HMeta-d: hierarchical Bayesian estimation of metacognitive efficiency from confidence ratings

Neurosci Conscious. 2017 Apr 22;2017(1):nix007. doi: 10.1093/nc/nix007. eCollection 2017.


Metacognition refers to the ability to reflect on and monitor one's cognitive processes, such as perception, memory and decision-making. Metacognition is often assessed in the lab by whether an observer's confidence ratings are predictive of objective success, but simple correlations between performance and confidence are susceptible to undesirable influences such as response biases. Recently, an alternative approach to measuring metacognition has been developed (Maniscalco and Lau 2012) that characterizes metacognitive sensitivity (meta-d') by assuming a generative model of confidence within the framework of signal detection theory. However, current estimation routines require an abundance of confidence rating data to recover robust parameters, and only provide point estimates of meta-d'. In contrast, hierarchical Bayesian estimation methods provide opportunities to enhance statistical power, incorporate uncertainty in group-level parameter estimates and avoid edge-correction confounds. Here I introduce such a method for estimating metacognitive efficiency (meta-d'/d') from confidence ratings and demonstrate its application for assessing group differences. A tutorial is provided on both the meta-d' model and the preparation of behavioural data for model fitting. Through numerical simulations I show that a hierarchical approach outperforms alternative fitting methods in situations where limited data are available, such as when quantifying metacognition in patient populations. In addition, the model may be flexibly expanded to estimate parameters encoding other influences on metacognitive efficiency. MATLAB software and documentation for implementing hierarchical meta-d' estimation (HMeta-d) can be downloaded at

Keywords: Bayes; confidence; metacognition; signal detection theory.