Randomized Item Response Theory Models

Abstract

The randomized response (RR) technique is often used to obtain answers on sensitive questions. A new method is developed to measure latent variables using the RR technique because direct questioning leads to biased results. Within the RR Keywords: analysis of variance, item response theory model, Markov chain Monte Carlo (MCMC), random effects, randomized responseThe collection of data through surveys on highly personal and sensitive issues may lead to answering refusals and false responses, making inferences difficult. Obtaining valid and reliable information depends on the cooperation of the respondents, and the willingness of the respondents depends on the confidentiality of their responses. Warner (1965) developed a data collection procedure, the randomized response (RR) technique, that allows researchers to obtain sensitive information while guaranteeing privacy to respondents. For example, a randomizing device is used to select a question from a group of questions and the respondent answers the selected question. The respondent is protected because the interviewer will not know which question is being answered. Warner's and related approaches were specifically developed to hide answers of the respondents and to estimate proportions and related confidence intervals in the population.In some applications, randomized response data can be hierarchically structured, and there is an interest in group differences regarding some sensitive individual characteristic. One could think of an application where it is of interest to know if cheating behavior differs across faculties or if social security fraud is more likely to appear in groups with certain characteristics. However, the usual randomized response models do not allow a hierarchical data analysis of the RR data. Statistical methods for hierarchically structured data, for example analysis of variance (ANOVA) or multilevel analysis, cannot be applied because the true individual

Bayesian randomized item response modeling for sensitive measurements

“…Lack of adequate means to analyse multivariate randomized response data hampered application of RR in a wide range of research areas. Recently Fox (2005b) proposed a class of Bayesian randomized item response theory models. With a comparable purpose, item randomized-response models in a frequentist framework were developed by Böckenholt and van der Heijden (2007).…”

“…However, it is possible to make individual-level inferences given multivariate randomized response data (Fox, 2005b). In other research fields, the RRT has obtained more attention and various studies have been performed successfully to measure the prevalence of a sensitive behavior.…”

“…Within a Bayesian framework, individual latent scores on the smoking scale are estimated using a mixture randomized item response model for mixed response types (ordinal and binary), which generalizes the models of van der Heijden et al (2000), De Jong et al (2010), and Fox (2005b. Furthermore, more general response-type specific latent class components are defined for non-compliance, since it is expected that the willingness of subjects to cooperate is influenced by the variety in response options.…”

“…De Jong et al (2010) reported on desires for products and services in the domain of adult entertainment. Fox and Meijer (2008) and Fox (2005b) analyzed students' academic cheating behavior at a Dutch university. Fox and Wyrick (2008) measured the prevalence of alcohol use, and alcohol-related problems among college students.…”

“…Although the individual answers are masked due to the RR technique, individual (sensitive) characteristics can be estimated when observing multivariate RR data. Fox (2005b) and Böckenholt and van der Heijden (2007) introduced item response models for binary RR data. The applications are focusing on surveys where the items measure an underlying sensitive construct.…”