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Through the Looking Glass: A Dynamic Lens Model Approach to Learning in MCPL Tasks

Maarten Speekenbrink and David R. Shanks
Department of Psychology, UCL

Central to rational analysis is the focus on the adaptation of an organism’s cognitive functions to the structure of the environment. Brunswik’s probabilistic functionalism and the associated lens model have been successfully applied in the study of judgment and choice in multiple cue probability learning (MCPL) tasks. In such tasks, the objective is to infer the value of a criterion variable on the basis of a number of available cues. The lens model consists of two linear regression models, one regressing the cues to the criterion, and the other regressing the cues to the response. By comparing the regression coefficients of the models, one can assess the match between cue validity (relation between cue and criterion) and cue utilization (relation between cue and judgment/response). We describe an approach which considerably improves on this classical framework by replacing linear regression with a formal dynamic model of learning (Kelley & Friedman, 2002; Lagnado, Newell, Kahan & Shanks, 2006). In the dynamic lens model, the focus is on the extent to which cue utilization tracks observable (i.e., empirical) cue validity. Essentially, this means a trial-by-trial comparison of an individual’s cue utilization to the utilization of an ‘ideal observer’, one that integrates past information to optimally predict the criterion. As such, it offers a fine-grained rational analysis of learning and adaptation of individuals’ inferences to the probabilistic structure of the environment. We describe two such models, an associative and a Bayesian learning model, and investigate their effectiveness in this type of analysis. We then describe the application of the approach to a study comparing the learning behaviour of amnesic individuals and matched individuals with normal memory function.


Kelley, H., & Friedman, D.(2002). Learning to forecast price. Economic Enquiry, 40, 556-573.

Lagnado, D. A., Newell, B. R., Kahan, S., & Shanks, D. R.(2006). Insight and strategy in multiple cue learning. Journal of Experimental Psychology: General (in press).