Bayes factor of model selection validates FLMP

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Abstract
The fuzzy logical model of perception (FLMP; Massaro, 1998) has been extremely successful at describing performance across a wide range of ecological domains as well as for a broad spectrum of individuals. An important issue is whether this descriptive ability is theoretically informative or whether it simply reflects the model's ability to describe a wider range of possible outcomes. Previous tests and contrasts of this model with others have been adjudicated on the basis of both a root mean square deviation (RMSD) for goodness-of-fit and an observed RMSD relative to a benchmark RMSD if the model was indeed correct. We extend the model evaluation by another technique called Bayes factor (Kass & Raftery, 1995; Myung & Pitt, 1997). The FLMP maintains its significant descriptive advantage with this new criterion. In a series of simulations, the RMSD also accurately recovers the correct model under actual experimental conditions. When additional variability was added to the results, the models continued to be recoverable. In addition to its descriptive accuracy, RMSD should not be ignored in model testing because it can be justified theoretically and provides a direct and meaningful index of goodness-of-fit. We also make the case for the necessity of free parameters in model testing. Finally, using Newton's law of universal gravitation as an analogy, we argue that it might not be valid to expect a model's fit to be invariant across the whole range of possible parameter values for the model. We advocate that model selection should be analogous to perceptual judgment, which is characterized by the optimal use of multiple sources of information (e.g., the FLMP). Conclusions about models should be based on several selection criteria.

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