Understanding the drivers of sensitive behavior using Poisson regression from quantitative randomized response technique data

Understanding sensitive behaviors—those that are socially unacceptable or non-compliant with rules or regulations—is essential for creating effective interventions. Sensitive behaviors are challenging to study, because participants are unlikely to disclose sensitive behaviors for fear of retribution or due to social undesirability. Methods for studying sensitive behavior include randomized response techniques, which provide anonymity to interviewees who answer sensitive questions. A variation on this approach, the quantitative randomized response technique (QRRT), allows researchers to estimate the frequency or quantity of sensitive behaviors. However, to date no studies have used QRRT to identify potential drivers of non-compliant behavior because regression methodology has not been developed for the nonnegative count data produced by QRRT. We develop a Poisson regression methodology for QRRT data, based on maximum likelihood estimation computed via the expectation-maximization (EM) algorithm. The methodology can be implemented with relatively minor modification of existing software for generalized linear models. We derive the Fisher information matrix in this setting and use it to obtain the asymptotic variance-covariance matrix of the regression parameter estimates. Simulation results demonstrate the quality of the asymptotic approximations. The method is illustrated with a case study examining potential drivers of non-compliance with hunting regulations in Sierra Leone. The new methodology allows assessment of the importance of potential drivers of different quantities of non-compliant behavior, using a likelihood-based, information-theoretic approach. Free, open-source software is provided to support QRRT regression.