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 differential 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 comparison of two models, a linear integration model (LIM) and the fuzzy-logical 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 statistically superior to FLMP, but the overall pattern of fits remained nearly the same for both models. Copyright 2000 Academic Press.