21 Mathematical Modeling

Explanations of human behavior are most often presented in a verbal form as theories. Psychologists can also harness the power and precision of mathematics by explaining behavior quantitatively. This chapter introduces the reader to how this is done and the advantages of doing so. It begins by contrasting mathematical modeling with hypothesis testing to highlight how the two methods of knowledge acquisition differ. The many styles of modeling are then surveyed, along with their advantages and disadvantages. This is followed by an in-depth example of how to create a mathematical model and fit it to experimental data. Issues in evaluating models are discussed, including a survey of quantitative methods of model selection. Particular attention is paid to the concept of generalizability and the trade-off of model fit with model complexity. The chapter closes by describing some of the challenges for the discipline in the years ahead