportion of subjects who possess the non-sensitive characteristic is assumed to be known, and the non-sensitive and sensitive questions are assumed to be independent. In this manuscript, we propose three new NRR models, which relax the aforementioned assumptions. Parameter and confidence interval estimates for the sensitive proportion will be developed. Optimal sample size allocations will be investigated. Performance of the proposed NRR models will be studied. A real survey on premarital sexual activity among college/university students in China is conducted to illustrate the proposed methodologies.

Two-valued response technique of polychotomous sensitive question

The randomized response (RR) technique is an effective survey method when collecting sensitive information. This paper proposes a new non-randomized response model for survey sampling with polychotomous sensitive questions: Two-valued response technique. The proportion of the sensitive attribute and its estimator’s variance are estimated under the simple random sampling without replacement and with replacement designs. The relation between the efficiency and the protection of privacy is discussed. The result indicates that the efficiency is in conflict with protection of privacy in the new proposed model, which is the same as that in the RR technique, but the new technique has better characteristics in sociological practice aspects than the RR technique, because it is of low cost, saving time and being operated easily.

Sample Surveys With Sensitive Questions: A Nonrandomized Response Approach

Since the Warners randomized response (RR) model to solicit sensitive information was proposed in 1965, it has been used and extended in a broad range of surveys involving sensitive questions. However, it is limited, for example, by a lack of reproducibility and trust from the interviewees as well as higher cost due to the use of randomizing devices. Recent developments of the alternative non-randomized response (NRR) approach have shown the promise to alleviate or eliminate such limitations. However, the efficiency and feasibility of the NRR models have not been adequately studied. This article introduces briefly the NRR approach, proposes several new NRR models, compares the efficiency of the NRR and RR models and studies the feasibility of the NRR models. In addition, we propose the concept of the degree of privacy protection between the NRR model and the Warner model to reflect the extent the privacy is protected. These studies show that not only the NRR approach is free of the limitations of the randomized approach but also the NRR model actually increases the relative efficiency and the degree of privacy protection. Thus, the non-randomized response approach offers an attractive alternative to the randomized response approach.

Bayesian non-randomized response models for surveys with sensitive questions

Three non-randomized response (NRR) models (namely, the non-randomized triangular, crosswise and hidden sensitivity models) have recently been developed for analyzing dichotomous sensitive questions. Unlike existing randomized response (RR) models, no randomizing device is required for NRR models. This helps to reduce the cost, increase the efficiency, ensure the reproducibility, widen the applicability and encourage the cooperation. However, in applications (e.g., estimating the proportion of a rare sensitive attribute in a population) with highly skewed likelihood functions, classical asymptotic methods based on maximum likelihood estimates and their asymptotic standard errors may not be adequate. The purposes of this article are two folds. First, we develop Bayesian approaches for analyzing dichotomous sensitive questions based on the aforementioned NRR models. For both the non-randomized triangular and crosswise models, we obtain the exact posterior distribution and its explicit posterior moments, derive posterior mode via the EM algorithm and provide procedure for generating i.i.d. posterior samples. For the hidden sensitivity model, we consider Bayesian analysis under the commonly used conjugate Dirichlet prior. Second, noting that the covariance structure associated with the Dirichlet distribution is completely nonpositive, we propose three new joint priors for modeling independence structure with restrictions, negative correlation structure and positive correlation structure, respectively. A new hierarchical modeling strategy is provided. Importance sampling and data augmentation algorithm are employed to compute posterior moments and generate posterior samples. Three data sets from a sensitive sexual behavior study, an induced abortion study and a HIV study are used to illustrate the proposed methodologies.