This book presents an integrated approach to the application of computational and mathematical models in psychology. Computational models have been extensively applied to better understand many domains of human behavior, such as perception, memory, reasoning, decision-making, communicating, and deciding. Modeling is often applied in these areas to different purposes – measurement, prediction, and model testing. Our major goal here is to provide a unified view on the interface between theories, simulations, and data, with a view to answering the central question: how can we learn from models of behavior?

We cover several topics. Part I of the book explains what a computational model is and gives a general overview of models that have been applied to understanding human behavior. We also examine the process of converting theoretical statements into simulation code and give an overview of the various concepts required to understand modeling. Part II examines one use of models: parameter estimation. By fitting models to data, inferences can be made from the resulting parameter estimates, and statements made about the psychological mechanism(s) or representations that generated those data. We cover maximum likelihood estimation and Bayesian estimation, including estimation across multiple participants and hierarchical estimation. Part III explores how inferences can be made from models by using model comparison. We consider under what conditions statements of sufficiency and necessity can be made from data, and how model complexity can be conceptualized and quantified. Part III examines several approaches to accounting for complexity in model comparison, including information criteria and Bayes Factors. Part IV considers the role of computational modeling in advancing psychological theory. We explore use of models as adjuncts to human reasoning, and the interaction between human and artificial intelligence to guide theorizing and generation of conceptual insights. We also consider the use of models as tools to arrive at shared understanding between researchers (i.e. the use of models as common terms of reference), and practices for communicating and sharing models. We finish by giving an overview of the application of models in several popular areas: neural network models, models of choice response time, and the application of models to understand neural data.

To accomplish all this, we use a freely available computer language, called R, which was initially developed for statistical data analysis but has broad applicability and is now used by many modellers.