Percentile analysis for goodness-of-fit comparisons of models to data

Sangeet KhemlaniNaval Research Laboratory
Greg TraftonNaval Research Laboratory

Abstract

In cognitive modeling, it is routine to report a goodness-of-fit index (e.g., R² or RMSE) between a putative model's predictions and an observed dataset. However, there exist no standard index values for what counts as “good” or “bad”, and most indices do not take into account the number of data points in an observed dataset. These limitations impair the interpretability of goodness-of-fit indices. We propose a generalized methodology, percentile analysis, which contextualizes goodness-of-fit measures in terms of performance that can be achieved by chance alone. A series of Monte Carlo simulations showed that the indices of randomized models systematically decrease as the number of data points to be fit increases, and that the relationship is nonlinear. We discuss the results of the simulation and how computational cognitive modelers can use them to place commonly used fit indices in context.

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Percentile analysis for goodness-of-fit comparisons of models to data (0.9 MB)



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