A Multinomial Processing Tree Model of the 2-back Working Memory Task

The $$-back task is a widely used behavioral task for measuring working memory and the ability to inhibit interfering information. We develop a novel model of the commonly used 2-back task using the cognitive psychometric framework provided by Multinomial Processing Trees. Our model involves three parameters: a memory parameter, corresponding to how well an individual encodes and updates sequence information about presented stimuli; a decision parameter corresponding to how well participants execute choices based on information stored in memory; and a base-rate parameter corresponding to bias for responding "yes" or "no". We test the parameter recovery properties of the model using existing 2-back experimental designs, and demonstrate the application of the model to two previous data sets: one from social psychology involving faces corresponding to different races (Stelter and Degner, British Journal of Psychology 109:777-798, 2018), and one from cognitive neuroscience involving more than 1000 participants from the Human Connectome Project (Van Essen et al., Neuroimage 80:62-79, 2013). We demonstrate that the model can be used to infer interpretable individual-level parameters. We develop a hierarchical extension of the model to test differences between stimulus conditions, comparing faces of different races, and comparing face to non-face stimuli. We also develop a multivariate regression extension to examine the relationship between the model parameters and individual performance on standardized cognitive measures including the List Sorting and Flanker tasks. We conclude by discussing how our model can be used to dissociate underlying cognitive processes such as encoding failures, inhibition failures, and binding failures.