Journal of Mathematical Psychology 44, 319 (2000) Accuracy, Scope, and Flexibility of Models

Traditionally, models are compared on the basis of their accuracy, their scope, and their simplicity. Simplicity is often represented by parameter counts; the fewer the parameters, the simpler the model. Arguments are presented here suggesting that simplicity has little place in discussions of modeling; instead, the concept of flexibility should be substituted. When comparing two models one should be wary of the possibility of their dif-ferential flexibility. Several methods for assessing relative flexibility are possible, as represented in this special issue of the Journal of Mathematical Psychology. Here, the method of cross-validation is applied in the com-parison of two models, a linear integration model (LIM) and the fuzzy-logi-cal model of perception (FLMP), in the fitting of 44 data sets concerning the perception of layout seen among three panels with the presence or absence of four sources of information for depth. Prior to cross-validation the two models performed about equally well; after cross-validation LIM was statisti-cally superior to FLMP, but the overall pattern of fits remained nearly the same for both models. 2000 Academic Press THEORIES, MODELS, AND PERCEPTS: ACCURACY, SCOPE, AND SIMPLICITY Across the practice of science in general, one finds suggestions concerning the goals of scientific theories. A good theory, among other things, should be more accurate, broader in scope, or simpler than its competitors (Kuhn, 1977; Thagard, 1990). Similarly, across cognitive science one finds suggestions that a good model should be descriptively adequate, general, and only as complex as is necessary (Jacobs Grainger, 1994). Finally, to complete a set of near parallels, in the field of perception a perceptual system should be well attuned to external affairs, it should operate smoothly in different environments with different stimuli, and it has often been said that it should prefer ‘‘goodness’ ’ in a form over less simple alternatives. Thus, in all three domains there is a concern with accuracy, which seems to have a well-defined basis, or at least a well-measured one; with scope, which would seem doi:10.1006jmps.1999.1274, available online a