Does response scaling cause the generalized context model to mimic a prototype model?

Abstract

Smith and Minda (1998, 2002) argued that the response scaling parameter γ in the exemplar-based generalized context model (GCM) makes the model unnecessarily complex and allows it to mimic the behavior of a prototype model. We evaluated this criticism in two ways. First, we estimated the complexity of the GCM with and without the γ parameter and also compared its complexity to that of a prototype model. Next, we assessed the extent to which the models mimic each other, using two experimental designs (Nosofsky & Zaki, 2002, Experiment 3; Smith & Minda, 1998, Experiment 2), chosen because these designs are thought to differ in the degree to which they can discriminate the models. The results show that γ can increase the complexity of the GCM, but this complexity does not necessarily allow mimicry. Furthermore, if statistical model selection methods such as minimum description length are adopted as the measure of model performance, the models will be highly discriminable, irrespective of design.