Evaluating Cognitive Models With Permutation Testing: A Case Study of Prototype and Exemplar Categorization
Abstract
Computational cognitive models offer powerful means for testing competing theoretical frameworks. A central challenge is determining which model best explains observed data, balancing goodness of fit with parsimony. Several fruitful approaches to model comparison have been used in the areas of cognitive and mathematical psychology, but the most popular in practice remain Akaike information criterion (AIC) and Bayesian information criterion (BIC), which penalize model complexity as measured by the number of free parameters. Here, we revisit these conventional approaches to model selection on a sample case of the prototype and exemplar models of categorization. We highlight the limitations of parameter count-based complexity measures, showing that they may fail to capture a model’s true flexibility. We then introduce a Monte Carlo permutation-testing approach as an alternative that has a rich tradition in many areas but whose use for model selection is still trailing that of AIC/BIC. We demonstrate that permutation testing offers at least three advantages: more robust comparison of models with chance, more robust comparison between models with equal or differing numbers of parameters, and quantification of uncertainty in model selection. After demonstrating how permutation testing offers a more nuanced and principled framework for evaluating cognitive models, we conclude with practical considerations for implementing permutation-based model selection in cognitive-modeling research.
