How does one choose among competing explanations of scientific data? When the explanations are mathematical models, researchers frequently apply quantitative methods to answer this question. The purpose of this research program is to develop such methods for selecting among quantitative models of cognition. Three lines of inquiry will be undertaken. In the first, theoretical work is proposed to increase our understanding of a central issues in model selection, model complexity, by exploring the use of one measure of complexity (Geometric Complexity) in new model-testing situations, and also by comparing it with other measures of complexity. In the second line of work, simulation experiments will be carried out to extend the application of geometric complexity and a particularly successful model selection method, Minimum Description Length, to more complex testing situations and to other types of models in cognitive psychology (e.g., connectionist, random walk). In a third line of research, simulation experiments will explore the application of Geometric Complexity and another quantitative tool (Response Surface Analysis) in other stages of the research process, such as in the analysis of a model's components and in guiding the design of future experiments to test models. This work should advance our understanding of model selection and provide researchers with new tools with which to test models of cognition. The fruits of this research should also extend into other areas of psychology and other social sciences.