The analysis of randomized response "ever" and "last year" questions: A non-saturated Multinomial model.

Randomized response (RR) is a well-known interview technique designed to eliminate evasive response bias that arises from asking sensitive questions. The most frequently asked questions in RR are either whether respondents were "ever" carriers of the sensitive characteristic, or whether they were carriers in a recent period, for instance, "last year". The present paper proposes a design in which both questions are asked, and derives a multinomial model for the joint analysis of these two questions. Compared to the separate analyses with the binomial model, the model makes a useful distinction between last year and former carriers of the sensitive characteristic, it is more efficient in estimating the prevalence of last year carriers, and it has a degree of freedom that allows for a goodness-of-fit test. Furthermore, it is easily extended to a multinomial logistic regression model to investigate the effects of covariates on the prevalence estimates. These benefits are illustrated in two studies on the use of anabolic androgenic steroids in the Netherlands, one using Kuk and one using both the Kuk and forced response. A salient result of our analyses is that the multinomial model provided ample evidence of response biases in the forced response condition.

Refinement of the extended crosswise model with a number sequence randomizer: Evidence from three different studies in the UK.

The Extended Crosswise Model (ECWM) is a randomized response model with neutral response categories, relatively simple instructions, and the availability of a goodness-of-fit test. This paper refines this model with a number sequence randomizer that virtually precludes the possibility to give evasive responses. The motivation for developing this model stems from a strategic priority of WADA (World Anti-Doping Agency) to monitor the prevalence of doping use by elite athletes. For this model we derived a maximum likelihood estimator that allows for binary logistic regression analysis. Three studies were conducted on online platforms with a total of over 6, 000 respondents; two on controlled substance use and one on compliance with COVID-19 regulations in the UK during the first lockdown. The results of these studies are promising. The goodness-of-fit tests showed little to no evidence for response biases, and the ECWM yielded higher prevalence estimates than direct questions for sensitive questions, and similar ones for non-sensitive questions. Furthermore, the randomizer with the shortest number sequences yielded the smallest response error rates on a control question with known prevalence.

Examining conservation compliance with randomized response technique analyses.

Understanding violations of laws or social norms designed to protect natural resources from overexploitation is a priority for conservation research and management. Because direct questioning about stigmatized behaviors can produce biased responses, researchers have adopted more complex, indirect questioning techniques. The randomized response technique (RRT) is one of the most powerful indirect survey methods, yet analyses of these data require sophisticated statistical models. To date, there has been limited user-friendly software to analyze RRT data, particularly for models that combine information from multiple RRT questions. We developed an R package, zapstRR (ZoologicAl Package for RRT) that provides functions for 3 RRT models that can be applied to single or multiple RRT questions. With these functions, researchers can estimate the prevalence of conservation noncompliance, determine the number of violations by individuals, perform regressions for univariate and multivariate RRT data, and correct prevalence estimates for evasive-response bias. We illustrate the use of these estimators for RRT data through an examination of 2 case studies: illegal bird hunting where the interview consisted of a standard RRT question design and a novel implementation designed to offer further anonymity to respondents and reveal the impact of educational interventions on illegal bushmeat consumption. The case studies demonstrate how the models can work in tandem to uncover distinct patterns within RRT data sets. The case studies also show how several assumptions are central to the application of the multivariate models.

The multidimensional randomized response design: Estimating different aspects of the same sensitive behavior.

The conventional randomized response design is unidimensional in the sense that it measures a single dimension of a sensitive attribute, like its prevalence, frequency, magnitude, or duration. This paper introduces a multidimensional design characterized by categorical questions that each measure a different aspect of the same sensitive attribute. The benefits of the multidimensional design are (i) a substantial gain in power and efficiency, and the potential to (ii) evaluate the goodness-of-fit of the model, and (iii) test hypotheses about evasive response biases in case of a misfit. The method is illustrated for a two-dimensional design measuring both the prevalence and the magnitude of social security fraud.

Estimating the prevalence of crack dependence using capture-recapture with institutional and field data: a three-city study in The Netherlands.

The aim of this study was to estimate the prevalence of crack dependence in the three largest Dutch cities (Amsterdam, Rotterdam, The Hague), stratified by gender and age. Three-sample capture-recapture, using data (collected between 2009 and 2011) from low threshold substitution treatment (n = 1,764), user rooms (n = 546), and a respondent-driven sample (n = 549), and applying log-linear modeling (covariates: gender, age, and city), provided a prevalence rate of 0.51% (95% CI: 0.46%-0.60%) for the population aged 15-64 years, with similar estimates for the three cities. Females (23.0% of total estimate) and younger crack users (12.8% aged <35 years) might be underrepresented in drug user treatment services.

Point and interval estimation of the population size using a zero-truncated negative binomial regression model.

This paper presents the zero-truncated negative binomial regression model to estimate the population size in the presence of a single registration file. The model is an alternative to the zero-truncated Poisson regression model and it may be useful if the data are overdispersed due to unobserved heterogeneity. Horvitz-Thompson point and interval estimates for the population size are derived, and the performance of these estimators is evaluated in a simulation study. To illustrate the model, the size of the population of opiate users in the city of Rotterdam is estimated. In comparison to the Poisson model, the zero-truncated negative binomial regression model fits these data better and yields a substantially higher population size estimate.