Methods for Selecting Among Mathematical Models of Cognition

Ohio State University, Columbus OH

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Abstract

[unreadable] DESCRIPTION (provided by applicant): Cognitive modeling continues to be a popular tool for cognitive scientists because it helps strengthen the link between theory and data, sharpening one's thinking about the theoretical assumptions built into the model and forcing one to confront precision in the data and model performance. However, models are only as useful as the tools available for evaluating them, and quantitative tools are in short supply. The purpose of this research program is to continue the development of such tools. Three complementary lines of inquiry will be undertaken. Each examines a model's relationship with a different part of the scientific enterprise, be it the data, theory, or experimentation. In the first, we apply a recently developed method (Parameter Space Partitioning) for determining how many data patterns a model can generate in an experimental design to studying representation in computational models. In the second line of work, a tool (Componential Analysis) will be developed for examining how faithfully the assumptions and principles of a theory have been instantiated in a model. A measure of model complexity, obtained from Minimum Description Length, will be decomposed into the contributions of each parameter in the model. The third line of research explores a method for optimizing an experimental design to distinguish between competing models. Information about model performance and the experimental design are integrated to identify the variable settings that will maximally discriminate the models. Whether one is conducting basic or applied research, data are the only link to the underlying cognitive process of interest. How data are interpreted, and their implications for a particular model, depends on how well we understand the models themselves. The proposed work will contribute to this understanding. The fruits of this research will extend into other areas of psychology and the broader behavioral sciences and health sciences. [unreadable] [unreadable] [unreadable]