A quantitative confidence signal detection model: 2. Confidence analysis.

Decision making is a fundamental subfield within neuroscience. While recent findings have yielded major advances in our understanding of decision making, confidence in such decisions remains poorly understood. In this paper, we present a confidence signal detection (CSD) model that combines a standard signal detection model yielding a noisy decision variable with a model of confidence. The CSD model requires quantitative measures of confidence obtained by recording confidence probability judgments. Specifically, we model confidence probability judgments for binary direction recognition (e.g., did I move left or right) decisions. We use our CSD model to study both confidence calibration (i.e., how does confidence compare with performance) and the distributions of confidence probability judgments. We evaluate two variants of our CSD model: a conventional model with two free parameters (CSD2) that assumes that confidence is well calibrated and our new model with three free parameters (CSD3) that includes an additional confidence scaling factor. On average, our CSD2 and CSD3 models explain 73 and 82%, respectively, of the variance found in our empirical data set. Furthermore, for our large data sets consisting of 3,600 trials per subject, correlation and residual analyses suggest that the CSD3 model better explains the predominant aspects of the empirical data than the CSD2 model, especially for subjects whose confidence is not well calibrated. Moreover, simulations show that asymmetric confidence distributions can lead traditional confidence calibration analyses to suggest "underconfidence" even when confidence is perfectly calibrated. These findings show that this CSD model can be used to help improve our understanding of confidence and decision making.