The confidence-noise confidence-boost (CNCB) model of confidence rating data

Over the last decade, different approaches have been proposed to interpret confidence rating judgments obtained after perceptual decisions. One very popular approach is to compute meta-d’ which is a global measure of the sensibility to discriminate the confidence rating distributions for correct and incorrect perceptual decisions. Here, we propose a generative model of confidence based on two main parameters, confidence noise and confidence boost, that we call CNCB model. Confidence noise impairs confidence judgements above and beyond how sensory noise affects perceptual sensitivity. The confidence boost parameter reflects whether confidence uses the same information that was used for perceptual decisions, or some new information. This CNCB model offers a principled way to estimate a confidence efficiency measure that is a theory-driven alternative to the popular M-ratio. We then describe two scenarios to estimate the confidence boost parameter, one where the experiment uses more than two confidence levels, the other where the experiment uses more than two stimulus strengths. We also extend the model to experiments using continuous confidence ratings and describe how the model can be fitted without binning these ratings. The continuous confidence model includes a non-linear mapping between objective and subjective confidence probabilities that can be estimated. Altogether, the CNCB model should help interpret confidence rating data at a deeper level. This manuscript is accompanied by a toolbox that will allow researchers to estimate all the parameters of the CNCB model in confidence ratings datasets. Some examples of re-analyses of previous datasets are provided in S1 File.Author summary: After each perceptual decision, humans have the ability to rate how confident they are that their decision is correct. While there is a growing number of models that attempt to explain how confidence judgments are built, there are very few objective measures of the sensitivity of these confidence judgments. We offer here a measure of confidence efficiency whose interpretation is simple. It takes a value of zero when participants are unable to evaluate the validity of their perceptual decision, a value of one when participants use the same information for their perceptual decision and their confidence judgment, and a value larger than one when participants use information for their confidence judgment that was not used for their perceptual decision. This measure of confidence efficiency is based on a generative model called CNCB that has two main parameters, confidence noise and confidence boost. These parameters again have a simple interpretation, and we show under which circumstances they can be estimated on their own. Finally, we extend the model to continuous confidence ratings where participants are not restricted to use a limited set of confidence levels.