A catastrophe model for the effects of a response set on a discrimination task.

Abstract

Zeeman (1976) has used catastrophe theory, a math­ ematical method for dealing with abrupt and discon­ tinuous changes (Thorn, 1970), to construct a number of graphic models that can be used in the behavioral sciences. The simplest model, the cusp catastrophe, consists of a behavioral surface whose height varies along a bipolar dimension as a function of changes in two stimulus dimensions. The behavioral surface in this model is distinguished by a fold or overlap that is cusp shaped. The fold or overlap in the surface of a cusp catas­ trophe is used to represent a variety of abrupt and discontinuous changes in behavior. The fold in the surface indicates, first, that there should be sudden changes from one end of the response dimension to the other end of the response dimension, and second, that these changes should exhibit a property called hysteresis. Hysteresis means that the change from one end of the response dimension to the other occurs at one point when moving in one direction but at another point when moving in the opposite direction. Because of the nature of hysteresis, some stimuli are expected to be associated with both ends of the re­ sponse dimension, a property called bimodality. Two additional properties of behavior, inaccessibility and divergence, are also associated with the fold or overlap in the surface. Inaccessibility means that responses are not available in the space between the overlapping planes. Divergence means that a jump to either the upper or lower plane in the surface is to be expected when moving toward the point of the cusp. Thus, the fold in the surface of a cusp catastrophe indicates that five distinctive behaviors should be observed: sudden changes, hysteresis, bimodality, inaccessibility, and divergence. The purpose of the present experiment was to deter­ mine if the manipulation of a response set, per sever a­ tion, would affect the judgments on a discrimination task so that the judgments would correspond to the features that distinguish a cusp catastrophe.