Estimating Signal Detection Models with regression using the brms R package

Signal Detection Theory is a widely used framework for understanding decisions by distinguishing between response bias and true discriminability in various psychological domains. Manual calculation approaches to estimating SDT models' parameters, while commonly used, can be cumbersome and limited. In this tutorial I connect SDT to regression models that researchers are already familiar with in order to bring the flexibility of modern regression techniques to modeling of SDT data. I begin with a glance at SDT's fundamentals, and then show how to manually calculate basic SDT parameters. In the bulk of the tutorial, I show step-by-step implementations of various SDT models using the brms R package. I progress from analyses of binary Yes/No tasks to rating task models with multilevel structures, unequal variances, and mixtures. Throughout, I highlight benefits of the regression-based approach, such as dealing with missing data, multilevel structures, and quantifying uncertainty. By framing SDT models as regressions, researchers gain access to a powerful set of flexible tools while maintaining the conceptual clarity that makes SDT valuable. A regression-based approach not only simplifies SDT analyses but also extends SDT's utility through flexible parameter estimation with uncertainty measures and the ability to incorporate predictors at multiple levels of analysis.