A Hierarchical Signal Detection Model with Unequal Variance for Binary Responses

Gaussian signal detection models with equal variance are commonly used in simple yes-no detection and discrimination experiments whereas more flexible models with unequal variance require additional data and/or conditions. Here, a hierarchical Bayesian model with equal-variance is extended to an unequal-variance model so that it becomes applicable to binary responses from a random sample of participants. This appears to be at odds with conventional wisdom whereby parameters of an unequal-variance model are not identifiable if only binary responses are observed in a single condition. Although this holds true for non-hierarchical models, the present model assumes randomly and independently sampled discriminability and criterion values and approximately constant signal variance across participants. This novel unequal-variance model is investigated analytically, in simulations and in applications to existing data sets. The results indicate that the five population parameters correspond to five observable parameters of a bivariate sampling distribution and that model parameters can be reliably and accurately recovered or estimated if the sample size is sufficiently large. It is concluded that this approach provides a promising alternative to the ubiquitous equal-variance model.