Author:

Abstract:

Joachim Vandekerckhove, Extensions and applications of the diffu sion model for two-choice response times. Dissertation submitted to obtain the degree of Doctor of Philosophy in Psychology, April 2009. Promoter: Prof. Dr. F. Tuerlinckx. Two-choice response time data (2CRT) is one of the most common formats o f empirical data in experimental psychology. Unfortunately, such data do not adhere to the requirements of standard statistical models (such as the general linear model). The main goal of this thesis is to develop, e xtend, and apply methods for the analysis of 2CRTs on the basis of diffu sion process models. The diffusion process is a generalization of a standard random walk to c ontinuous time and with a continuous state space. In our applications, w e will always consider one-dimensional diffusions—a mathematical formali sm to describe continuous changes in a single number over time. The cent ral dogma of the diffusion model framework is that this fluctuating numb er represents an abstract ‘evidence counter’, hidden in the decider’s mi nd. It is further assumed that the decider executes a response as soon a s one of two boundaries is crossed, that the diffusion process may drift towards one of these boundaries at a lesser or greater rate, and that t he process may be biased to start at a value near or far from a certain boundary. The challenge in diffusion modeling then lies in recovering th e numerical values of these boundaries, the drift rate, and the bias, gi ven only the times at which each boundary was hit. This challenge, and v ariations on the theme, are the focus of this thesis. In the Introduction, we give a brief introduction to the general problem of analyzing two-choice response times, and a bird's-eye overview of th e five chapters of the dissertation. In Chapter 1, we describe a general method for fitting a diffusion model to empirical data. This method extends existing methods with a flexible way to constrain parameters across experimental conditions. Using desig n matrices as a constraining framework, this Chapter also discusses issu es of statistical inference as applied to the design matrix method for d iffusion models. Additionally, strategies are presented for handling out liers and contaminants—observed data points that are not generated by th e decision process of interest. We demonstrate this collection of method s with several real examples. In Chapter 2, we introduce and describe the Diffusion Model Analysis Too lbox, a MATLAB toolbox that accompanies the design matrix method outline d in Chapter 1. Until this point, we had only considered classical, ‘frequentist’ method s for statistical inference. In Chapter 3, we move to the more general B ayesian statistical framework and demonstrate that this framework allows for more flexibility in modeling. We also experienced fewer numerical p roblems using Bayesian estimation methods. The novel Bayesian methods proved most useful in extending the diffusion model into a hierarchical framework, which we describe in Chapter 4. Th e hierarchical Bayesian diffusion model allows for the inclusion of rand om effects—something which would be technically possible, but highly imp ractical in a frequentist framework. The inclusion of random effects per mits us to pool data across stimuli or participants that otherwise share nothing beyond being random draws from a common superpopulation. The ra ndom effects concept allows for more robust estimation, and it has the a dded virtue of being an accurate representation of the sampling scheme u sed in many empirical studies. The possibility of accounting for individ ual differences inside a population while retaining a conceptually inter esting process model as the measurement level makes the hierarchical dif fusion model an instance of cognitive psychometrics. Finally, in Chapter 5, we apply this novel method to a large data set, r elating two-choice reaction times to semantic properties of the stimulus items. While the classical analysis, involving mainly general linear mo deling, painted a heterogeneous and confusing picture, the hierarchical diffusion model approach succeeded in disentangling different sources of variability between items.