An efficient new “Partial” randomized response model

ABSTRACT

In this article, a new “Partial” randomized response model has been proposed. Its properties are studied both theoretically and empirically. The proposed model is proved to be more efficient than the randomized response models studied by Eichhorn and Hayre (1983 Eichhorn, B.H., Hayre, L.S. (1983). Scrambled randomized response methods for obtaining sensitive quantitative dada. J. Stat. Plann. Inference. 7:307–316.[Crossref], [Web of Science ®] , [Google Scholar]) and the “Partial” randomized response model.     

A modified optimal orthogonal new additive model

ABSTRACT

In this article, a new randomized response model has been proposed. The proposed model is found to be more efficient than the randomized response models studied by Singh (2010 Singh, S. (2010). Proposed optimal orthogonal new additive model (POONAM). Statistica. Anno LXX(1):73–81. [Google Scholar]). The relative efficiency of the proposed model has been studied with respect to the Singh (2010 Singh, S. (2010). Proposed optimal orthogonal new additive model (POONAM). Statistica. Anno LXX(1):73–81. [Google Scholar]) model. Numerical illustrations are also given in support of the present study.     

The Design of Scoring Schemes for Surveys Using the Block Total Response Method

ABSTRACT

In this article we investigate the design of scoring schemes for surveys using the block total response method. This method was first proposed by Raghavarao and Federer (1979 Raghavarao , D. , Federer , W. T. ( 1979 ). Block total response as an alternative to the randomized response method in surveys . J. Roy. Statist. Soc. 41 ( 1 ): 40 – 45 . [CSA] [CROSSREF]  [Google Scholar]) to provide accurate estimates of the base rates of sensitive characteristics using balanced incomplete block designs. The scoring scheme used in Raghavarao and Federer (1979 Raghavarao , D. , Federer , W. T. ( 1979 ). Block total response as an alternative to the randomized response method in surveys . J. Roy. Statist. Soc. 41 ( 1 ): 40 – 45 . [CSA] [CROSSREF]  [Google Scholar]) did not guarantee anonymity of answers and so the possibility of improving on this basic scoring scheme is considered in this article.     

The effects of covariate adjustment in generalized linear models

Results from classical linear regression regarding the effects of covariate adjustment, with respect to the issues of confounding, the precision with which an exposure effect can be estimated, and the efficiency of hypothesis tests for no treatment effect in randomized experiments, are often assumed to apply more generally to other types of regression models. In this paper results pertaining to several generalized linear models involving a dichotomous response variable are given, demonstrating that with respect to the issues of confounding and precision, for models having a linear or log link function the results of classical linear regression do generally apply, whereas for other models, including those having a logit, probit, log-log, complementary log-log, or generalized logistic link function, the results of classical linear regression do not always apply. It is also shown, however, that for any link function, covariate adjustment results in improved efficiency of hypothesis tests for no treatment effect in randomized experiments, and hence that the classical linear regression results regarding efficiency do apply for all models having a dichotomous response variable.     

Some New Results on the Multinomial Randomized Response Model

ABSTRACT

The randomized response technique is an effective survey method designed to elicit sensitive information while ensuring the privacy of the respondents. In this article, we present some new results on the randomization response model in situations wherein one or two response variables are assumed to follow a multinomial distribution. For a single sensitive question, we use the well-known Hopkins randomization device to derive estimates, both under the assumption of truthful and untruthful responses, and present a technique for making pairwise comparisons. When there are two sensitive questions of interest, we derive a Pearson product moment correlation estimator based on the multinomial model assumption. This estimator may be used to quantify the linear relationship between two variables when multinomial response data are observed according to a randomized-response protocol.     

Confidence Intervals for Univariate Impulse Responses With a Near Unit Root

This article proposes a method for constructing confidence intervals for the impulse response function of a univariate time series with a near unit root. These confidence intervals control coverage, whereas the existing techniques can all have coverage far below the nominal level. I apply the proposed method to several measures of U.S. aggregate output.     

CUSUM Hypothesis Tests and Alternative Response Probabilities for Finite Poisson Trials

This article develops a new cumulative sum statistic to identify aberrant behavior in a sequentially administered multiple-choice standardized examination. The examination responses can be described as finite Poisson trials, and the statistic can be used for other applications which fit this framework. The standardized examination setting uses a maximum likelihood estimate of examinee ability and an item response theory model. Aberrant and non aberrant probabilities are computed by an odds ratio analogous to risk adjusted CUSUM schemes. The significance level of a hypothesis test, where the null hypothesis is non-aberrant examinee behavior, is computed with Markov chains. A smoothing process is used to spread probabilities across the Markov states. The practicality of the approach to detect aberrant examinee behavior is demonstrated with results from both simulated and empirical data.     

Modified ridge analyses under nonstandard

A well-known procedure for the optimization of a second-degree response function over a spherical region of interest is that of ridge analysis. Khuri and Myers (1979) introduced a modification of this procedure by incorporating a certain constraint on the prediction variance. Both procedures, however, assume that the response variable has a constant variance throughtout the experimental region. In the present article, we consider two extensions to Khuri and Myers modifioed ridge analysis. The first extension relaxes the constant variance assumption. In the second extension. generalised linear models are used instead of the trasitional linear model. which are commenly used in responce variables that are not necessaily continusly distribution, including these have discreate distributions, Two examples are presented to illustrate the implementation of the proposed extensions.     

Item count technique with no floor and ceiling effects

Abstract

Conclusions of sample surveys dealing with matters of privacy are often disputed. Many people either refuse to participate or provide false answers. Indirect questioning techniques are designed so that reliable estimates can be produced while the privacy of the participants is protected. One such method, the Item Count Technique is gaining increasing popularity. However, the original version of the method does not fully protect the privacy of the participants. In this paper we propose a new version of the technique which better protects the privacy of the respondents and does not have the so-called floor and ceiling effects.     

A new unrelated question randomized response model

In this paper, we extend the work of Gjestvang and Singh [A new randomized response model, J. R. Statist. Soc. Ser. B (Methodological) 68 (2006), pp. 523–530] to propose a new unrelated question randomized response model that can be used for any sampling scheme. The interesting thing is that the estimator based on one sample is free from the use of known proportion of an unrelated character, unlike Horvitz et al. [The unrelated question randomized response model, Social Statistics Section, Proceedings of the American Statistical Association, 1967, pp. 65–72], Greenberg et al. [The unrelated question randomized response model: Theoretical framework, J. Amer. Statist. Assoc. 64 (1969), pp. 520–539] and Mangat et al. [An improved unrelated question randomized response strategy, Calcutta Statist. Assoc. Bull. 42 (1992), pp. 167–168] models. The relative efficiency of the proposed model with respect to the existing competitors has been studied.