The bhsdtr package: a general-purpose method of Bayesian inference for signal detection theory models

We describe a novel method of Bayesian inference for hierarchical or non-hierarchical equal variance normal signal detection theory models with one or more criteria. The method is implemented as an open-source R package that uses the state-of-the-art Stan platform for sampling from posterior distributions. Our method can accommodate binary responses as well as additional ratings and an arbitrary number of nested or crossed random grouping factors. The SDT parameters can be regressed on additional predictors within the same model via intermediate unconstrained parameters, and the model can be extended by using automatically generated human-readable Stan code as a template. In the paper, we explain how our method improves on other similar available methods, give an overview of the package, demonstrate its use by providing a real-study data analysis walk-through, and show that the model successfully recovers known parameter values when fitted to simulated data. We also demonstrate that ignoring a hierarchical data structure may lead to severely biased estimates when fitting signal detection theory models.