Randomized Response Model Research Articles

An Analysis on the Influence of R&D Fiscal and Tax Subsidies on Regional Innovation Efficiency: Empirical Evidence from China

To promote the National Mid-andLong-Term Scientific and Technical Development Program, utilizing the technical innovation data from 30 provinces of China from2002–2016, this paper evaluates the inter-provincial differences of China’s regional innovation efficiency from four aspects of technical efficiency, efficiency index change, returns to scale, and projection analysis by using the DEA-Malmquist index method and constructs of the DEA-Tobit random response model to explore the impact of government funding on regional innovation efficiency. The research results show that: (1) The local development of regional innovation efficiency in China is unbalanced, and the level of pure technical efficiency restricts the improvement of innovation efficiency. (2) In the prophase of the scientific and technical development plan, technological progress has led to the growth of total factor productivity, resulting in the formation of scale effect; in the later stage, the scale return shows an overall increasing trend, and the continuous expansion of technological scale and opportunities has improved the regional innovation efficiency. (3) The R&D fiscal and tax subsidies have policy sustainability, and the direct government funding can significantly improve innovation efficiency, while the enterprises investment is opposite, and the pretax additional deduction has a negative but not significant impact. The government should give priority to direct subsidy and supplemented by tax preference, making reasonable policy allocations to expand the policy effect.

A Mixed Multiplicative Quantitative Randomized Response Model by Two Stage Cluster Sampling

본 연구에서는 민감한 내용을 조사하는데 있어서 모집단이 집락으로 구성되어 있을 경우, 1단계로 모집단에서 집락을 단순임의비복원으로 추출한 후, 2단계로 추출된 각 집락에서 조사단위를 단순임의복원으로 추출하는 2단계 집락추출법을 Lee, Hong, Son(2018)의 혼합 승법 양적속성확률화응답모형에 적용한 2단계 집락추출법에 의한 혼합 승법 양적속성 확률화응답모형을 제안하였다. 민감한 변수에 대한 추정량과 그 분산을 구하였으며, 주어진 비용 하에서 분산을 최소화하는 1단계 집락과 2단계 조사단위 수의 최적값을 구하였다. 또한 제안한 2단계 집락추출법에 의한 혼합 승법 양적속성 모형과 Eichhorn, Hayre(1983)의 모형, Bar-Lev, Bobovitch, Boukai(2004)의 모형, Gjestvang, Singh(2009)의 모형에 2단계 집락추출법을 적용한 모형과의 비교를 통해 기존의 2단계 집락 혼합 승법모형들이 제안한 모형의 특별한 경우임을 확인하였고, 제안한 2단계 집락추출법에 의한 혼합 승법 양적속성 모형과 2단계 집락추출법에 의한 Bar-Lev, Bobovitch, Boukai(2004)의 모형과의 효율성을 비교해 본 결과 Cxi값이 작을수록, Czi값이 클수록 제안한 2단계 집락추출법에 의한 혼합 승법 양적속성 확률응답모형의 효율적임을 알 수 있었다.

A randomized response model based on blank card and geometric distribution to estimate sensitive proportion

Using geometric probability (GP) distribution as a randomization device, a new randomized response (RR) model has been proposed which has an immense potential to estimate the human population proportion that possess a stigmatized character. Privacy protection measure of proposed model and some of its properties have been investigated. In addition, empirical experiments are conducted to validate the theoretical results, which demonstrate the better performance of the suggested estimators over their direct competitors. Finally, results are analyzed and appropriate suggestions are made available to survey practitioners when dealing with sensitive aspects.

Multi-choice stratified randomized response model with two-stage classification

Generally, stratification gives a small error and greater precision than the simple random sampling method in estimating the sample for the study. This paper aims to formulate the sampling problem as a multi-choice programming problem for determining the optimum allocation in the presence of non-response and considering a two-stage stratified Warner's randomized response model with cost constraint. But, mostly in real-life situations, the cost is not certain. Therefore, in cost constraint, the right-hand side parameter, i.e. total available budget, has been considered as multi-choice in nature. Multiple choices may exist for the fixed cost in the constraint, out of which exactly one has to be selected. The selection should make so that the combination of each choice should provide the best compromise optimum solution. The problem has been formulated as a multi-choice integer nonlinear programming problem, and an illustrative numerical example has been presented to demonstrate the proposed model.

An efficient new scrambled response model for estimating sensitive population mean in successive sampling

In this paper, a new scrambled randomized response (SRR) model has been proposed for estimating the population mean of a sensitive variable in presence of scrambled response under simple random sampling with replacement (SRSWR). The utility of proposed SRR model under two occasions successive sampling is also explored. It is found that the proposed SRR model is superior to the additive model of Gjestvang and Singh (2009) under SRSWR and successive sampling. We also proposed a composite class of estimators for estimating the population mean of sensitive variable under two occasions successive sampling. The proposed composite class of estimators under optimum conditions is shown to be more efficient than the classical ratio and exponential ratio type estimators respectively.

An alternative approach for construction of strata using quantified sensitivity level

The study is investigated on an alternative method for the construction of strata using sensitivity level when the samples are selected with simple random sampling with replacement (SRSWR) and the data are collected by scrambled optional randomization technique on the sensitive characters. Thus, the optional randomized response model , where k is a random variable having value 1 if the response is scrambled and 0 otherwise, was considered for finding out Approximate Optimum Strata Boundaries by minimizing the variance of the estimator . The cum. was proposed for finding out Approximate Optimum Strata Boundary in Neyman allocation for the optional scrambled response. This is applicable for wider classes of sampling design and estimators in stratification. The proposed rule on optional scrambled randomized response is efficient and can be used effectively for the construction of optimum strata boundary via Rectangular, Right triangular and Exponential distribution.

Two sensitive characteristics and their overlap with two questions per card

AbstractIn this paper, we developed a new unique unrelated question randomized response model in which each card has two questions, either both questions on the sensitive characteristics or both questions on the two unrelated characteristics. The proposed model is unique in the sense this is the only way of asking two questions printed on each card that leads to protection of the privacy of the respondent. We first develop estimators of the prevalence of the two sensitive characteristics and of their overlap. Then we show that the resultant estimators are unbiased. Next we derive variance expressions for the developed estimators of the proportions. We also compute the relative efficiency and relative privacy protection of the proposed model with respect to its competitors. The variances of the proposed estimators are also verified by comparing them to the Cramer–Rao lower bounds of variance–covariance of the estimators. Estimators of conditional proportion, relative risk, and correlation coefficient are also discussed. Lastly, a real data application of the proposed model is considered, which shows the importance of the use of the proposed model in medical and social science studies.

An improved scrambled model for estimating the mean of a sensitive character

This paper suggests a new randomized response model useful for gathering information on quantitative sensitive variable such as drug usage, tax evasion and induced abortions etc. The resultant estimator has been found to more efficient than the estimator of the Saha (2007) under some realistic conditions. We have illustrated results numerically.

A Theory of Higher Order Interactions Between Sensitive Variables: Empirical Evidences and an Application to a Variety of Smoking

In carrying out surveys involving sensitive characteristics, randomized response models have been considered among the best techniques since they provide the maximum privacy protection to the respondents and procure honest responses. Over the years, researchers have carried out studies on the estimation of proportions of the population possessing sensitive characteristics. However, there is a paucity of research studies that have addressed higher order interactions between these sensitive characters. In this article, we develop a new theory based on three proposed randomized response models which we name as: simple model, semi-crossed model, and fully crossed model. Twenty-one new unbiased estimators of seven parameters are introduced, their variance expressions are derived, and unbiased estimators of variances are developed. The three models are compared under various values of the parameters by computing the percent relative efficiency of one model over another model. The most efficient model is then applied to study the population proportions of three varieties of smoking habits among students, and their first- and second-order interactions. The last four sections (Ninth to Twelfth) are verifications of theoretical results using the Cramer–Rao lower bounds of variances for the developed 21 new estimators in randomized response sampling.

A randomized response model for sensitive attribute with privacy measure using Poisson distribution

In sample surveys, when we need information regarding rare sensitive issues which people often do not prefer to share with others. In such situations this is also awkward for interviewers to ask the direct questions related to confidential and private matters of interviewees. An approach towards the open queries about sensitive issues generally results in the high non-response rates or misleading answers. The aim of this paper is to develop an effective randomized response model to overcome with these types of challenges arising due to sensitive nature of characteristic under study. In this paper we have proposed three-stage randomized response model for estimating mean number of individuals who possessed rare sensitive attribute which makes use of Poisson distribution. The properties of the proposed estimation procedures have been deeply examined when the parameter of a rare unrelated attribute is known as well as unknown. Privacy protection of respondents is also an equally important matter of concern. So measure of privacy protection for the proposed randomized response model has also been examined. Empirical studies are performed to support the theoretical results, which show the dominance of the proposed estimators over well-known contemporary estimators. From the findings of this study we may conclude that proposed randomized response model is rewarding in terms of percent relative efficiencies and privacy protection and may be recommended to survey practitioners for real life applications.

An Improved Two-stage Randomized Response Model for Estimating the Proportion of Sensitive Attribute

The randomized response technique (RRT) is an effective method designed to obtain the stigmatized information from respondents while assuring the privacy. In this study, we propose a new two-stage RRT model to estimate the prevalence of sensitive attribute ([Formula: see text]). A simulation study shows that the empirical mean and variance of proposed estimator are close to corresponding theoretical values. The utility of proposed two-stage RRT model under stratification is also explored. An efficiency comparison between proposed two-stage RRT model and some existing RRT models is carried out numerically under simple and stratified random sampling.

Estimation of stigmatized population total: A new additive quantitative randomized response model

In this article, we propose a new randomized response model to estimate the population total of a sensitive variable of quantitative nature. The objective is achieved by introducing additive scrambling mechanism when sample is drawn through probability proportional to size sampling scheme. The performance evaluation of the proposed model is carried with respect to notable model of Odumade and Singh (2010). To maintain the generality, we consider variety of settings of design parameters. Furthermore, log-log model approach is employed to assess the predictive effects of design parameters over the percentage relative efficiency of the proposed scheme. The gain of using proposed method over contemporary model is documented throughout the article.

On Bayesian Analysis of a General Class of Randomized Response Models In Social Surveys about Stigmatized Traits

While conducting a social survey on stigmatized/sensitive traits, obtaining efficient (truthful) data is an intricate issue and estimates are generally biased in such surveys. To obtain trustworthy data and to reduce false response bias, a technique, known as randomized response technique, is now being used in many surveys. In this study, we performed a Bayesian analysis of a general class of randomized response models. Suitable simple Beta prior and mixture of Beta priors are used in a common prior structure to obtain the Bayes estimates for the proportion of a stigmatized/sensitive attributes in the population of interest. We also extended our proposal to stratified random sampling. The Bayes and the maximum likelihood estimators are compared. For further understanding of variability, we have also compared the prior and posterior distributions for different values of the design constants through graphs and credible intervals. The condition to develop a new randomized response model is also discussed.

A randomized response model based on blank card and geometric distribution to estimate sensitive proportion

Using geometric probability (GP) distribution as a randomization device, a new randomized response (RR) model has been proposed which has an immense potential to estimate the human population proportion that possess a stigmatized character. Privacy protection measure of proposed model and some of its properties have been investigated. In addition, empirical experiments are conducted to validate the theoretical results, which demonstrate the better performance of the suggested estimators over their direct competitors. Finally, results are analyzed and appropriate suggestions are made available to survey practitioners when dealing with sensitive aspects.

Application of a randomized response technique for the sensitive question survey in female sex workers in Xichang, China.

The technique of sampling is a particularly important aspect of sampling surveys, and the method of determining sample size is the key link in sampling technique. However, a sample size determination method for complex sampling surveys of sensitive issues using a randomized response model is not yet available. In this work, we drew from the theory of probability and mathematical statistics, and developed a series of formulas for sample size determination that are required to estimate the overall proportion and mean on dichotomous sensitive questions in 3-stage sampling using Simmons models. Shortly after generating the formulas, we successfully applied them to a pre-survey regarding sensitive issues among female sex workers (FSWs) in Xichang, and found their practical application to achieve satisfactory effects. By using a large number of Monte Carlo simulation sampling tests, the reliability of the survey methods and formulas for sensitive question surveys were found to be high, but the randomized response technique (RRT) cannot completely eliminate the possibility of social acceptability bias. RRT is an acceptable method for sensitive question surveys within sensitive populations, and this new sampling method is liable to be used for sensitive question surveys of large populations. We believe that the results obtained in the field of public health can provide some data support for clinical practice.

Unbiased estimator modeling in unrelated dichotomous randomized response

Abstract The unrelated design has been shown to improve the efficiency of a randomized response method and reduces respondents’ suspicion. In the light of this, the paper proposes a new Unrelated Randomized Response Model constructed by incorporating an unrelated question into the alternative unbiased estimator in the dichotomous randomized response model proposed by Ewemooje in 2019. An unbiased estimate and variance of the model are thus obtained. The variance of the proposed model decreases as the proportion of the sensitive attribute π_A and the unrelated attribute π_U increases, in contrast to the earlier Ewemooje model, whose variance increases as the proportion of the sensitive attribute increases. The relative efficiency of the proposed model over the earlier Ewemooje model decreases as π_U increases when 0.1≤π_A≤ 0.3 and increases as π_U increases when 0.35≤π_A≤ 0.45. Application of the proposed model also revealed its efficiency over the direct method in estimating the prevalence of examination malpractices among university students;the direct method gave an estimate of 19.0%, compared to the proposed method’s estimate of 23.0%. Hence, the proposed model is more efficient than the direct method and the earlier Ewemooje model as the proportion of people belonging to the sensitive attribute increases.

Development of an assessment tool for mathematical reading, analytical thinking and mathematical writing

<p>The main objective of this research was to develop and validate the quality of an assessment tool for evaluating the mathematical reading, analytical thinking, and mathematical writing skills of fourth-grade students. We randomly selected 222 fourth grade students across multiple schools of varying sizes to take the assessment. Multidimensional Random Coefficients Multinomial Item Response Model was applied to validate the quality of the developed assessment tool. A design-based research methodology was adopted to develop the assessment tool encompassing four phases as follows: 1) analyze how students solve mathematical problems; 2) develop the assessment tool; 3) validation of the tool; and 4) reflection. The results of this research indicate that the assessment tool consisting of 19 items and two dimensions is a reliable and valid metric to measure mathematical reading, mathematical writing and analytical ability of fourth graders. The Likelihood-Ratio test showed that the multidimensional model fits better in comparison to the unidimensional model. It can be concluded that each item is qualified to assess the students and relevant to the developed dimensional examination structure.</p>

A generalized class of exponential type estimators for estimating the mean of the sensitive variable when using optional randomized response model

In this article, we propose a generalized class of exponential type estimators for estimating the mean of delicate variable in the existence of non-sensitive two auxiliary variables. The performance of mean estimator is obtained by using generalized two stage optional randomized response model. The expression for the bias and the mean square error are obtained up to first degree of approximation. Certain special cases for the generalized class are discussed. An extensive simulation study is performed to determine the performance of the estimators. It is observed that the suggested class of estimators performs more efficiently than some existing estimators.

The independence assumption in the mixed randomized response model

We study the independence assumption in the mixed randomized response model to show that it is unnecessary for unbiasedness and yet preferable for efficiency. The unconditional variance of MRR estimators without the independence condition is shown.

Estimating the proportion of non-heterosexuals in Taiwan using Christofides’ randomized response model: A comparison of different estimation methods

In social research, investigating sensitive, highly personal or embarrassing issues by means of standard survey techniques based on direct questioning leads to refusals to answer or false responses which, generally, flaw the validity of the analyses and produce incorrect inferences. To correct biases induced by nonresponse or underreporting of sensitive matters, Warner (1965) introduced an indirect questioning approach, known as the randomized response technique, which allows researchers to estimate the proportion of individuals with sensitive attributes or behaviors, while ensuring respondents’ privacy protection. In this article, we consider the randomized response model proposed by Christofides (2003) and, through a simulation and an empirical study, compare different estimation methods for the prevalence of a sensitive attribute. Specifically, we discuss how the model has been implemented in a pilot study to collect data and derive maximum likelihood and Bayesian estimates for the proportion of non-heterosexuals aged 20 years or older for the Taiwanese population and for some subgroups of it by sex and age. Our analysis, and in particular the Bayesian approach, seems to meet the expectation of social researchers and experts of sexual behaviors. In fact, the produced estimates are higher than official findings in Taiwan obtained by direct questioning in face-to-face interviews and provide a more reliable picture of sexual identity in the country. Moreover, Bayesian estimates appear more accurate than those produced by the method of moment and the maximum likelihood method.