The bhsdtr package: a general-purpose method of Bayesian inference for signal detection theory models
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The bhsdtr package: a general-purpose method of Bayesian inference for signal detection theory models Borysław Paulewicz1
· Agata Blaut2
© The Psychonomic Society, Inc. 2020
Abstract 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-ofthe-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. Keywords Signal detection theory · Bayesian inference · Hierarchical models
Introduction Many tasks used in psychology studies are essentially classification tasks. In a memory study, for example, participants may be required to decide if a given test item is old or new, or, in a perceptual study, an object may be either a letter or a digit. If a task requires classification, it is always possible that conclusions based on accuracy or percent correct are invalid because the ability to discriminate between stimulus classes (i.e., sensitivity) is confounded with bias, which is a tendency to classify stimuli as belonging to a particular class. In principle, any effect that manifests itself in differences in classification accuracy may reflect differences in sensitivity, bias, or both. Signal detection theory (Peterson et al., 1954; Tanner & Swets, 1954) provides a simple and popular solution to this common problem: according to Google Scholar, the seminal B. Paulewicz
[email protected] 1
Faculty of Psychology in Katowice, SWPS University of Social Sciences and Humanities, Katowice, Poland
2
Institute of Psychology, Jagiellonian University, Krakow, Poland
book by Green and Swets (1966) which introduced SDT to psychology researchers was cited more than 15,000 times before the year 2020. Despite the fact that the theory solves a common and important problem and is even described in cognitive psychology handbooks, there are reasons to believe that it may be heavily underutilized (Stanislaw & Todorov, 1992). Because the SDT model is non-linear, variability in its parameters due to factors such as participants or items has to be accounted for. When they are not accounted for, e.g., by aggregating data across participants or items,
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