Characterizing noncompliance in conservation: a multidimensional Randomized Response Technique for multinomial responses

Rule violation is critical for biological conservation worldwide. Conventional questionnaires are not suitable to survey these violations and specialized questioning techniques that preserve respondents’ privacy, like the forced-response RRT, have been increasingly adopted by conservationists. However, most of these approaches do not measure multinomial answers and conservationists need a specialized questioning technique for real-world settings where non-compliance could occur in different forms. We developed a multidimensional, statistically-efficient, RRT which is suitable for multinomial answers (mRRT) and which allows researchers to test for respondents’ noncompliance during completion. Then, we applied it to measure the frequency of the various forms of illegal restocking of European catfish from specialized anglers in Italy, developing an operational code for the statistical software R. A total of 75 questionnaires were administered at a large fishing fair in Northern Italy, in winter 2018. Our questionnaires were easily compiled and the multinomial model revealed that around 6% of respondents had moved catfish across public freshwater bodies and private ponds. Future studies should better address their characteristics, and the mRRT could allow for modeling the effect of co-variates over restocking behavior. The multinomial mRRT could be adopted to measure many forms of rule violation in conservation that could take different forms, like various forms of fish restocking or different modes of wildlife persecution.

Kernel probability estimation for binomial and multinomial data

Kernel-based smoothers have enjoyed considerable success in the estimation of both probability densities and event frequencies. Existing procedures can be modified to yield a similar kernel-based estimator of instantaneous probability over the course of a binomial or multinomial time series. The resulting nonparametric estimate can be described in terms of one bandwidth per outcome alternative, facilitating both the understanding and reporting of results relative to more sophisticated methods for binomial outcome estimation. Also described is a method for sample size estimation, which in turn can be used to obtain credible intervals for the resulting estimate given mild assumptions. One application of this analysis is to model response accuracy in tasks with heterogeneous trial types. An example is presented from a study of transitive inference, showing how kernel probability estimates provide a method for inferring response accuracy during the first trial following training. This estimation procedure is also effective in describing the multinomial responses typical in the study of choice and decision making. An example is presented showing how the procedure may be used to describe changing distributions of choices over time when eight response alternatives are simultaneously available.

Kernel probability estimation for binomial and multinomial data

Kernel-based smoothers have enjoyed considerable success in the estimation of both probability densities and event frequencies. Existing procedures can be modified to yield a similar kernel-based estimator of instantaneous probability over the course of a binomial or multinomial time series. The resulting nonparametric estimate can be described in terms of one bandwidth per outcome alternative, facilitating both the understanding and reporting of results relative to more sophisticated methods for binomial outcome estimation. Also described is a method for sample size estimation, which in turn can be used to obtain credible intervals for the resulting estimate given mild assumptions. One application of this analysis is to model response accuracy in tasks with heterogeneous trial types. An example is presented from a study of transitive inference, showing how kernel probability estimates provide a method for inferring response accuracy during the first trial following training. This estimation procedure is also effective in describing the multinomial responses typical in the study of choice and decision making. An example is presented showing how the procedure may be used to describe changing distributions of choices over time when eight response alternatives are simultaneously available.