Randomized response model in a matched pair study

The development of randomized response models for personal interview surveys has attracted much attention since the pioneering work of Warner [1965. Randomized response: a survey technique for eliminating evasive answer bias. J. Amer. Statist. Assoc. 60, 63–69]. Several randomized response models have been developed by researchers for collecting data on both qualitative and the quantitative variables, but none of these models discuss matched pair data. In this paper, we develop a new randomized response model and study its application to an important political question.     

Analyzing continuous randomized response data with an indifference-zone selection procedure

A review of the randomized response model introduced by Warner (1965) is given, then a randomized response model applicable to continuous data that considers a mixture of two normal distributions is considered. The target here is not to estimate any parameter, but rather to select the population with the best parameter value. This article provides a study on how to choose the best population between k distinct populations using an indifference-zone procedure. Also, this article includes tables for the required sample size needed in order to have a probability of correct selection higher than some specified value in the preference zone for the randomized response model considered.     

Violation of respondent's privacy in moors* model- its rectification through a random group strategy

The primary objective of the randomized response techniques introduced by Warner (1965) and Greenberg et al. (1969) was to protect the privacy of the respondents while eliciting information on sensitive issues. However, Moors' (1971) model, which is considered to be the best in the sense of optimality and convenience to use, fails to protect the privacy of respondents in certain cases. The present paper aims at pointing out this serious draw back. An alternative model termed as 'random group method ' is proposed. The proposed model is free from the above mentioned drawback and provides more efficient estimator as compared to the usual Greenberg at al. 's (1969) model.     

Estimating sensitive proportions by Warner’s randomized response technique using multiple randomized responses from distinct persons sampled

In 1965 Warner pioneered randomized response techniques to estimate the proportion of people bearing a sensitive characteristic. He restricted applying his randomized response device to gather data on sensitive issues from respondents chosen by simple random sampling with replacement (SRSWR). It has spawned numerous ramifications. We present results for the situation where the distinct persons chosen in an SRSWR are identified but each one independently gives a randomized response by Warner’s device, repeated as many times as he/she is selected. Two new estimators are proposed for the sensitive proportion and compared against relevant competitors.     

On using non identical and independent Bernoulli trials in human surveys

Unlike the usual randomized response techniques, as a pioneering attempt, this article focuses on using non identical independent Bernoulli trials in sensitive surveys. For this purpose, a general class of randomized response techniques is considered. The usual randomized response techniques are based on a fixed probability of having a yes answer. Contrary to usual techniques, in the proposed technique every respondent has a different probability of reporting a yes answer. With this setting, in most of the situations, the proposed technique is observed performing better in terms of variability. To illustrate and support the superiority of the proposed technique it is compared with models such as Warner (1965), Greenberg et al. (1969), Mangat and Singh (1990), and Mangat (1994) using identical Bernoulli trials. Relative efficiency and privacy protection are studied in detail using Warner (1965) and Mangat (1994) models.     

Pseudo-Bayes and pseudo-empirical Bayes estimators in randomized response sampling

In this article, new pseudo-Bayes and pseudo-empirical Bayes estimators for estimating the proportion of a potentially sensitive attribute in a survey sampling have been introduced. The proposed estimators are compared with the recent estimator proposed by Odumade and Singh [Efficient use of two decks of cards in randomized response sampling, Comm. Statist. Theory Methods 38 (2009), pp. 439–446] and Warner [Randomized response: A survey technique for eliminating evasive answer bias, J. Amer. Statist. Assoc. 60 (1965), pp. 63–69].     

改进的随机截尾模型

在随机截尾模型的基础上,为了保护被调查者的隐私,文章提出了一种改进的调查数量敏感性问题的随机化回答方法,并把改进模型的精度与随机截尾模型、随机截尾Warner模型进行了比较。     

A stratified Warner''s randomized response model

This paper proposes a new stratified randomized response model based on Warner's (J. Amer. Statist. Assoc. 60 (1965) 63) model that has an optimal allocation and large gain in precision. It also presents a drawback of the Hong et al. (Korean J. Appl. Statist. 7 (1994) 141) model under their proportional sampling assumption. It is shown that the proposed model is more efficient than the Hong et al. (Korean J. Appl. Statist. 7 (1994) 141) stratified randomized response model. Additionally, it is shown that the estimator based on the proposed method is more efficient than the Warner (J. Amer. Statist. Assoc. 60 (1965) 63), the Mangat and Singh (Biometrika 77 (1990) 439) and the Mangat (J. Roy. Statist. SQC. Ser. B 56 (1) (1994) 93) estimators under the conditions presented in both the case of completely truthful reporting and that of not completely truthful reporting by the respondents.     

Augmented-limited regression models with an application to the study of the risk perceived using continuous scales

Studies of risk perceived using continuous scales of [0,100] were recently introduced in psychometrics, which can be transformed to the unit interval, but the presence of zeros or ones are commonly observed. Motivated by this, we introduce a full inferential set of tools that allows for augmented and limited data modeling. We considered parameter estimation, residual analysis, influence diagnostic and model selection for zero-and/or-one augmented beta rectangular (ZOABR) regression models and their particular nested models, which is based on a new parameterization of the beta rectangular distribution. Different from other alternatives, we performed maximum-likelihood estimation using a combination of the EM algorithm (for the continuous part) and Fisher scoring algorithm (for the discrete part). Also, we perform an additional step, by considering other link functions, besides the usual logistic link, for modeling the response mean. By considering randomized quantile residuals, (local) influence diagnostics and model selection tools, we identified that the ZOABR regression model is the best one. We also conducted extensive simulations studies, which indicate that all developed tools work properly. Finally, we discuss the use of this type of models to treat psychometric data. It is worthwhile to mention that applications of the developed methods go beyond to Psychometric data. Indeed, they can be useful when the response variable in bounded, including or not the respective limits.     

Optional versus compulsory randomized response techniques in complex surveys

In estimating the proportion of people bearing a sensitive attribute in a community, to mitigate possible evasive answer biases, Warner (J. Amer. Statist. Assoc. 60 (1965) 63) introduced a technique of randomized response (RR) in human surveys, by way of protecting individual privacy. Chaudhuri and Mukerjee (Calcutta Statist. Assoc. Bull. 34 (1985) 225; Randomized Response: Theory and Techniques, Marcel Dekker, New York) presented a modification allowing a direct response (DR) option to whom the attribute does not appear to be stigmatizing enough. Warner himself and many of his followers restrict the application of their RR devices to surveys with selection exclusively by ‘simple random sampling with replacement’. Chaudhuri (J. Statist. Plann. Inference 34 (2001a) 37; Pakistan J. Statist. 17 (3) (2001b) 259; Calcutta Statist. Assoc. Bull. 52 (205–208) (2002) 315) showed the efficacy of some of these devices when sample selection is by general unequal probabilities possibly even without replacement. Here, we present theories for unbiased estimation of the proportion along with unbiased estimation of the variances of the estimators when ‘compulsory’ or ‘optional’ RR's are gathered from persons sampled with varying probabilities. Gains in efficiency by allowing DR option rather than RR compulsion are illustrated numerically through simulation from data.     

Randomized Response Techniques Using Maximum Likelihood Estimator

The randomized response (RR) technique with two decks of cards proposed by Odumade and Singh (2009) can always be made more efficient than the RR techniques proposed by Warner (1965), Mangat and Singh (1990), and Mangat (1994) by adjusting the proportion of cards in the decks. Arnab et al. (2012) generalized Odumade and Singh strategy (2009) for complex survey designs and wider class of estimators. In this paper improvement of Arnab et al. (2012) estimator has been made by using maximum likelihood method.     

Joint modeling of mixed skewed continuous and ordinal longitudinal responses: a Bayesian approach

In this paper, a joint model for analyzing multivariate mixed ordinal and continuous responses, where continuous outcomes may be skew, is presented. For modeling the discrete ordinal responses, a continuous latent variable approach is considered and for describing continuous responses, a skew-normal mixed effects model is used. A Bayesian approach using Markov Chain Monte Carlo (MCMC) is adopted for parameter estimation. Some simulation studies are performed for illustration of the proposed approach. The results of the simulation studies show that the use of the separate models or the normal distributional assumption for shared random effects and within-subject errors of continuous and ordinal variables, instead of the joint modeling under a skew-normal distribution, leads to biased parameter estimates. The approach is used for analyzing a part of the British Household Panel Survey (BHPS) data set. Annual income and life satisfaction are considered as the continuous and the ordinal longitudinal responses, respectively. The annual income variable is severely skewed, therefore, the use of the normality assumption for the continuous response does not yield acceptable results. The results of data analysis show that gender, marital status, educational levels and the amount of money spent on leisure have a significant effect on annual income, while marital status has the highest impact on life satisfaction.     

Utilization of higher order moments of scrambling variables in randomized response sampling

In this paper, a new estimator for estimating the proportion of a potentially sensitive attribute in survey sampling has been introduced. The proposed estimator makes use of higher order moments of the scrambling variable at the estimation stage. The proposed estimator has been found to be more efficient than the estimator due to Kuk [1990. Asking sensitive questions indirectly. Biomerika 77(2), 436–438] and Franklin [1989. A comparison of estimators for randomized response sampling with continuous distributions from a dichotomous population. Comm. Statist. Theory Methods 18, 489–505] type estimators in randomized response sampling. Recently, Guerriero and Sandri [2007. A note on the comparison of some randomized response procedures. J. Statist. Plann. Inference 137, 2184–2190] have shown that the family of randomized response models proposed by Kuk [1990. Asking sensitive questions indirectly. Biomerika 77(2), 436–438] is better than the Simmons’ family in terms of efficiency and protection.     

An improved two stage randomized response strategy

Mangat and Singh (1990) have suggested a two stage randomized response technique to estimate the proportion of population possessing a sensitive attribute. The procedure was shown to be more efficient than the procedure due to Warner (1965). Recently, Tracy and Osahan (1993) have suggested a modification to the Mangat and Singh (1990) procedure which results in a more efficient strategy in practice. In this paper we propose a modification to the Tracy and Osahan (1993) procedure. The modified procedure is a generalization of Tracy and Osahan (1993) and is always more efficient than their strategy. An empirical study has also been undertaken to find the extent of relative efficiency.     

Models with Errors due to Misreported Measurements

Measurement error and misclassification models feature prominently in the literature. This paper describes misreporting error, which can be considered to fall somewhere between these two broad types of model. Misreporting is concerned with situations where a continuous random variable X is measured with error and only reported as the discrete random variable Z. Data grouping or rounding are the simplest examples of this, but more generally X may be reported as a value z of Z which refers to a different interval from the one in which X lies. The paper discusses a method for handling misreported data and draws links with measurement error and misclassification models. A motivating example is considered from a prenatal Down's syndrome screening, where the gestational age at which mothers present for screening is a true continuous variable but is misreported because it is only ever observed as a discrete whole number of weeks which may in fact be in error. The implications this misreporting might have for the screening are investigated.     

Generalized additive models for location, scale and shape

Summary.  A general class of statistical models for a univariate response variable is presented which we call the generalized additive model for location, scale and shape (GAMLSS). The model assumes independent observations of the response variable y given the parameters, the explanatory variables and the values of the random effects. The distribution for the response variable in the GAMLSS can be selected from a very general family of distributions including highly skew or kurtotic continuous and discrete distributions. The systematic part of the model is expanded to allow modelling not only of the mean (or location) but also of the other parameters of the distribution of y , as parametric and/or additive nonparametric (smooth) functions of explanatory variables and/or random-effects terms. Maximum (penalized) likelihood estimation is used to fit the (non)parametric models. A Newton–Raphson or Fisher scoring algorithm is used to maximize the (penalized) likelihood. The additive terms in the model are fitted by using a backfitting algorithm. Censored data are easily incorporated into the framework. Five data sets from different fields of application are analysed to emphasize the generality of the GAMLSS class of models.     

Latent Variable Modelling: A Survey*

Abstract. Latent variable modelling has gradually become an integral part of mainstream statistics and is currently used for a multitude of applications in different subject areas. Examples of ‘traditional’ latent variable models include latent class models, item–response models, common factor models, structural equation models, mixed or random effects models and covariate measurement error models. Although latent variables have widely different interpretations in different settings, the models have a very similar mathematical structure. This has been the impetus for the formulation of general modelling frameworks which accommodate a wide range of models. Recent developments include multilevel structural equation models with both continuous and discrete latent variables, multiprocess models and nonlinear latent variable models.     

Estimation for generalized partially functional linear additive regression model

In practice, it is not uncommon to encounter the situation that a discrete response is related to both a functional random variable and multiple real-value random variables whose impact on the response is nonlinear. In this paper, we consider the generalized partial functional linear additive models (GPFLAM) and present the estimation procedure. In GPFLAM, the nonparametric functions are approximated by polynomial splines and the infinite slope function is estimated based on the principal component basis function approximations. We obtain the estimator by maximizing the quasi-likelihood function. We investigate the finite sample properties of the estimation procedure via Monte Carlo simulation studies and illustrate our proposed model by a real data analysis.     

Review: Reversed low-rank ANOVA model for transforming high dimensional genetic data into low dimension

A general modeling procedure for analyzing genetic data is reviewed. We review ANOVA type model that can handle both the continuous and discrete genetic variables in one modeling framework. Unlike the regression type models which typically set the phenotype variable as a response, this ANOVA model treats the phenotype variable as an explanatory variable. By reversely treating the phenotype variable, usual high dimensional problem is turned into low dimension. Instead, the ANOVA model always includes interaction term between the genetic locations and phenotype variable to find potential association between them. The interaction term is designed to be low rank with the multiplication of bilinear terms so that the required number of parameters is kept in a manageable degree. We compare the performance of the reviewed ANOVA model to the other popular methods via microarray and SNP data sets.     

Application of Dirichlet mixture of normals in growth curve models

In this paper, we present growth curve models with an auxiliary variable which contains an uncertain data distribution based on mixtures of standard components, such as normal distributions. The multimodality of the auxiliary random variable motivates and necessitates the use of mixtures of normal distributions in our model. We have observed that Dirichlet process priors, composed of discrete and continuous components, are appropriate in addressing the two problems of determining the number of components and estimating the parameters simultaneously and are especially useful in the aforementioned multimodal scenario. A model for the application of Dirichlet mixture of normals (DMN) in growth curve models under Bayesian formulation is presented and algorithms for computing the number of components, as well as estimating the parameters are also rendered. The simulation results show that our model gives improved goodness of fit statistics over models without DMN and the estimates for the number of components and for parameters are reasonably accurate.