Novel regression methods for metacognition

Metacognition is an important component in basic science and clinical psychology, often studied through complex, cognitive experiments. While Signal Detection Theory (SDT) provides a popular and pervasive framework for modelling responses from such experiments, a shortfall remains that it cannot in a straightforward manner account for the often complex designs. Additionally, SDT does not provide direct estimates of metacognitive ability. This latter shortcoming has recently been sought remedied by introduction of a measure for metacognitive sensitivity dubbed meta-d. The need for a flexible regression model framework remains, however, which should also incorporate the new sensitivity measure. In the present paper, we argue that a straightforward extension of SDT is obtained by identifying the model with the proportional odds model, a widely implemented, ordinal regression technique. We go on to develop a formal statistical framework for metacognitive sensitivity by defining a model that combines standard SDT with meta-d in a latent variable model. We show how this agrees with the literature on meta-d and constitutes a practical framework for extending the model. We supply several teoretical considerations on the model, including closed-form approximate estimates of meta-d and optimal weighing of response-specific meta-sensitivities. We discuss regression analysis as an application of the obtained model and illustrate our points through simulations. Lastly, we present R-software that implements the model. Our methods and their implementation extend the computational possibilities of SDT and meta-d and are useful for theoretical and practical researchers of metacognition.